diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.ats b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.ats
new file mode 100644
index 00000000000..b7f470b932f
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.ats
@@ -0,0 +1,18 @@
+from geos.ats.test_builder import TestDeck, RestartcheckParameters, generate_geos_tests
+
+restartcheck_params = {}
+restartcheck_params['atol'] = 1.0E-8
+restartcheck_params['rtol'] = 1.0E-8
+
+decks = [
+    TestDeck(
+        name="immiscibleTwoPhase_GravitySegregation_1d",
+        description=
+        'Test that 2 fluids can be seperated based on gravity.',
+        partitions=((1, 1, 1), ),
+        restart_step=0,
+        check_step=45,
+        restartcheck_params=RestartcheckParameters(**restartcheck_params))
+]
+
+generate_geos_tests(decks)
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.xml
new file mode 100644
index 00000000000..62d4f6cf3bb
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/immiscibleTwoPhase_GravitySegregation_1d.xml
@@ -0,0 +1,203 @@
+<?xml version="1.0"?>
+
+<Problem>
+  <Solvers
+    gravityVector="{ 0.0, 0.0, -10 }">
+    <ImmiscibleMultiphaseFlow
+      name="FlowSolver"
+      discretization="TPFA"
+      targetRegions="{ Domain }"
+      writeLinearSystem="0"
+      temperature="300"
+      initialDt="0.001">
+      <NonlinearSolverParameters
+        newtonTol="1.0e-6"
+        lineSearchAction="None"
+        newtonMaxIter="10" />
+      <LinearSolverParameters
+        directParallel="0" />
+    </ImmiscibleMultiphaseFlow>
+  </Solvers>
+
+  <Mesh>
+    <InternalMesh
+      name="mesh1"
+      elementTypes="{ C3D8 }"
+      xCoords="{ 0, 1 }"
+      yCoords="{ 0, 1 }"
+      zCoords="{ 0, 10 }"
+      nx="{ 1 }"
+      ny="{ 1 }"
+      nz="{ 10 }"
+      cellBlockNames="{ block1 }" />
+  </Mesh>
+  
+  <Geometry>
+    <Box
+      name="sink"
+      xMin="{ -0.01, -0.01, -0.01 }"
+      xMax="{ 1.01, 1.01, 1.01 }" />
+  </Geometry>
+
+  <Events
+    maxTime="0.4">
+    <PeriodicEvent
+      name="outputs"
+      timeFrequency="0.01"
+      target="/Outputs/vtkOutput" />
+
+    <PeriodicEvent
+      name="solverApplications"
+      target="/Solvers/FlowSolver" />
+
+    <PeriodicEvent
+      name="restarts"
+      timeFrequency="0.1"
+      targetExactTimestep="0"
+      target="/Outputs/restartOutput"/>
+  </Events>
+
+  <NumericalMethods>
+    <FiniteVolume>
+      <TwoPointFluxApproximation
+        name="TPFA" />
+    </FiniteVolume>
+  </NumericalMethods>
+
+  <ElementRegions>
+    <CellElementRegion
+      name="Domain"
+      cellBlocks="{ block1 }"
+      materialList="{ fluid, rock, relperm }" />
+  </ElementRegions>
+
+  <Functions>
+    <TableFunction
+      name="densityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 10 }" />
+
+    <TableFunction
+      name="densityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 1 }" />
+
+    <TableFunction
+      name="viscosityTablePhase1"
+      coordinates="{ 0.0 }"
+      values="{ 1.0 }" />
+
+    <TableFunction
+      name="viscosityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 1.0 }" />
+
+    <TableFunction
+      name="saturationTable1"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialSaturation1.txt"
+      interpolation="nearest" />
+
+    <TableFunction
+      name="saturationTable2"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialSaturation2.txt"
+      interpolation="nearest" />
+    
+    <TableFunction
+      name="pressureTable"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialPressure.txt"
+      interpolation="nearest" />
+  </Functions>
+
+  <Constitutive>
+    <TwoPhaseImmiscibleFluid
+      name="fluid"
+      phaseNames="{ water, gas }"
+      densityTableNames="{ densityTablePhase1, densityTablePhase2 }"
+      viscosityTableNames="{ viscosityTablePhase1, viscosityTablePhase2 }" />
+
+    <CompressibleSolidConstantPermeability
+      name="rock"
+      solidModelName="nullSolid"
+      porosityModelName="rockPorosity"
+      permeabilityModelName="rockPerm" />
+
+    <NullModel
+      name="nullSolid" />
+
+    <PressurePorosity
+      name="rockPorosity"
+      defaultReferencePorosity="1.0"
+      referencePressure="0.0"
+      compressibility="1e-9" />
+
+    <ConstantPermeability
+      name="rockPerm"
+      permeabilityComponents="{ 1, 1, 1 }" />
+
+    <BrooksCoreyRelativePermeability
+      name="relperm"
+      phaseNames="{ water, oil }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.0, 1.0 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }" />
+  </Constitutive>
+
+  <FieldSpecifications>
+    <FieldSpecification
+      name="Porosity"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="rockPorosity_referencePorosity"
+      scale="1.0" />
+
+    <FieldSpecification
+      name="initialPressure"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="pressure"
+      scale="1.0"
+      functionName="pressureTable" />
+
+    <FieldSpecification
+      name="initialSat1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="phaseVolumeFraction"
+      component="0"
+      scale="1.0"
+      functionName="saturationTable1" />
+
+    <FieldSpecification
+      name="initialSat2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="phaseVolumeFraction"
+      component="1"
+      scale="1.0"
+      functionName="saturationTable2" />
+
+    <FieldSpecification
+      name="sinkTermP"
+      objectPath="ElementRegions/Domain/block1"
+      fieldName="pressure"
+      scale="500.0"
+      setNames="{ sink }" />
+  </FieldSpecifications>
+
+  <Outputs>
+    <VTK
+      name="vtkOutput" />
+    <Restart
+      name="restartOutput"/>      
+  </Outputs>
+</Problem>
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialPressure.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialPressure.txt
new file mode 100644
index 00000000000..85a30e13876
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialPressure.txt
@@ -0,0 +1,10 @@
+495.0
+485.0
+475.0
+465.0
+455.0
+400.0
+300.0
+200.0
+100.0
+0.0
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation1.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation1.txt
new file mode 100644
index 00000000000..99f11f6b2e7
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation1.txt
@@ -0,0 +1,10 @@
+0
+0
+0
+0
+0
+1
+1
+1
+1
+1
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation2.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation2.txt
new file mode 100644
index 00000000000..1c03b9c1871
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/initialSaturation2.txt
@@ -0,0 +1,10 @@
+1
+1
+1
+1
+1
+0
+0
+0
+0
+0
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/x.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/x.txt
new file mode 100644
index 00000000000..2eb3c4fe4ee
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/x.txt
@@ -0,0 +1 @@
+0.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/y.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/y.txt
new file mode 100644
index 00000000000..2eb3c4fe4ee
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/y.txt
@@ -0,0 +1 @@
+0.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/z.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/z.txt
new file mode 100644
index 00000000000..f43a1f14d26
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_GravitySegregation_1d/z.txt
@@ -0,0 +1,10 @@
+0.5
+1.5
+2.5
+3.5
+4.5
+5.5
+6.5
+7.5
+8.5
+9.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialPressure.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialPressure.txt
new file mode 100644
index 00000000000..63943bfa00d
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialPressure.txt
@@ -0,0 +1,10 @@
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
+1e7
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation1.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation1.txt
new file mode 100644
index 00000000000..1859fabae78
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation1.txt
@@ -0,0 +1,10 @@
+0.95
+0.95
+0.95
+0.95
+0.95
+0.95
+0.95
+0.05
+0.05
+0.05
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation2.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation2.txt
new file mode 100644
index 00000000000..d113536f2fd
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/initialSaturation2.txt
@@ -0,0 +1,10 @@
+0.05
+0.05
+0.05
+0.05
+0.05
+0.05
+0.05
+0.95
+0.95
+0.95
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/jFunction_linear.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/jFunction_linear.txt
new file mode 100644
index 00000000000..c3dfd50073f
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/jFunction_linear.txt
@@ -0,0 +1,2 @@
+4.33172935918785
+1.66604975353379
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permx.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permx.geos
new file mode 100644
index 00000000000..4d47d8fa568
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permx.geos
@@ -0,0 +1,10 @@
+50
+50
+50
+50
+50
+200
+200
+200
+200
+200
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permy.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permy.geos
new file mode 100644
index 00000000000..4d47d8fa568
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permy.geos
@@ -0,0 +1,10 @@
+50
+50
+50
+50
+50
+200
+200
+200
+200
+200
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permz.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permz.geos
new file mode 100644
index 00000000000..4d47d8fa568
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/permz.geos
@@ -0,0 +1,10 @@
+50
+50
+50
+50
+50
+200
+200
+200
+200
+200
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/phaseVolumeFraction_water_linear.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/phaseVolumeFraction_water_linear.txt
new file mode 100644
index 00000000000..0d66ea1aee9
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/phaseVolumeFraction_water_linear.txt
@@ -0,0 +1,2 @@
+0
+1
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction.txt
new file mode 100644
index 00000000000..72a78a75b85
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction.txt
@@ -0,0 +1,76 @@
+99.9980934
+17.78445609
+11.20350909
+8.549878542
+7.057769576
+6.082201546
+5.386086427
+4.86006559
+4.446116454
+4.110353325
+3.831547061
+3.595663494
+3.393021946
+3.216710174
+3.061649542
+2.924017691
+2.800877928
+2.68993357
+2.589360389
+2.497689435
+2.413723433
+2.336475912
+2.265126101
+2.198985069
+2.137469915
+2.080083807
+2.02640045
+1.976051821
+1.928718377
+1.884121218
+1.842015737
+1.802186411
+1.764442543
+1.728614745
+1.694551981
+1.662119113
+1.631194842
+1.601669938
+1.573445757
+1.546432977
+1.520550493
+1.495724483
+1.471887601
+1.448978263
+1.426940034
+1.405721104
+1.385273798
+1.365554178
+1.346521677
+1.328138769
+1.310370692
+1.293185194
+1.276552299
+1.260444114
+1.244834648
+1.229699646
+1.215016445
+1.200763848
+1.186921998
+1.173472275
+1.160397205
+1.147680364
+1.135306301
+1.123260469
+1.111529155
+1.100099423
+1.088959056
+1.078096509
+1.067500858
+1.057161765
+1.047069433
+1.03721457
+1.027588362
+1.018182437
+1.008988837
+0.999999998
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction_linear.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction_linear.txt
new file mode 100644
index 00000000000..13036f8fd03
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/jFunction_linear.txt
@@ -0,0 +1,2 @@
+100.00
+1.00
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water.txt
new file mode 100644
index 00000000000..f38627d4e85
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water.txt
@@ -0,0 +1,76 @@
+0.001
+0.013333333
+0.026666667
+0.04
+0.053333333
+0.066666667
+0.08
+0.093333333
+0.106666667
+0.12
+0.133333333
+0.146666667
+0.16
+0.173333333
+0.186666667
+0.2
+0.213333333
+0.226666667
+0.24
+0.253333333
+0.266666667
+0.28
+0.293333333
+0.306666667
+0.32
+0.333333333
+0.346666667
+0.36
+0.373333333
+0.386666667
+0.4
+0.413333333
+0.426666667
+0.44
+0.453333333
+0.466666667
+0.48
+0.493333333
+0.506666667
+0.52
+0.533333333
+0.546666667
+0.56
+0.573333333
+0.586666667
+0.6
+0.613333333
+0.626666667
+0.64
+0.653333333
+0.666666667
+0.68
+0.693333333
+0.706666667
+0.72
+0.733333333
+0.746666667
+0.76
+0.773333333
+0.786666667
+0.8
+0.813333333
+0.826666667
+0.84
+0.853333333
+0.866666667
+0.88
+0.893333333
+0.906666667
+0.92
+0.933333333
+0.946666667
+0.96
+0.973333333
+0.986666667
+1
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water_linear.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water_linear.txt
new file mode 100644
index 00000000000..0a269ee3741
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/tables/phaseVolumeFraction_water_linear.txt
@@ -0,0 +1,2 @@
+0.0
+1.0
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_base.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_base.xml
new file mode 100644
index 00000000000..efbd5b34421
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_base.xml
@@ -0,0 +1,293 @@
+<?xml version="1.0" ?>
+
+<Problem>
+  <!-- SPHINX_SOLVER -->
+  <Solvers
+   gravityVector="{ 0.0, 0.0, 9.81 }">
+    <ImmiscibleMultiphaseFlow
+      name="FlowSolver"
+      logLevel="2"
+      discretization="TPFA"
+      temperature="300"
+      initialDt="0.001"
+      targetRegions="{ region_left, region_right }"
+      interfaceFaceSetNames = "{ Interface }">
+      <NonlinearSolverParameters
+        newtonTol="1.0e-5"
+        newtonMaxIter="20"
+        maxTimeStepCuts="20"
+	maxSubSteps="2000"/>
+      <LinearSolverParameters
+        solverType="direct"
+        directParallel="0"  
+        logLevel="0"/>
+    </ImmiscibleMultiphaseFlow>  
+  </Solvers>
+  <!-- SPHINX_SOLVER_END -->
+ 
+  <!-- SPHINX_NUMERICAL -->
+  <NumericalMethods>
+    <FiniteVolume>
+      <TwoPointFluxApproximation
+        name="TPFA"/>
+    </FiniteVolume>
+  </NumericalMethods>
+  <!-- SPHINX_NUMERICAL_END -->
+
+  <!-- SPHINX_ELEMENTREGIONS -->
+  <ElementRegions>
+    <CellElementRegion
+      name="region_left"
+      cellBlocks="{ cb_left }"
+      materialList="{ fluid_left, rock, relperm_left, capPressure_left }"/>
+
+    <CellElementRegion
+      name="region_right"
+      cellBlocks="{ cb_right }"
+      materialList="{ fluid_right, rock, relperm_right, capPressure_right }"/>      
+
+    <SurfaceElementRegion
+      name="Interface"
+      defaultAperture="1.0e-5"
+      materialList="{ fluid_left, fluid_right }"/>
+
+  </ElementRegions>
+  <!-- SPHINX_ELEMENTREGIONS_END -->
+
+  <!-- SPHINX_MATERIAL -->
+  <Functions>
+    <TableFunction
+      name="densityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 900 }" />
+    <TableFunction
+      name="densityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 400 }" />
+    <TableFunction
+      name="viscosityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 0.001 }" />                  
+    <TableFunction
+      name="viscosityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 0.001 }" />
+    <TableFunction
+      name="saturationTable1"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialSaturation1.txt"
+      interpolation="nearest" />
+    <TableFunction
+      name="saturationTable2"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialSaturation2.txt"
+      interpolation="nearest" />
+    <TableFunction
+      name="pressureTable"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ x.txt, y.txt, z.txt }"
+      voxelFile="initialPressure.txt"
+      interpolation="nearest" />
+   <TableFunction
+      name="jFunctionTable"
+      coordinateFiles="{ tables/phaseVolumeFraction_water.txt }"
+      voxelFile="tables/jFunction.txt"/>
+    <TableFunction 
+      name="permxFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{x.txt,y.txt,z.txt}"
+      voxelFile="permx.geos"
+      interpolation="nearest" />
+    <TableFunction 
+      name="permyFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{x.txt,y.txt,z.txt}"
+      voxelFile="permy.geos"
+      interpolation="nearest" />
+    <TableFunction 
+      name="permzFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{x.txt,y.txt,z.txt}"
+      voxelFile="permz.geos"
+      interpolation="nearest" />
+      
+ </Functions>
+
+  <Constitutive>
+    <CompressibleSolidConstantPermeability
+      name="rock"
+      solidModelName="nullSolid"
+      porosityModelName="rockPorosity"
+      permeabilityModelName="rockPerm"/>
+
+    <NullModel
+      name="nullSolid"/>
+
+    <PressurePorosity
+      name="rockPorosity"
+      defaultReferencePorosity="0.25"
+      referencePressure="1e7"
+      compressibility="1.0e-15"/>
+
+    <ConstantPermeability
+      name="rockPerm"
+      permeabilityComponents="{ 1.0e-14, 1.0e-14, 1.0e-14}"/>   
+
+    <BrooksCoreyRelativePermeability
+      name="relperm_left"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.5, 1.5 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }"/>
+
+    <BrooksCoreyRelativePermeability
+      name="relperm_right"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.5, 1.5 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }"/>
+
+  <!--  <JFunctionCapillaryPressure
+      name="capPressure_left"
+      phaseNames="{ water, gas }" 
+      wettingNonWettingJFunctionTableName="jFunctionTable"
+      wettingNonWettingSurfaceTension="6.12e-3"
+      permeabilityDirection="XY"/>
+
+    <JFunctionCapillaryPressure
+      name="capPressure_right"
+      phaseNames="{ water, gas }" 
+      wettingNonWettingJFunctionTableName="jFunctionTable"
+      wettingNonWettingSurfaceTension="6.12e-3"
+      permeabilityDirection="XY"/> -->   
+
+<BrooksCoreyCapillaryPressure
+      name="capPressure_left"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseCapPressureExponentInv="{ 4 , 1 }"
+      phaseEntryPressure="{ 4e3, 0 }"
+      capPressureEpsilon="1e-8" />
+
+<BrooksCoreyCapillaryPressure
+      name="capPressure_right"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseCapPressureExponentInv="{ 4 , 1 }"
+      phaseEntryPressure="{ 2e3, 0 }"
+      capPressureEpsilon="1e-8" />
+
+    <TwoPhaseImmiscibleFluid
+      name="fluid_left"
+      phaseNames="{ water, gas }"
+      densityTableNames="{densityTablePhase1, densityTablePhase2}"    
+      viscosityTableNames="{viscosityTablePhase1, viscosityTablePhase2}" />
+
+    <TwoPhaseImmiscibleFluid
+      name="fluid_right"
+      phaseNames="{ water, gas }"
+      densityTableNames="{densityTablePhase1, densityTablePhase2}"    
+      viscosityTableNames="{viscosityTablePhase1, viscosityTablePhase2}" />
+
+  </Constitutive>
+  <!-- SPHINX_MATERIAL_END -->
+
+  <!-- SPHINX_BC --> 
+  <FieldSpecifications>
+    <FieldSpecification
+      name="Porosity"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPorosity_referencePorosity"
+      scale="0.25" />
+
+    <FieldSpecification
+      name="initialPressure"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="pressure"
+      scale="1.0"
+      functionName="pressureTable" />
+
+    <FieldSpecification
+      name="initialSaturation1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="phaseVolumeFraction"
+      component="0"
+      scale="1.0"
+      functionName="saturationTable1" />
+
+    <FieldSpecification
+      name="initialSaturation2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="phaseVolumeFraction"
+      component="1"
+      scale="1.0"
+      functionName="saturationTable2" />
+
+   <FieldSpecification
+      name="permx"
+      component="0"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permxFunc"
+      scale="1.0e-14"/>
+
+    <FieldSpecification
+      name="permy"
+      component="1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permyFunc"
+      scale="1.0e-14"/>
+
+    <FieldSpecification
+      name="permz"
+      component="2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permzFunc"
+      scale="1.0e-14"/>
+
+  </FieldSpecifications>
+  <!-- SPHINX_BC_END -->
+
+  <!-- SPHINX_OUTPUT -->  
+  <Outputs>
+    <VTK
+      name="vtkOutput"/>
+<!--
+    <TimeHistory
+      name="timeHistoryOutput"
+      sources="{/Tasks/phaseVolumeFractionCollection}"
+      filename="saturationHistory" />
+-->
+    <Restart
+      name="restartOutput"/> 
+  </Outputs>
+  <!-- SPHINX_OUTPUT_END -->
+
+  <!-- SPHINX_TASKS --> 
+<!--  <Tasks>
+    <PackCollection
+      name="phaseVolumeFractionCollection"
+      objectPath="ElementRegions/region_left/cb_left"
+      fieldName="phaseVolumeFraction"/>      
+  </Tasks>
+-->
+  <!-- SPHINX_TASKS_END -->   
+</Problem>
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_interface_condition.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_interface_condition.xml
new file mode 100644
index 00000000000..41ba4e3ed92
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/uni_directional_flow_interface_condition.xml
@@ -0,0 +1,66 @@
+<?xml version="1.0" ?>
+
+<Problem>
+  <Included>
+    <File name="./uni_directional_flow_base.xml"/>
+  </Included>
+
+  <!-- SPHINX_MESH -->
+  <Mesh>
+    <InternalMesh
+      name="mesh"
+      elementTypes="{ C3D8 }"
+      xCoords="{ 0, 1 }"
+      yCoords="{ 0, 1 }"
+      zCoords="{ 0, 5, 10 }"
+      nx="{ 1 }"
+      ny="{ 1 }"
+      nz="{ 10, 10 }"
+      cellBlockNames="{ cb_left, cb_right }"/>
+  </Mesh>
+  <!-- SPHINX_MESH_END -->
+
+  <Geometry>
+<!--    <Box
+      name="source"
+      xMin="{0.0, -0.00001, -0.00001}"
+      xMax="{0.01, 1.00001, 1.00001}"/> -->
+
+    <Box
+      name="sink"
+      xMin="{ -0.00001, -0.00001, -0.00001}"
+      xMax="{ 1.00001, 1.00001, 1.00001}"/>
+
+    <Box
+      name="Interface"
+      xMin="{ -0.01, -0.01, 4.99 }"
+      xMax="{  1.01, 1.01, 5.01 }"/>      
+  </Geometry>
+
+  <Events
+    maxTime="86.4e+05">
+      
+    <PeriodicEvent
+      name="outputs"
+      timeFrequency="86.4e+03"
+      targetExactTimestep="1"
+      target="/Outputs/vtkOutput"/>
+<!--
+    <PeriodicEvent
+      name="timeHistoryOutput"
+      timeFrequency="20000"
+      targetExactTimestep="1"
+      target="/Outputs/timeHistoryOutput" />
+
+    <PeriodicEvent
+      name="timeHistoryCollection"
+      timeFrequency="20000"
+      targetExactTimestep="1"
+      target="/Tasks/phaseVolumeFractionCollection" />
+-->
+    <PeriodicEvent
+      name="solverApplications"
+      maxEventDt="86.4e+03"
+      target="/Solvers/FlowSolver"/>    
+  </Events>
+</Problem>
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/x.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/x.txt
new file mode 100644
index 00000000000..2eb3c4fe4ee
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/x.txt
@@ -0,0 +1 @@
+0.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/y.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/y.txt
new file mode 100644
index 00000000000..2eb3c4fe4ee
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/y.txt
@@ -0,0 +1 @@
+0.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/z.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/z.txt
new file mode 100644
index 00000000000..f43a1f14d26
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/1D_case/z.txt
@@ -0,0 +1,10 @@
+0.5
+1.5
+2.5
+3.5
+4.5
+5.5
+6.5
+7.5
+8.5
+9.5
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialPressure.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialPressure.txt
new file mode 100644
index 00000000000..6963bb6148c
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialPressure.txt
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation1.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation1.txt
new file mode 100644
index 00000000000..90ddc12151e
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation1.txt
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation2.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation2.txt
new file mode 100644
index 00000000000..d5ef52f254b
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/initialSaturation2.txt
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permx.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permx.geos
new file mode 100644
index 00000000000..439bd535a86
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permx.geos
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permy.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permy.geos
new file mode 100644
index 00000000000..439bd535a86
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permy.geos
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permz.geos b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permz.geos
new file mode 100644
index 00000000000..439bd535a86
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/permz.geos
@@ -0,0 +1,1200 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/x.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/x.txt
new file mode 100644
index 00000000000..283fc50e7fb
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/x.txt
@@ -0,0 +1,10 @@
+5.00000000e-01
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/y.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/y.txt
new file mode 100644
index 00000000000..a01763bc5d1
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/y.txt
@@ -0,0 +1,6 @@
+5.00000000e-01
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/z.txt b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/z.txt
new file mode 100644
index 00000000000..d122a370abe
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/input/z.txt
@@ -0,0 +1,20 @@
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diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_base.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_base.xml
new file mode 100644
index 00000000000..3982a2b12c6
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_base.xml
@@ -0,0 +1,299 @@
+<?xml version="1.0" ?>
+
+<Problem>
+  <!-- SPHINX_SOLVER -->
+  <Solvers
+   gravityVector="{ 0.0, 0.0, 9.81 }">
+    <ImmiscibleMultiphaseFlow
+      name="FlowSolver"
+      logLevel="1"
+      discretization="TPFA"
+      temperature="300"
+      initialDt="0.001"
+      targetRegions="{ region_left, region_right }">
+      <!-- interfaceFaceSetNames = "{ Interface }"> -->
+      <NonlinearSolverParameters
+        newtonTol="1e-4"
+        newtonMaxIter="20"
+        maxTimeStepCuts="50"
+        maxSubSteps="100"
+        lineSearchAction="None"
+        timeStepDecreaseFactor="0.9"
+        timeStepIncreaseFactor="1.5" 
+        timeStepDecreaseIterLimit="0.8"
+        timeStepIncreaseIterLimit="0.6"/>
+<!--       <LinearSolverParameters
+        solverType="direct"
+        directParallel="0"  
+        logLevel="0"/> -->
+      <LinearSolverParameters solverType="gmres" preconditionerType="amg" krylovTol="1.0e-7" logLevel="1"/>        
+    </ImmiscibleMultiphaseFlow>  
+  </Solvers>
+  <!-- SPHINX_SOLVER_END -->
+ 
+  <!-- SPHINX_NUMERICAL -->
+  <NumericalMethods>
+    <FiniteVolume>
+      <TwoPointFluxApproximation
+        name="TPFA"/>
+    </FiniteVolume>
+  </NumericalMethods>
+  <!-- SPHINX_NUMERICAL_END -->
+
+  <!-- SPHINX_ELEMENTREGIONS -->
+  <ElementRegions>
+    <CellElementRegion
+      name="region_left"
+      cellBlocks="{ cb_left }"
+      materialList="{ fluid_left, rock, relperm_left, capPressure_left }"/>
+
+    <CellElementRegion
+      name="region_right"
+      cellBlocks="{ cb_right }"
+      materialList="{ fluid_right, rock, relperm_right, capPressure_right }"/>      
+
+    <SurfaceElementRegion
+      name="Interface"
+      defaultAperture="1.0e-5"
+      materialList="{ fluid_left, fluid_right }"/>
+
+  </ElementRegions>
+  <!-- SPHINX_ELEMENTREGIONS_END -->
+
+  <!-- SPHINX_MATERIAL -->
+  <Functions>
+    <TableFunction
+      name="densityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 900 }" />
+    <TableFunction
+      name="densityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 400 }" />
+    <TableFunction
+      name="viscosityTablePhase1"
+      coordinates="{ 0.0}"
+      values="{ 0.001 }" />                  
+    <TableFunction
+      name="viscosityTablePhase2"
+      coordinates="{ 0.0 }"
+      values="{ 0.001 }" />
+    <TableFunction
+      name="saturationTable1"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ input/x.txt, input/y.txt, input/z.txt }"
+      voxelFile="input/initialSaturation1.txt"
+      interpolation="nearest" />
+    <TableFunction
+      name="saturationTable2"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ input/x.txt, input/y.txt, input/z.txt }"
+      voxelFile="input/initialSaturation2.txt"
+      interpolation="nearest" />
+    <TableFunction
+      name="pressureTable"
+      inputVarNames="{ elementCenter }"
+      coordinateFiles="{ input/x.txt, input/y.txt, input/z.txt }"
+      voxelFile="input/initialPressure.txt"
+      interpolation="nearest" />
+<!--   <TableFunction
+      name="jFunctionTable"
+      coordinateFiles="{ tables/phaseVolumeFraction_water.txt }"
+      voxelFile="tables/jFunction.txt"/> -->
+    <TableFunction 
+      name="permxFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{input/x.txt,input/y.txt,input/z.txt}"
+      voxelFile="input/permx.geos"
+      interpolation="nearest" />
+    <TableFunction 
+      name="permyFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{input/x.txt,input/y.txt,input/z.txt}"
+      voxelFile="input/permy.geos"
+      interpolation="nearest" />
+    <TableFunction 
+      name="permzFunc"
+      inputVarNames="{elementCenter}"
+      coordinateFiles="{input/x.txt,input/y.txt,input/z.txt}"
+      voxelFile="input/permz.geos"
+      interpolation="nearest" />
+      
+ </Functions>
+
+  <Constitutive>
+    <CompressibleSolidConstantPermeability
+      name="rock"
+      solidModelName="nullSolid"
+      porosityModelName="rockPorosity"
+      permeabilityModelName="rockPerm"/>
+
+    <NullModel
+      name="nullSolid"/>
+
+    <PressurePorosity
+      name="rockPorosity"
+      defaultReferencePorosity="0.25"
+      referencePressure="1e7"
+      compressibility="1.0e-15"/>
+
+    <ConstantPermeability
+      name="rockPerm"
+      permeabilityComponents="{ 1.0e-14, 1.0e-14, 1.0e-14}"/>   
+
+    <BrooksCoreyRelativePermeability
+      name="relperm_left"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.5, 1.5 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }"/>
+
+    <BrooksCoreyRelativePermeability
+      name="relperm_right"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseRelPermExponent="{ 1.5, 1.5 }"
+      phaseRelPermMaxValue="{ 1.0, 1.0 }"/>
+
+  <!--  <JFunctionCapillaryPressure
+      name="capPressure_left"
+      phaseNames="{ water, gas }" 
+      wettingNonWettingJFunctionTableName="jFunctionTable"
+      wettingNonWettingSurfaceTension="6.12e-3"
+      permeabilityDirection="XY"/>
+
+    <JFunctionCapillaryPressure
+      name="capPressure_right"
+      phaseNames="{ water, gas }" 
+      wettingNonWettingJFunctionTableName="jFunctionTable"
+      wettingNonWettingSurfaceTension="6.12e-3"
+      permeabilityDirection="XY"/> -->   
+
+<BrooksCoreyCapillaryPressure
+      name="capPressure_left"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseCapPressureExponentInv="{ 4 , 1 }"
+      phaseEntryPressure="{ 4e3, 0 }"
+      capPressureEpsilon="1e-8" />
+
+<BrooksCoreyCapillaryPressure
+      name="capPressure_right"
+      phaseNames="{ water, gas }"
+      phaseMinVolumeFraction="{ 0.0, 0.0 }"
+      phaseCapPressureExponentInv="{ 4 , 1 }"
+      phaseEntryPressure="{ 2e3, 0 }"
+      capPressureEpsilon="1e-8" />
+
+    <TwoPhaseImmiscibleFluid
+      name="fluid_left"
+      phaseNames="{ water, gas }"
+      densityTableNames="{densityTablePhase1, densityTablePhase2}"    
+      viscosityTableNames="{viscosityTablePhase1, viscosityTablePhase2}" />
+
+    <TwoPhaseImmiscibleFluid
+      name="fluid_right"
+      phaseNames="{ water, gas }"
+      densityTableNames="{densityTablePhase1, densityTablePhase2}"    
+      viscosityTableNames="{viscosityTablePhase1, viscosityTablePhase2}" />
+
+  </Constitutive>
+  <!-- SPHINX_MATERIAL_END -->
+
+  <!-- SPHINX_BC --> 
+  <FieldSpecifications>
+    <FieldSpecification
+      name="Porosity"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPorosity_referencePorosity"
+      scale="0.25" />
+
+    <FieldSpecification
+      name="initialPressure"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="pressure"
+      scale="1.0"
+      functionName="pressureTable" />
+
+    <FieldSpecification
+      name="initialSaturation1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="phaseVolumeFraction"
+      component="0"
+      scale="1.0"
+      functionName="saturationTable1" />
+
+    <FieldSpecification
+      name="initialSaturation2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="phaseVolumeFraction"
+      component="1"
+      scale="1.0"
+      functionName="saturationTable2" />
+
+   <FieldSpecification
+      name="permx"
+      component="0"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permxFunc"
+      scale="1.0e-14"/>
+
+    <FieldSpecification
+      name="permy"
+      component="1"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permyFunc"
+      scale="1.0e-14"/>
+
+    <FieldSpecification
+      name="permz"
+      component="2"
+      initialCondition="1"
+      setNames="{ all }"
+      objectPath="ElementRegions/region_*"
+      fieldName="rockPerm_permeability"
+      functionName="permzFunc"
+      scale="1.0e-14"/>
+
+  </FieldSpecifications>
+  <!-- SPHINX_BC_END -->
+
+  <!-- SPHINX_OUTPUT -->  
+  <Outputs>
+    <VTK
+      name="vtkOutput"/>
+<!--
+    <TimeHistory
+      name="timeHistoryOutput"
+      sources="{/Tasks/phaseVolumeFractionCollection}"
+      filename="saturationHistory" />
+-->
+    <Restart
+      name="restartOutput"/> 
+  </Outputs>
+  <!-- SPHINX_OUTPUT_END -->
+
+  <!-- SPHINX_TASKS --> 
+<!--  <Tasks>
+    <PackCollection
+      name="phaseVolumeFractionCollection"
+      objectPath="ElementRegions/region_left/cb_left"
+      fieldName="phaseVolumeFraction"/>      
+  </Tasks>
+-->
+  <!-- SPHINX_TASKS_END -->   
+</Problem>
diff --git a/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_interface_condition.xml b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_interface_condition.xml
new file mode 100644
index 00000000000..9bac844ae7b
--- /dev/null
+++ b/inputFiles/immiscibleMultiphaseFlow/immiscibleTwoPhase_interface_conditions/3D_case/uni_directional_flow_interface_condition.xml
@@ -0,0 +1,66 @@
+<?xml version="1.0" ?>
+
+<Problem>
+  <Included>
+    <File name="./uni_directional_flow_base.xml"/>
+  </Included>
+
+  <!-- SPHINX_MESH -->
+  <Mesh>
+    <InternalMesh
+      name="mesh"
+      elementTypes="{ C3D8 }"
+      xCoords="{ 0, 10 }"
+      yCoords="{ 0, 6 }"
+      zCoords="{ 0, 5, 10 }"
+      nx="{ 40 }"
+      ny="{ 1 }"
+      nz="{ 40, 40 }"
+      cellBlockNames="{ cb_left, cb_right }"/>
+  </Mesh>
+  <!-- SPHINX_MESH_END -->
+
+  <Geometry>
+<!--    <Box
+      name="source"
+      xMin="{0.0, -0.00001, -0.00001}"
+      xMax="{0.01, 1.00001, 1.00001}"/> -->
+
+    <Box
+      name="sink"
+      xMin="{ -0.00001, -0.00001, -0.00001}"
+      xMax="{ 1.00001, 1.00001, 1.00001}"/>
+
+    <Box
+      name="Interface"
+      xMin="{ -0.01, -0.01, 4.99 }"
+      xMax="{  10.01, 6.01, 5.01 }"/>      
+  </Geometry>
+
+  <Events
+    maxTime="86.4e+05">
+      
+    <PeriodicEvent
+      name="outputs"
+      timeFrequency="86.4e+03"
+      targetExactTimestep="1"
+      target="/Outputs/vtkOutput"/>
+<!--
+    <PeriodicEvent
+      name="timeHistoryOutput"
+      timeFrequency="20000"
+      targetExactTimestep="1"
+      target="/Outputs/timeHistoryOutput" />
+
+    <PeriodicEvent
+      name="timeHistoryCollection"
+      timeFrequency="20000"
+      targetExactTimestep="1"
+      target="/Tasks/phaseVolumeFractionCollection" />
+-->
+    <PeriodicEvent
+      name="solverApplications"
+      maxEventDt="86.4e03"
+      target="/Solvers/FlowSolver"/>    
+  </Events>
+</Problem>
diff --git a/src/coreComponents/common/DataLayouts.hpp b/src/coreComponents/common/DataLayouts.hpp
index cd09af18ef0..0f23039b745 100644
--- a/src/coreComponents/common/DataLayouts.hpp
+++ b/src/coreComponents/common/DataLayouts.hpp
@@ -21,6 +21,7 @@
 #define GEOS_COMMON_DATALAYOUTS_HPP_
 
 #include "common/GeosxConfig.hpp"
+#include "common/DataTypes.hpp"
 
 #include "LvArray/src/Array.hpp"
 #include "RAJA/RAJA.hpp"
diff --git a/src/coreComponents/common/logger/Logger.hpp b/src/coreComponents/common/logger/Logger.hpp
index e59cfa05256..1224ec6ee66 100644
--- a/src/coreComponents/common/logger/Logger.hpp
+++ b/src/coreComponents/common/logger/Logger.hpp
@@ -978,6 +978,7 @@ struct InputError : public std::runtime_error
   InputError( std::exception const & subException, std::string const & msgToInsert );
 };
 
+
 /**
  * @brief Exception class used to report errors in user input.
  */
diff --git a/src/coreComponents/constitutive/CMakeLists.txt b/src/coreComponents/constitutive/CMakeLists.txt
index 6af439fe23f..bfb182dfe89 100644
--- a/src/coreComponents/constitutive/CMakeLists.txt
+++ b/src/coreComponents/constitutive/CMakeLists.txt
@@ -27,12 +27,14 @@ set( constitutive_headers
      ConstitutivePassThruHandler.hpp
      ExponentialRelation.hpp
      NullModel.hpp
+     KilloughHysteresis.hpp
      capillaryPressure/BrooksCoreyCapillaryPressure.hpp
      capillaryPressure/CapillaryPressureBase.hpp
      capillaryPressure/CapillaryPressureFields.hpp
      capillaryPressure/InverseCapillaryPressure.hpp
      capillaryPressure/JFunctionCapillaryPressure.hpp
      capillaryPressure/TableCapillaryPressure.hpp
+     capillaryPressure/TableCapillaryPressureHysteresis.hpp
      capillaryPressure/TableCapillaryPressureHelpers.hpp
      capillaryPressure/VanGenuchtenCapillaryPressure.hpp
      capillaryPressure/CapillaryPressureSelector.hpp
@@ -226,11 +228,13 @@ set( constitutive_sources
      ConstitutiveBase.cpp
      ConstitutiveManager.cpp
      NullModel.cpp
+     KilloughHysteresis.cpp
      capillaryPressure/BrooksCoreyCapillaryPressure.cpp
      capillaryPressure/CapillaryPressureBase.cpp
      capillaryPressure/InverseCapillaryPressure.cpp
      capillaryPressure/JFunctionCapillaryPressure.cpp
      capillaryPressure/TableCapillaryPressure.cpp
+     capillaryPressure/TableCapillaryPressureHysteresis.cpp
      capillaryPressure/TableCapillaryPressureHelpers.cpp
      capillaryPressure/VanGenuchtenCapillaryPressure.cpp
      contact/BartonBandis.cpp
@@ -369,6 +373,7 @@ if( ENABLE_PVTPackage )
 endif()
 
 if (ENABLE_HPCREACT)
+  if( EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/HPCReact/CMakeLists.txt" )
     set( constitutive_headers
         ${constitutive_headers}
         fluid/reactivefluid/ReactiveFluidSelector.hpp 
@@ -383,8 +388,9 @@ if (ENABLE_HPCREACT)
          ${constitutive_sources}
          fluid/reactivefluid/ReactiveSinglePhaseFluid.cpp 
         )
-  add_subdirectory( HPCReact )
-  list( APPEND dependencyList hpcReact )
+    add_subdirectory( HPCReact )
+    list( APPEND dependencyList hpcReact )
+  endif()
 endif()
 
 geos_decorate_link_dependencies( LIST decoratedDependencies
diff --git a/src/coreComponents/constitutive/KilloughHysteresis.cpp b/src/coreComponents/constitutive/KilloughHysteresis.cpp
new file mode 100644
index 00000000000..453a8b0585b
--- /dev/null
+++ b/src/coreComponents/constitutive/KilloughHysteresis.cpp
@@ -0,0 +1,144 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2018-2020 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2020 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2018-2020 TotalEnergies
+ * Copyright (c) 2019-     GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/***
+ *  @file KilloughHysteresis.cpp
+ */
+
+#include "KilloughHysteresis.hpp"
+
+
+namespace geos
+{
+
+using namespace dataRepository;
+
+namespace constitutive
+{
+
+
+void KilloughHysteresis::postProcessInput(real64 const &jerauldParam_a, real64 const &jerauldParam_b,
+                                          real64 const &killoughCurvatureParamRelPerm,
+                                          real64 const &killoughCurvatureParamPc)
+{
+  GEOS_THROW_IF( jerauldParam_a < 0,
+                  GEOS_FMT( "{}: the parameter {} must be positive",
+                             catalogName(),
+                             viewKeyStruct::jerauldParameterAString() ),
+                  InputError );
+
+  GEOS_THROW_IF( jerauldParam_b < 0,
+                  GEOS_FMT( "{}: the paramater {} must be postitive",
+                             catalogName(),
+                             viewKeyStruct::jerauldParameterBString() ),
+                  InputError );
+
+  GEOS_THROW_IF( killoughCurvatureParamRelPerm < 0,
+                  GEOS_FMT( "{}: the paramater {} must be postitive",
+                             catalogName(),
+                             viewKeyStruct::killoughCurvatureParameterRelPermString() ),
+                  InputError );
+
+  GEOS_THROW_IF( killoughCurvatureParamPc < 0,
+                    GEOS_FMT( "{}: the paramater {} must be postitive",
+                               catalogName(),
+                               viewKeyStruct::killoughCurvatureParameterPcString() ),
+                    InputError );
+
+}
+
+
+
+//TODO
+void KilloughHysteresis::computeLandCoefficient( KilloughHysteresis::HysteresisCurve const & hcurve,
+                                                 real64 & landParam )
+{
+
+  // Note: for simplicity, the notations are taken from IX documentation (although this breaks our phaseVolFrac naming convention)
+
+  // Step 1: Land parameter for the wetting phase
+  if( hcurve.isWetting() )
+  {
+    real64 const Scrd = hcurve.oppositeBoundPhaseVolFraction;
+    real64 const Smxd = hcurve.drainageExtremaPhaseVolFraction;
+    real64 const Smxi = hcurve.imbibitionExtremaPhaseVolFraction;
+    real64 const Swc = Scrd;
+    GEOS_THROW_IF(  (Smxi - Smxd) > 0,
+                     GEOS_FMT( "{}: For wetting phase hysteresis, imbibition end-point saturation Smxi( {} ) must be smaller than the drainage saturation end-point Smxd( {} ).\n"
+                                "Crossing relative permeability curves.\n",
+                                catalogName(),
+                                Smxi,
+                                Smxd ),
+                     InputError );
+
+    landParam = ( Smxd - Swc ) / LvArray::math::max( KilloughHysteresis::minScriMinusScrd, ( Smxd - Smxi ) ) - 1.0;
+  }
+  else
+  // Step 2: Land parameter for the non-wetting phase
+
+  {
+    real64 const Smx =  hcurve.oppositeBoundPhaseVolFraction;
+    real64 const Scrd = hcurve.drainageExtremaPhaseVolFraction;
+    real64 const Scri = hcurve.imbibitionExtremaPhaseVolFraction;
+    GEOS_THROW_IF( (Scrd - Scri) > 0,
+                    GEOS_FMT( "{}: For non-wetting phase hysteresis, drainage trapped saturation Scrd( {} ) must be smaller than the imbibition saturation Scri( {} ).\n"
+                               "Crossing relative permeability curves.\n",
+                               catalogName(),
+                               Scrd,
+                               Scri ),
+                    InputError );
+
+    landParam = ( Smx - Scrd ) / LvArray::math::max( KilloughHysteresis::minScriMinusScrd, ( Scri - Scrd ) ) - 1.0;
+  }
+}
+
+GEOS_HOST_DEVICE
+void
+KilloughHysteresis::
+  computeTrappedCriticalPhaseVolFraction( HysteresisCurve const & hcurve,
+                                          real64 const & Shy,
+                                          real64 const & landParam,
+                                          real64 const & jerauldParam_a,
+                                          real64 const & jerauldParam_b,
+                                          real64 & Scrt )
+{
+
+  if( hcurve.isWetting())
+  {
+    //unpack values
+    real64 const Smxd = hcurve.drainageExtremaPhaseVolFraction;
+    real64 const Swc = hcurve.oppositeBoundPhaseVolFraction;
+
+    real64 const A = 1 + jerauldParam_a * (Shy - Swc);
+    real64 const numerator = Shy - Smxd;
+    real64 const denom = A + landParam * pow((Smxd - Shy) / (Smxd - Swc), 1 + jerauldParam_b / landParam );
+    Scrt = Smxd + numerator / denom;
+  }
+  else
+  {
+    //unpack values
+    real64 const Scrd = hcurve.drainageExtremaPhaseVolFraction;
+    real64 const Smx = hcurve.oppositeBoundPhaseVolFraction;
+
+    real64 const A = 1 + jerauldParam_a * (Smx - Shy);
+    real64 const numerator = Shy - Scrd;
+    real64 const denom = A + landParam * pow((Shy - Scrd) / (Smx - Scrd), 1 + jerauldParam_b / landParam );
+    Scrt = LvArray::math::max( 0.0,
+                               Scrd + numerator / denom );           // trapped critical saturation from equation 2.162
+  }
+
+}
+
+}//end namespace
+}//end namespace
diff --git a/src/coreComponents/constitutive/KilloughHysteresis.hpp b/src/coreComponents/constitutive/KilloughHysteresis.hpp
new file mode 100644
index 00000000000..ce151f3aeae
--- /dev/null
+++ b/src/coreComponents/constitutive/KilloughHysteresis.hpp
@@ -0,0 +1,179 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2018-2020 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2020 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2018-2020 TotalEnergies
+ * Copyright (c) 2019-     GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file TableRelativePermeabilityHysteresis.hpp
+ */
+
+#ifndef GEOS_KILLOUGHHYSTERESIS_HPP
+#define GEOS_KILLOUGHHYSTERESIS_HPP
+
+#include "constitutive/ConstitutiveBase.hpp"
+#include "functions/TableFunction.hpp"
+
+#include "relativePermeability/Layouts.hpp"
+#include "capillaryPressure/Layouts.hpp"
+
+namespace geos
+{
+
+using namespace dataRepository;
+
+namespace constitutive
+{
+
+/***
+ * @brief KilloughHysteresis is designed to hold Killough hystereis model parameters and
+ *        be in charge of all compuration related to this model (trapped Saturation,Land Coefficient?)
+ */
+
+
+
+//should be up to constitutiveBase or some new SCALConstitutiveBase but for now let's POC on relativePermeabilityBase
+class KilloughHysteresis
+{
+public:
+
+  static constexpr real64 minScriMinusScrd = 1e-12;
+  /// To avoid frequent changes from drainage to imbibition and vice versa, we use this buffer
+  static constexpr real64 flowReversalBuffer = 1e-12;
+
+  struct PhaseWettability
+  {
+    enum : integer
+    {
+      WETTING = 0,
+      NONWETTING = 1
+    };
+  };
+
+  /**
+   * @brief  struct to represent hysteresis curves (relperm or capillary pressure)
+   * whether they are wetting or non wetting, storing key point as pairs of
+   * saturations and value, being either the relperm value (S,kr) or capillary pressure value (S,pc).
+   * this way we can tell wetting curve from non wetting by the ordering of drainage/imbibition key values.
+   * Indeed if imbibition comes at lower saturation than drainage then it is wetting curve, on the opposite
+   * if drainage comes before imbibition this is a non-wetting hysteresis. This is completed by an opposite
+   * point that is either the connate wetting saturation Swc or the maximum non wetting saturation Sgmax.
+   * @param  oppositeBoundPhaseVolFraction represents either Swc or Sgmax depending if a wetting curve or nonwetting is described
+   * @param imbibitionExtremaPhaseVolFraction represents in wetting case the imibibition max and in non-wetting the imbibition residual
+   * @param drainageExtremaPhaseVolFraction represents in wetting case the drainage max and in non-wetting the drainage residual
+   * @param oppositeBoundSCALValue represents the associate relperm or capillary pressure value
+   * @param imbibitionExtremaSCALValue represents the associate relperm or capillary pressure value
+   * @param drainageExtremaSCALValue represents the associate relperm or capillary pressure value
+   */
+
+  struct HysteresisCurve
+  {
+    real64 oppositeBoundPhaseVolFraction = -1.;
+    real64 imbibitionExtremaPhaseVolFraction = -1.;
+    real64 drainageExtremaPhaseVolFraction = -1.;
+
+    real64 oppositeBoundSCALValue = -1.;
+    real64 imbibitionExtremaSCALValue = -1.;
+    real64 drainageExtremaSCALValue = -1.;
+
+    HysteresisCurve() = default;
+
+    HysteresisCurve( std::pair< real64, real64 > const & opp, std::pair< real64, real64 > const & imbE, std::pair< real64, real64 > const & drainE )
+    {
+      setPoints( opp, imbE, drainE );
+    }
+
+    void setPoints( std::pair< real64, real64 > const & opp, std::pair< real64, real64 > const & imbE, std::pair< real64, real64 > const & drainE )
+    {
+      oppositeBoundPhaseVolFraction = opp.first;
+      imbibitionExtremaPhaseVolFraction = imbE.first;
+      drainageExtremaPhaseVolFraction = drainE.first;
+
+      oppositeBoundSCALValue = opp.second;
+      imbibitionExtremaSCALValue = imbE.second;
+      drainageExtremaSCALValue = drainE.second;
+    }
+
+    //tODO (jacques) check if relevant to invert relation with same SCAL value // might be misleading for kr
+    HysteresisCurve toWetting() const
+    {
+        if(!isWetting())
+            return HysteresisCurve({1.-oppositeBoundPhaseVolFraction,oppositeBoundSCALValue},
+                                   {1.- imbibitionExtremaPhaseVolFraction,imbibitionExtremaSCALValue},
+                                   {1.-drainageExtremaPhaseVolFraction,drainageExtremaSCALValue});
+        else
+            return *this;
+    }
+
+      HysteresisCurve toNonWetting() const
+      {
+          if(isWetting())
+              return HysteresisCurve({1.-oppositeBoundPhaseVolFraction,oppositeBoundSCALValue},
+                                     {1.-imbibitionExtremaPhaseVolFraction,imbibitionExtremaSCALValue},
+                                     {1.-drainageExtremaPhaseVolFraction,drainageExtremaSCALValue});
+          else
+              return *this;
+      }
+
+    bool isWetting() const
+    {
+      return ((drainageExtremaPhaseVolFraction > oppositeBoundPhaseVolFraction) ? PhaseWettability::WETTING : PhaseWettability::NONWETTING) == PhaseWettability::WETTING;
+    }
+    bool isZero() const
+    {
+      return (oppositeBoundPhaseVolFraction <= 0.0) && (imbibitionExtremaPhaseVolFraction <= 0.0) && (drainageExtremaPhaseVolFraction <= 0.0);
+    }
+
+  };
+
+//  void setRelPermParameters( real64 const & jerauldA, real64 const & jerauldB, real64 const & relpermCurv );
+
+  static std::string catalogName() { return "KilloughHysteresis"; }
+
+  static void postProcessInput(real64 const &jerauldParam_a, real64 const &jerauldParam_b,
+                               real64 const &killoughCurvatureParamRelPerm,
+                               real64 const &killoughCurvatureParamPc);
+
+  GEOS_HOST_DEVICE
+  static void computeLandCoefficient( HysteresisCurve const & hcruve, real64 & landParam );
+  /**
+   * @brief Function computing the trapped critical phase volume fraction
+   * @param[in] hcurve the hysteresis curve to be used and dispatched on
+   * @param[in] Shy the max historical phase volume fraction
+   * @param[in] landParam Land trapping parameter
+   * @param[in] jerauldParam_a jerauld expononent
+   * @param[in] jerauldParam_b jerauld expononent
+   * @param[out] Scrt the trapped critical phase volume fraction
+   */
+  GEOS_HOST_DEVICE
+  static void computeTrappedCriticalPhaseVolFraction( HysteresisCurve const & hcurve,
+                                                      real64 const & Shy,
+                                                      real64 const & landParam,
+                                                      real64 const & jerauldParam_a,
+                                                      real64 const & jerauldParam_b,
+                                                      real64 & Scrt );
+
+  struct viewKeyStruct
+  {
+    static constexpr char const * jerauldParameterAString() { return "jerauldParameterA"; }
+    static constexpr char const * jerauldParameterBString() { return "jerauldParameterB"; }
+
+    static constexpr char const * killoughCurvatureParameterRelPermString() { return "killoughCurvatureParameterRelPerm"; }
+      static constexpr char const * killoughCurvatureParameterPcString() { return "killoughCurvatureParameterPc"; }
+  };
+
+};
+
+}
+
+}
+
+#endif //GEOS_KILLOUGHHYSTERESIS_HPP
diff --git a/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.cpp b/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.cpp
index f068365eb35..d7cc96a1dd1 100644
--- a/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.cpp
@@ -114,6 +114,7 @@ BrooksCoreyCapillaryPressure::createKernelWrapper()
                         m_volFracScale,
                         m_phaseTypes,
                         m_phaseOrder,
+                        m_phaseTrappedVolFrac,
                         m_phaseCapPressure,
                         m_dPhaseCapPressure_dPhaseVolFrac );
 }
diff --git a/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp b/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp
index 39d93e48858..e0c971492b2 100644
--- a/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp
@@ -39,10 +39,12 @@ class BrooksCoreyCapillaryPressureUpdate final : public CapillaryPressureBaseUpd
                                       real64 const volFracScale,
                                       arrayView1d< integer const > const & phaseTypes,
                                       arrayView1d< integer const > const & phaseOrder,
+                                      arrayView3d< real64, cappres::USD_CAPPRES > const & phaseTrapped,
                                       arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPressure,
                                       arrayView4d< real64, cappres::USD_CAPPRES_DS > const & dPhaseCapPressure_dPhaseVolFrac )
     : CapillaryPressureBaseUpdate( phaseTypes,
                                    phaseOrder,
+                                   phaseTrapped,
                                    phaseCapPressure,
                                    dPhaseCapPressure_dPhaseVolFrac ),
     m_phaseMinVolumeFraction( phaseMinVolumeFraction ),
@@ -57,6 +59,11 @@ class BrooksCoreyCapillaryPressureUpdate final : public CapillaryPressureBaseUpd
                 arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
                 arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
 
+  GEOS_HOST_DEVICE
+  void computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+                   arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+                   arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
+
   GEOS_HOST_DEVICE
   virtual void update( localIndex const k,
                        localIndex const q,
@@ -80,14 +87,32 @@ class BrooksCoreyCapillaryPressureUpdate final : public CapillaryPressureBaseUpd
                                real64 & phaseCapPressure,
                                real64 & dPhaseCapPressure_dVolFrac );
 
+
+  GEOS_HOST_DEVICE
+  GEOS_FORCE_INLINE
+  static void
+  evaluateBrooksCoreyFunctionInv( real64 const phaseCapPressure,
+                                  int const ip,
+                                  real64 const volFracScaleInv,
+                                  real64 const exponentInv,
+                                  real64 const entryPressure,
+                                  real64 const maxCapPres_eps,
+                                  real64 const phaseMinVolumeFraction,
+                                  arrayView1d< integer const > const phaseOrder,
+                                  real64 & phaseVolFraction,
+                                  real64 & dPhaseCapPressure_dVolFrac );
+
   arrayView1d< real64 const > m_phaseMinVolumeFraction;
   arrayView1d< real64 const > m_phaseCapPressureExponentInv;
   arrayView1d< real64 const > m_phaseEntryPressure;
 
   real64 m_capPressureEpsilon;
   real64 m_volFracScale;
+
 };
 
+
+
 class BrooksCoreyCapillaryPressure : public CapillaryPressureBase
 {
 public:
@@ -169,11 +194,14 @@ BrooksCoreyCapillaryPressureUpdate::
 
   // compute first gas-oil capillary pressure as a function of gas-phase vol fraction
   integer const ip_gas = m_phaseOrder[CapillaryPressureBase::PhaseType::GAS];
-  if( ip_gas >= 0 )
+  integer const ip_oil = m_phaseOrder[CapillaryPressureBase::PhaseType::OIL];
+
+  GEOS_UNUSED_VAR( ip_gas );
+  if( ip_oil >= 0 )
   {
-    real64 const volFracScaled = (phaseVolFraction[ip_gas] - m_phaseMinVolumeFraction[ip_gas]) * volFracScaleInv;
-    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_gas];
-    real64 const entryPressure = -m_phaseEntryPressure[ip_gas]; // for gas capillary pressure, take the opposite of the
+    real64 const volFracScaled = (phaseVolFraction[ip_oil] - m_phaseMinVolumeFraction[ip_oil]) * volFracScaleInv;
+    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_oil];
+    real64 const entryPressure = -m_phaseEntryPressure[ip_oil]; // for gas capillary pressure, take the opposite of the
                                                                 // BC function
 
     real64 const wettingVolFracScaled           = 1-volFracScaled;
@@ -184,11 +212,103 @@ BrooksCoreyCapillaryPressureUpdate::
                                  exponentInv,
                                  entryPressure,
                                  eps,
-                                 phaseCapPres[ip_gas],
-                                 dPhaseCapPres_dPhaseVolFrac[ip_gas][ip_gas] );
+                                 phaseCapPres[ip_oil],
+                                 dPhaseCapPres_dPhaseVolFrac[ip_oil][ip_oil] );
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+BrooksCoreyCapillaryPressureUpdate::
+  computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+              arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+              arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const
+{
+  LvArray::forValuesInSlice( dPhaseCapPres_dPhaseVolFrac, []( real64 & val ){ val = 0.0; } );
+
+  real64 const volFracScaleInv = 1.0 / m_volFracScale;
+
+  // the Brooks-Corey model does not support volFracScaled = 0,
+  // hence we need an epsilon value to avoid a division by zero
+  // TODO: for S < epsilon, replace the original unbounded BC curve with a bounded power-law extension
+  real64 const eps = m_capPressureEpsilon;
+
+
+  // compute first water-oil capillary pressure as a function of water-phase vol fraction
+  integer const ip_water = m_phaseOrder[CapillaryPressureBase::PhaseType::WATER];
+  integer const ip_gas = m_phaseOrder[CapillaryPressureBase::PhaseType::GAS];
+  if( ip_water >= 0 )
+  {
+    real64 const volFracScaled_eps = (eps - m_phaseMinVolumeFraction[ip_water]) * volFracScaleInv;
+    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_water];
+    real64 const entryPressure = m_phaseEntryPressure[ip_water];
+
+    real64 const wettingVolFracScaled_eps           = volFracScaled_eps;
+    real64 const dWettingVolFracScaled_dVolFrac = volFracScaleInv;
+
+    real64 maxCapPres_eps = 0.0;
+    real64 max_dpc_eps = 0.0;
+
+    evaluateBrooksCoreyFunction( wettingVolFracScaled_eps,
+                                 dWettingVolFracScaled_dVolFrac,
+                                 exponentInv,
+                                 entryPressure,
+                                 eps,
+                                 maxCapPres_eps,
+                                 max_dpc_eps );
+
+    evaluateBrooksCoreyFunctionInv( phaseCapPres[ip_water],
+                                    ip_water,
+                                    volFracScaleInv,
+                                    exponentInv,
+                                    entryPressure,
+                                    maxCapPres_eps,
+                                    m_phaseMinVolumeFraction[ip_water],
+                                    m_phaseOrder,
+                                    phaseVolFraction[ip_water],
+                                    dPhaseCapPres_dPhaseVolFrac[ip_water][ip_water] );
+    phaseVolFraction[ip_gas] = 1.0 - phaseVolFraction[ip_water];
+  }
+
+
+  // compute first gas-oil capillary pressure as a function of gas-phase vol fraction
+
+
+  // if( ip_gas >= 0 )
+  // {
+  //   real64 const volFracScaled_eps = (eps - m_phaseMinVolumeFraction[ip_gas]) * volFracScaleInv;
+  //   real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_gas];
+  //   real64 const entryPressure = -m_phaseEntryPressure[ip_gas]; // for gas capillary pressure, take the opposite of the
+  //                                                               // BC function
+
+  //   real64 const wettingVolFracScaled_eps           = 1-volFracScaled_eps;
+  //   real64 const dWettingVolFracScaled_dVolFrac =  -volFracScaleInv;
+
+  //   real64 maxCapPres_eps = 0.0;
+  //   real64 max_dpc_eps = 0.0;
+
+  //   evaluateBrooksCoreyFunction( wettingVolFracScaled_eps,
+  //                                dWettingVolFracScaled_dVolFrac,
+  //                                exponentInv,
+  //                                entryPressure,
+  //                                eps,
+  //                                maxCapPres_eps,
+  //                                max_dpc_eps );
+
+  //   evaluateBrooksCoreyFunctionInv( phaseCapPres[ip_gas],
+  //                                   ip_gas,
+  //                                   volFracScaleInv,
+  //                                   exponentInv,
+  //                                   entryPressure,
+  //                                   maxCapPres_eps,
+  //                                   m_phaseMinVolumeFraction[ip_gas],
+  //                                   m_phaseOrder,
+  //                                   phaseVolFraction[ip_gas],
+  //                                   dPhaseCapPres_dPhaseVolFrac[ip_gas][ip_gas] );
+  //  phaseVolFraction[ip_water] = 1.0 - phaseVolFraction[ip_gas];
+  // }
+}
+
 GEOS_HOST_DEVICE
 inline void
 BrooksCoreyCapillaryPressureUpdate::
@@ -222,6 +342,49 @@ BrooksCoreyCapillaryPressureUpdate::
 
 }
 
+GEOS_HOST_DEVICE
+inline void
+BrooksCoreyCapillaryPressureUpdate::
+  evaluateBrooksCoreyFunctionInv( real64 const phaseCapPressure,
+                                  int const ip,
+                                  real64 const volFracScaleInv,
+                                  real64 const exponentInv,
+                                  real64 const entryPressure,
+                                  real64 const maxCapPres_eps,
+                                  real64 const phaseMinVolumeFraction,
+                                  arrayView1d< integer const > const phaseOrder,
+                                  real64 & phaseVolFraction,
+                                  real64 & dPhaseCapPressure_dVolFrac )
+{
+
+
+  phaseVolFraction           = 0.0;
+  real64 value               = 0.0;
+  dPhaseCapPressure_dVolFrac = 0.0;
+  integer const ip_oil = phaseOrder[CapillaryPressureBase::PhaseType::OIL];
+
+  real64 const dScaledWettingPhaseVolFrac_dVolFrac = (ip == ip_oil)
+  ? -volFracScaleInv : volFracScaleInv;
+
+  if( phaseCapPressure <= maxCapPres_eps && phaseCapPressure >= entryPressure )
+  {
+    // intermediate value
+    real64 const val =  pow( entryPressure, exponentInv ) / pow( phaseCapPressure, exponentInv + 1 );
+
+    value           = (phaseCapPressure  * val) * volFracScaleInv + phaseMinVolumeFraction; // entryPressure * (S_w)^( - 1 / exponentInv )
+    dPhaseCapPressure_dVolFrac = -dScaledWettingPhaseVolFrac_dVolFrac * val * exponentInv;
+    phaseVolFraction = (ip == ip_oil) ? 1.0 - value : value;
+  }
+  else // enforce a constant and bounded capillary pressure
+  {
+    real64 const val = (phaseCapPressure > maxCapPres_eps)
+                     ? pow( entryPressure, exponentInv ) / pow( maxCapPres_eps, exponentInv ) : 1.0;
+    value           = val * volFracScaleInv + phaseMinVolumeFraction;
+    phaseVolFraction = (ip == ip_oil) ? 1.0 - value : value;
+  }
+
+}
+
 
 } // namespace constitutive
 
diff --git a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureBase.cpp b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureBase.cpp
index 9f1db0231ed..69d4280fb77 100644
--- a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureBase.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureBase.cpp
@@ -50,8 +50,9 @@ CapillaryPressureBase::CapillaryPressureBase( string const & name,
     setSizedFromParent( 0 ).
     setDescription( "Minimum volume fraction value for each phase" );
 
-  registerField< fields::cappres::phaseCapPressure >( &m_phaseCapPressure );
-  registerField< fields::cappres::dPhaseCapPressure_dPhaseVolFraction >( &m_dPhaseCapPressure_dPhaseVolFrac );
+    registerField< fields::cappres::phaseCapPressure >( &m_phaseCapPressure );
+    registerField< fields::cappres::dPhaseCapPressure_dPhaseVolFraction >( &m_dPhaseCapPressure_dPhaseVolFrac );
+    registerField< fields::cappres::phaseTrappedVolFraction >( &m_phaseTrappedVolFrac );
 }
 
 void CapillaryPressureBase::postInputInitialization()
@@ -93,19 +94,31 @@ void CapillaryPressureBase::postInputInitialization()
 void CapillaryPressureBase::allocateConstitutiveData( Group & parent, localIndex const numPts )
 {
   integer const NP = numFluidPhases();
-
+  //phase trapped for stats
+  m_phaseTrappedVolFrac.resize( 0, numPts, NP );
+  m_phaseTrappedVolFrac.zero();
   m_phaseCapPressure.resize( 0, numPts, NP );
   m_dPhaseCapPressure_dPhaseVolFrac.resize( 0, numPts, NP, NP );
-
+  
   ConstitutiveBase::allocateConstitutiveData( parent, numPts );
 }
 
 void CapillaryPressureBase::setLabels()
 {
+  getField< fields::cappres::phaseTrappedVolFraction >().
+    setDimLabels( 2, m_phaseNames );
   getField< fields::cappres::phaseCapPressure >().
     setDimLabels( 2, m_phaseNames );
 }
 
+void CapillaryPressureBase::resizeFields( localIndex const size, localIndex const numPts )
+{
+  integer const NP = numFluidPhases();
+  m_phaseTrappedVolFrac.resize( size, numPts, NP );
+  m_phaseCapPressure.resize( size, numPts, NP );
+  m_dPhaseCapPressure_dPhaseVolFrac.resize( size, numPts, NP, NP );
+}
+
 } // namespace constitutive
 
 } // namespace geos
diff --git a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureBase.hpp b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureBase.hpp
index b0617841488..34a4701b957 100644
--- a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureBase.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureBase.hpp
@@ -60,16 +60,19 @@ class CapillaryPressureBaseUpdate
 
   CapillaryPressureBaseUpdate( arrayView1d< integer const > const & phaseTypes,
                                arrayView1d< integer const > const & phaseOrder,
+                               arrayView3d< real64, cappres::USD_CAPPRES > const & phaseTrapped,
                                arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPressure,
                                arrayView4d< real64, cappres::USD_CAPPRES_DS > const & dPhaseCapPressure_dPhaseVolFrac )
     : m_phaseTypes( phaseTypes ),
     m_phaseOrder( phaseOrder ),
+    m_phaseTrappedVolFrac( phaseTrapped ),
     m_phaseCapPressure( phaseCapPressure ),
     m_dPhaseCapPressure_dPhaseVolFrac( dPhaseCapPressure_dPhaseVolFrac )
   {}
 
   arrayView1d< integer const > m_phaseTypes;
   arrayView1d< integer const > m_phaseOrder;
+  arrayView3d< real64, cappres::USD_CAPPRES > m_phaseTrappedVolFrac;
 
   arrayView3d< real64, cappres::USD_CAPPRES > m_phaseCapPressure;
   arrayView4d< real64, cappres::USD_CAPPRES_DS > m_dPhaseCapPressure_dPhaseVolFrac;
@@ -130,6 +133,14 @@ class CapillaryPressureBase : public ConstitutiveBase
                                        arrayView3d< real64 const > const & convergedPermeability ) const
   { GEOS_UNUSED_VAR( convergedPorosity, convergedPermeability ); }
 
+
+  /**
+   * @brief Save converged phase volume fraction at the end of a time step (needed for hysteresis)
+   * @param[in] phaseVolFraction an array containing the phase volume fractions at the end of a converged time step
+   */
+  virtual void saveConvergedPhaseVolFractionState( arrayView2d< real64 const, compflow::USD_PHASE > const & phaseVolFraction ) const
+  { GEOS_UNUSED_VAR( phaseVolFraction ); }
+
   /*
    * @brief Getter for the number of fluid phases
    * @return the number of fluid phases
@@ -182,9 +193,17 @@ class CapillaryPressureBase : public ConstitutiveBase
   void setLabels();
 
 protected:
+/**
+ * @brief Function called internally to resize member arrays
+ * @param size primary dimension (e.g. number of cells)
+ * @param numPts secondary dimension (e.g. number of gauss points per cell)
+ */
+  virtual void resizeFields( localIndex const size, localIndex const numPts );
 
   virtual void postInputInitialization() override;
 
+  std::tuple<integer, integer> phaseIndex(const arrayView1d<const integer> &phaseOrder);
+
   // phase names read from input
   string_array m_phaseNames;
 
@@ -198,8 +217,45 @@ class CapillaryPressureBase : public ConstitutiveBase
   // output quantities
   array3d< real64, cappres::LAYOUT_CAPPRES >  m_phaseCapPressure;
   array4d< real64, cappres::LAYOUT_CAPPRES_DS >  m_dPhaseCapPressure_dPhaseVolFrac;
+
+  // trapped fraction
+  array3d< real64, cappres::LAYOUT_CAPPRES > m_phaseTrappedVolFrac;
 };
 
+    inline std::tuple< integer, integer > CapillaryPressureBase::phaseIndex( arrayView1d< integer const > const & phaseOrder )
+    {
+        using PT = PhaseType;
+        integer const ipWater = phaseOrder[PT::WATER];
+        integer const ipOil = phaseOrder[PT::OIL];
+        integer const ipGas = phaseOrder[PT::GAS];
+
+        integer ipWetting = -1, ipNonWetting = -1;
+
+        if( ipWater >= 0 && ipOil >= 0 && ipGas >= 0 )
+        {
+            ipWetting = ipWater;
+            ipNonWetting = ipGas;
+        }
+        else if( ipWater < 0 )
+        {
+            ipWetting = ipOil;
+            ipNonWetting = ipGas;
+        }
+        else if( ipOil < 0 )
+        {
+            ipWetting = ipWater;
+            ipNonWetting = ipGas;
+        }
+        else if( ipGas < 0 )
+        {
+            ipWetting = ipWater;
+            ipNonWetting = ipOil;
+        }
+
+        //maybe a bit too pythonic
+        return std::make_tuple( ipWetting, ipNonWetting );
+    }
+
 } // namespace constitutive
 
 } // namespace geos
diff --git a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureFields.hpp b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureFields.hpp
index 653b7faeda8..a91ea22c1c6 100644
--- a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureFields.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureFields.hpp
@@ -23,45 +23,95 @@
 #include "constitutive/capillaryPressure/Layouts.hpp"
 #include "mesh/MeshFields.hpp"
 
-namespace geos
-{
-
-namespace fields
-{
-
-namespace cappres
-{
-
-using array3dLayoutCapPressure = array3d< real64, constitutive::cappres::LAYOUT_CAPPRES >;
-using array4dLayoutCapPressure_dS = array4d< real64, constitutive::cappres::LAYOUT_CAPPRES_DS >;
-
-DECLARE_FIELD( phaseCapPressure,
-               "phaseCapPressure",
-               array3dLayoutCapPressure,
-               0,
-               LEVEL_0,
-               WRITE_AND_READ,
-               "Phase capillary pressure" );
-
-DECLARE_FIELD( dPhaseCapPressure_dPhaseVolFraction,
-               "dPhaseCapPressure_dPhaseVolFraction",
-               array4dLayoutCapPressure_dS,
-               0,
-               NOPLOT,
-               WRITE_AND_READ,
-               "Derivative of phase capillary pressure with respect to phase volume fraction" );
-
-DECLARE_FIELD( jFuncMultiplier,
-               "jFuncMultiplier",
-               array2d< real64 >,
-               0,
-               NOPLOT,
-               WRITE_AND_READ,
-               "Multiplier for the Leverett J-function" );
+namespace geos {
 
-}
+    namespace fields {
 
-}
+        namespace cappres {
+
+            using array2dLayoutPhase = array2d<real64, compflow::LAYOUT_PHASE>;
+            using array3dLayoutCapPressure = array3d<real64, constitutive::cappres::LAYOUT_CAPPRES>;
+            using array4dLayoutCapPressure_dS = array4d<real64, constitutive::cappres::LAYOUT_CAPPRES_DS>;
+
+
+
+            enum ModeIndexType : integer {
+                DRAINAGE = 0,//to be used in array of Kernels
+                IMBIBITION = 1,
+                DRAINAGE_TO_IMBIBITION = 2,
+                IMBIBITION_TO_DRAINAGE = 3,
+                IMBIBITION_TO_DRAINAGE_FROM_SCANNING = 4
+            };
+
+            DECLARE_FIELD(phaseCapPressure,
+                          "phaseCapPressure",
+                          array3dLayoutCapPressure,
+                          0,
+                          LEVEL_0,
+                          WRITE_AND_READ,
+                          "Phase capillary pressure");
+
+            DECLARE_FIELD(dPhaseCapPressure_dPhaseVolFraction,
+                          "dPhaseCapPressure_dPhaseVolFraction",
+                          array4dLayoutCapPressure_dS,
+                          0,
+                          NOPLOT,
+                          WRITE_AND_READ,
+                          "Derivative of phase capillary pressure with respect to phase volume fraction");
+
+            DECLARE_FIELD(jFuncMultiplier,
+                          "jFuncMultiplier",
+                          array2d<real64>,
+                          0,
+                          NOPLOT,
+                          WRITE_AND_READ,
+                          "Multiplier for the Leverett J-function");
+
+            DECLARE_FIELD(phaseTrappedVolFraction,
+                          "phaseTrappedVolumeFraction",
+                          array3dLayoutCapPressure,
+                          0,
+                          LEVEL_0,
+                          WRITE_AND_READ,
+                          "Phase Trapped Volume Fraction");
+
+            DECLARE_FIELD(mode,
+                          "Hysteresis Mode",
+                          array1d<integer>,
+                          0,
+                          LEVEL_0,
+                          WRITE_AND_READ,
+                          "Hysteresis mode");
+
+
+            DECLARE_FIELD(phaseMaxHistoricalVolFraction,
+                          "phaseMaxHistoricalVolFraction",
+                          array2dLayoutPhase,
+                          0,
+                          LEVEL_0,
+                          WRITE_AND_READ,
+                          "Phase max historical phase volume fraction");
+
+            DECLARE_FIELD(phaseMinHistoricalVolFraction,
+                          "phaseMinHistoricalVolFraction",
+                          array2dLayoutPhase,
+                          0,
+                          LEVEL_0,
+                          WRITE_AND_READ,
+                          "Phase min historical phase volume fraction");
+
+            DECLARE_FIELD(phaseMode2PeakVolFraction,
+                          "phaseMode2PeakVolFraction",
+                          array2dLayoutPhase,
+                          0,
+                          LEVEL_0,
+                          WRITE_AND_READ,
+                          "Peak saturation reached during Mode 2 (DRAINAGE_TO_IMBIBITION)");
+
+
+        }
+
+    }
 
 }
 
diff --git a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureSelector.hpp b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureSelector.hpp
index b164f55aa16..a8382183ba4 100644
--- a/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureSelector.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/CapillaryPressureSelector.hpp
@@ -24,6 +24,7 @@
 #include "constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp"
 #include "constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp"
 #include "constitutive/capillaryPressure/TableCapillaryPressure.hpp"
+#include "constitutive/capillaryPressure/TableCapillaryPressureHysteresis.hpp"
 #include "constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp"
 
 namespace geos
@@ -39,6 +40,7 @@ void constitutiveUpdatePassThru( CapillaryPressureBase const & capPres,
   ConstitutivePassThruHandler< BrooksCoreyCapillaryPressure,
                                JFunctionCapillaryPressure,
                                TableCapillaryPressure,
+                               TableCapillaryPressureHysteresis,
                                VanGenuchtenCapillaryPressure >::execute( capPres, std::forward< LAMBDA >( lambda ) );
 }
 
@@ -49,6 +51,7 @@ void constitutiveUpdatePassThru( CapillaryPressureBase & capPres,
   ConstitutivePassThruHandler< BrooksCoreyCapillaryPressure,
                                JFunctionCapillaryPressure,
                                TableCapillaryPressure,
+                               TableCapillaryPressureHysteresis,
                                VanGenuchtenCapillaryPressure >::execute( capPres, std::forward< LAMBDA >( lambda ) );
 }
 
diff --git a/src/coreComponents/constitutive/capillaryPressure/InverseCapillaryPressure.cpp b/src/coreComponents/constitutive/capillaryPressure/InverseCapillaryPressure.cpp
index 534037c55f4..0156d06ab67 100644
--- a/src/coreComponents/constitutive/capillaryPressure/InverseCapillaryPressure.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/InverseCapillaryPressure.cpp
@@ -20,6 +20,7 @@
 #include "InverseCapillaryPressure.hpp"
 #include "constitutive/capillaryPressure/BrooksCoreyCapillaryPressure.hpp"
 #include "constitutive/capillaryPressure/TableCapillaryPressure.hpp"
+#include "constitutive/capillaryPressure/TableCapillaryPressureHysteresis.hpp"
 #include "constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp"
 #include "constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp"
 
@@ -317,6 +318,7 @@ void InverseCapillaryPressure< CAP_PRESSURE >::calculateJFunctionIndex( integer
 
 template class InverseCapillaryPressure< BrooksCoreyCapillaryPressure >;
 template class InverseCapillaryPressure< TableCapillaryPressure >;
+template class InverseCapillaryPressure< TableCapillaryPressureHysteresis >;
 template class InverseCapillaryPressure< JFunctionCapillaryPressure >;
 template class InverseCapillaryPressure< VanGenuchtenCapillaryPressure >;
 template class InverseCapillaryPressure< NoOpCapillaryPressure >;
diff --git a/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.cpp b/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.cpp
index e4eb76d02ba..fbb31266692 100644
--- a/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.cpp
@@ -119,6 +119,14 @@ JFunctionCapillaryPressure::JFunctionCapillaryPressure( std::string const & name
     .setInputFlag( InputFlags::FALSE );
 
   registerField< fields::cappres::jFuncMultiplier >( &m_jFuncMultiplier );
+
+  registerWrapper( viewKeyStruct::jFunctionWrappersString(), &m_jFuncKernelWrappers ).
+    setSizedFromParent( 0 ).
+    setRestartFlags( RestartFlags::NO_WRITE );
+
+  registerWrapper( viewKeyStruct::inverseJFunctionWrappersString(), &m_inverseJFuncKernelWrappers ).
+    setSizedFromParent( 0 ).
+    setRestartFlags( RestartFlags::NO_WRITE );
 }
 
 void JFunctionCapillaryPressure::postInputInitialization()
@@ -187,6 +195,7 @@ void JFunctionCapillaryPressure::initializePreSubGroups()
       ? true   // pc on the gas phase, function must be increasing
       : false; // pc on the water phase, function must be decreasing
     TableCapillaryPressureHelpers::validateCapillaryPressureTable( jFuncTable, getFullName(), jFuncMustBeIncreasing );
+
   }
   else if( numPhases == 3 )
   {
@@ -205,6 +214,7 @@ void JFunctionCapillaryPressure::initializePreSubGroups()
                    InputError, getDataContext() );
     TableFunction const & jFuncTableNWI = functionManager.getGroup< TableFunction >( m_nonWettingIntermediateJFuncTableName );
     TableCapillaryPressureHelpers::validateCapillaryPressureTable( jFuncTableNWI, getFullName(), true );
+
   }
 }
 
@@ -300,11 +310,48 @@ void JFunctionCapillaryPressure::createAllTableKernelWrappers()
   // we want to make sure that the wrappers are always up-to-date, so we recreate them everytime
 
   m_jFuncKernelWrappers.clear();
+  m_inverseJFuncKernelWrappers.clear();
+
   if( numPhases == 2 )
   {
+
     TableFunction const & jFuncTable = functionManager.getGroup< TableFunction >( m_wettingNonWettingJFuncTableName );
     m_jFuncKernelWrappers.emplace_back( jFuncTable.createKernelWrapper() );
 
+    auto const & satArrayView = jFuncTable.getCoordinates()[0];
+    auto const & jArrayView   = jFuncTable.getValues();
+
+    std::vector< real64 > satVec( satArrayView.size() );
+    std::vector< real64 > jVec( jArrayView.size() );
+
+    std::copy( satArrayView.begin(), satArrayView.end(), satVec.begin() );
+    std::copy( jArrayView.begin(), jArrayView.end(), jVec.begin() );
+
+    // Reverse both arrays (if original J is decreasing in S)
+    std::reverse( jVec.begin(), jVec.end() );
+    std::reverse( satVec.begin(), satVec.end() );
+
+
+    auto inverseTable = std::make_shared< TableFunction >( "inverseJFunc", this );
+
+    real64_array invJVec( jVec.size() );
+    real64_array invSatVec( satVec.size() );
+    std::copy( jVec.begin(), jVec.end(), invJVec.data() );
+    std::copy( satVec.begin(), satVec.end(), invSatVec.data() );
+
+    array1d< real64_array > coordinates;
+    coordinates.emplace_back( std::move( invJVec ) );
+
+
+    std::vector< units::Unit > dimUnits = { units::Unknown }; // or actual unit if available
+
+    inverseTable->setTableCoordinates( coordinates, dimUnits );
+    inverseTable->setTableValues( std::move( invSatVec ), units::Unknown );
+    inverseTable->setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+    m_inverseJFuncKernelWrappers.emplace_back( inverseTable->createKernelWrapper() );
+    m_inverseTables.emplace_back( std::move( inverseTable ) );
+
     // Populate the end-points from the tables
     TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction( m_phaseOrder.toSliceConst(), jFuncTable, m_phaseMinVolumeFraction );
   }
@@ -313,8 +360,10 @@ void JFunctionCapillaryPressure::createAllTableKernelWrappers()
     // the assumption used everywhere in this class is that the WI information comes before the NWI information
     TableFunction const & jFuncTableWI = functionManager.getGroup< TableFunction >( m_wettingIntermediateJFuncTableName );
     m_jFuncKernelWrappers.emplace_back( jFuncTableWI.createKernelWrapper() );
+    m_inverseJFuncKernelWrappers.emplace_back( jFuncTableWI.createKernelWrapper() );
     TableFunction const & jFuncTableNWI = functionManager.getGroup< TableFunction >( m_nonWettingIntermediateJFuncTableName );
     m_jFuncKernelWrappers.emplace_back( jFuncTableNWI.createKernelWrapper() );
+    m_inverseJFuncKernelWrappers.emplace_back( jFuncTableNWI.createKernelWrapper() );
 
     // Populate the end-points from the tables
     TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction( m_phaseOrder.toSliceConst(), jFuncTableWI, jFuncTableNWI, m_phaseMinVolumeFraction );
@@ -323,16 +372,20 @@ void JFunctionCapillaryPressure::createAllTableKernelWrappers()
 
 JFunctionCapillaryPressure::KernelWrapper::
   KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & jFuncKernelWrappers,
+                 arrayView1d< TableFunction::KernelWrapper const > const & inverseJFuncKernelWrappers,
                  arrayView2d< real64 const > const & jFuncMultiplier,
                  arrayView1d< integer const > const & phaseTypes,
                  arrayView1d< integer const > const & phaseOrder,
+                 arrayView3d< real64, cappres::USD_CAPPRES > const & phaseTrapped,
                  arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPres,
                  arrayView4d< real64, cappres::USD_CAPPRES_DS > const & dPhaseCapPres_dPhaseVolFrac )
   : CapillaryPressureBaseUpdate( phaseTypes,
                                  phaseOrder,
+                                 phaseTrapped,
                                  phaseCapPres,
                                  dPhaseCapPres_dPhaseVolFrac ),
   m_jFuncKernelWrappers( jFuncKernelWrappers ),
+  m_inverseJFuncKernelWrappers( inverseJFuncKernelWrappers ),
   m_jFuncMultiplier( jFuncMultiplier )
 {}
 
@@ -341,9 +394,11 @@ JFunctionCapillaryPressure::createKernelWrapper()
 {
   createAllTableKernelWrappers();
   return KernelWrapper( m_jFuncKernelWrappers,
+                        m_inverseJFuncKernelWrappers,
                         m_jFuncMultiplier,
                         m_phaseTypes,
                         m_phaseOrder,
+                        m_phaseTrappedVolFrac,
                         m_phaseCapPressure,
                         m_dPhaseCapPressure_dPhaseVolFrac );
 }
diff --git a/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp b/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp
index 4e42189d92e..29e7692bd95 100644
--- a/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp
@@ -65,9 +65,11 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
 public:
 
     KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & jFuncKernelWrappers,
+                   arrayView1d< TableFunction::KernelWrapper const > const & inverseJFuncKernelWrappers,
                    arrayView2d< real64 const > const & jFuncMultiplier,
                    arrayView1d< integer const > const & phaseTypes,
                    arrayView1d< integer const > const & phaseOrder,
+                   arrayView3d< real64, cappres::USD_CAPPRES > const & phaseTrapped,
                    arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPres,
                    arrayView4d< real64, cappres::USD_CAPPRES_DS > const & dPhaseCapPres_dPhaseVolFrac );
 
@@ -77,6 +79,13 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
                   arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
                   arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
 
+    GEOS_HOST_DEVICE
+    void computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+                     arraySlice1d< real64 const > const & jFuncMultiplier,
+                     arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+                     arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
+
+
     GEOS_HOST_DEVICE
     virtual void update( localIndex const k,
                          localIndex const q,
@@ -87,6 +96,7 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
     /// Array of kernel wrappers for the J-function
     /// Is of size 1 for two-phase flow, and of size 2 for three-phase flow
     arrayView1d< TableFunction::KernelWrapper const > const m_jFuncKernelWrappers;
+    arrayView1d< TableFunction::KernelWrapper const > const m_inverseJFuncKernelWrappers;
 
     /// Array of cell-wise J-function multipliers
     /// The second dimension is of size 1 for two-phase flow, and of size 2 for three-phase flow
@@ -112,6 +122,8 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
     static constexpr char const * porosityExponentString() { return "porosityExponent"; }
     static constexpr char const * permeabilityExponentString() { return "permeabilityExponent"; }
     static constexpr char const * permeabilityDirectionString() { return "permeabilityDirection"; }
+    static constexpr char const * jFunctionWrappersString() { return "jFunctionWrappers"; }
+    static constexpr char const * inverseJFunctionWrappersString() { return "inverseJFunctionWrappers"; }
   };
 
   /**
@@ -168,6 +180,9 @@ class JFunctionCapillaryPressure : public CapillaryPressureBase
 
   /// J-function kernel wrapper for the first pair (wetting-intermediate if NP=3, wetting-non-wetting otherwise)
   array1d< TableFunction::KernelWrapper > m_jFuncKernelWrappers;
+  array1d< TableFunction::KernelWrapper > m_inverseJFuncKernelWrappers;
+
+  std::vector< std::shared_ptr< TableFunction > > m_inverseTables;
 
 };
 
@@ -242,6 +257,42 @@ JFunctionCapillaryPressure::KernelWrapper::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+JFunctionCapillaryPressure::KernelWrapper::
+  computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+              arraySlice1d< real64 const > const & jFuncMultiplier,
+              arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+              arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const
+{
+  LvArray::forValuesInSlice( dPhaseCapPres_dPhaseVolFrac, []( real64 & val ){ val = 0.0; } );
+
+  using PT = CapillaryPressureBase::PhaseType;
+  integer const ipWater = m_phaseOrder[PT::WATER];
+  integer const ipOil   = m_phaseOrder[PT::OIL];
+  integer const ipGas   = m_phaseOrder[PT::GAS];
+
+  GEOS_UNUSED_VAR( ipOil );
+  // apply multiplier
+  real64 capPresWater_J = phaseCapPres[ipWater] / jFuncMultiplier[0];
+  // std::cout << GEOS_FMT( "        JM_2 = ( {:4.2e} )", jFuncMultiplier[0] );
+  array1d< real64 > input( 1 );
+  input[0] = capPresWater_J;
+  // std::cout << GEOS_FMT( "        J_int2 = ( {:4.2e} )", input[0] );
+  // std::cout << GEOS_FMT( "        Pc_int2 = ( {:4.2e} )", phaseCapPres[ipWater] );
+  auto inputSlice = input.toSliceConst();
+
+
+
+  phaseVolFraction[ipWater] =
+    m_inverseJFuncKernelWrappers[0].compute( inputSlice,
+                                             &(dPhaseCapPres_dPhaseVolFrac)[ipWater][ipWater] );
+  dPhaseCapPres_dPhaseVolFrac[ipWater][ipWater] /= jFuncMultiplier[0];
+  // std::cout << GEOS_FMT( "        S_int2 = ( {:4.2e} )", phaseVolFraction[ipWater] );
+  // std::cout << GEOS_FMT( "        dS/dP = ( {:4.2e} )", dPhaseCapPres_dPhaseVolFrac[ipWater][ipWater] );
+  phaseVolFraction[ipGas] = 1.0 - phaseVolFraction[ipWater];
+}
+
 GEOS_HOST_DEVICE
 inline void
 JFunctionCapillaryPressure::KernelWrapper::
diff --git a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.cpp b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.cpp
index 17b94f4730f..ded882f76d0 100644
--- a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.cpp
@@ -69,6 +69,10 @@ TableCapillaryPressure::TableCapillaryPressure( std::string const & name,
   registerWrapper( viewKeyStruct::capPresWrappersString(), &m_capPresKernelWrappers ).
     setSizedFromParent( 0 ).
     setRestartFlags( RestartFlags::NO_WRITE );
+
+  registerWrapper( viewKeyStruct::inverseCapPresWrappersString(), &m_inverseCapPresWrappers ).
+    setSizedFromParent( 0 ).
+    setRestartFlags( RestartFlags::NO_WRITE );
 }
 
 void TableCapillaryPressure::postInputInitialization()
@@ -154,11 +158,46 @@ void TableCapillaryPressure::createAllTableKernelWrappers()
   // we want to make sure that the wrappers are always up-to-date, so we recreate them everytime
 
   m_capPresKernelWrappers.clear();
+  m_inverseCapPresWrappers.clear();
+
   if( numPhases == 2 )
   {
     TableFunction const & capPresTable = functionManager.getGroup< TableFunction >( m_wettingNonWettingCapPresTableName );
     m_capPresKernelWrappers.emplace_back( capPresTable.createKernelWrapper() );
 
+    auto const & satArrayView = capPresTable.getCoordinates()[0];
+    auto const & capPresArrayView   = capPresTable.getValues();
+
+    std::vector< real64 > satVec( satArrayView.size() );
+    std::vector< real64 > pcVec( capPresArrayView.size() );
+
+    std::copy( satArrayView.begin(), satArrayView.end(), satVec.begin() );
+    std::copy( capPresArrayView.begin(), capPresArrayView.end(), pcVec.begin() );
+
+    // Reverse both arrays (if original J is decreasing in S)
+    std::reverse( pcVec.begin(), pcVec.end() );
+    std::reverse( satVec.begin(), satVec.end() );
+
+    auto inverseTable = std::make_shared< TableFunction >( "inverseCapPres", this );
+
+    real64_array invPcVec( pcVec.size() );
+    real64_array invSatVec( satVec.size() );
+    std::copy( pcVec.begin(), pcVec.end(), invPcVec.data() );
+    std::copy( satVec.begin(), satVec.end(), invSatVec.data() );
+
+    array1d< real64_array > coordinates;
+    coordinates.emplace_back( std::move( invPcVec ) );
+
+
+    std::vector< units::Unit > dimUnits = { units::Unknown }; // or actual unit if available
+
+    inverseTable->setTableCoordinates( coordinates, dimUnits );
+    inverseTable->setTableValues( std::move( invSatVec ), units::Unknown );
+    inverseTable->setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+    m_inverseCapPresWrappers.emplace_back( inverseTable->createKernelWrapper() );
+    m_inverseTables.emplace_back( std::move( inverseTable ) );
+
     // Populate the end-points from the tables
     TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction( m_phaseOrder.toSliceConst(), capPresTable, m_phaseMinVolumeFraction );
   }
@@ -166,8 +205,10 @@ void TableCapillaryPressure::createAllTableKernelWrappers()
   {
     TableFunction const & capPresTableWI = functionManager.getGroup< TableFunction >( m_wettingIntermediateCapPresTableName );
     m_capPresKernelWrappers.emplace_back( capPresTableWI.createKernelWrapper() );
+    m_inverseCapPresWrappers.emplace_back( capPresTableWI.createKernelWrapper() );
     TableFunction const & capPresTableNWI = functionManager.getGroup< TableFunction >( m_nonWettingIntermediateCapPresTableName );
     m_capPresKernelWrappers.emplace_back( capPresTableNWI.createKernelWrapper() );
+    m_inverseCapPresWrappers.emplace_back( capPresTableNWI.createKernelWrapper() );
 
     // Populate the end-points from the tables
     TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction( m_phaseOrder.toSliceConst(), capPresTableWI, capPresTableNWI, m_phaseMinVolumeFraction );
@@ -177,15 +218,19 @@ void TableCapillaryPressure::createAllTableKernelWrappers()
 
 TableCapillaryPressure::KernelWrapper::
   KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & capPresKernelWrappers,
+                 arrayView1d< TableFunction::KernelWrapper const > const & inverseCapPresWrappers,
                  arrayView1d< integer const > const & phaseTypes,
                  arrayView1d< integer const > const & phaseOrder,
+                 arrayView3d< real64, cappres::USD_CAPPRES > const & phaseTrapped,
                  arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPres,
                  arrayView4d< real64, cappres::USD_CAPPRES_DS > const & dPhaseCapPres_dPhaseVolFrac )
   : CapillaryPressureBaseUpdate( phaseTypes,
                                  phaseOrder,
+                                 phaseTrapped,
                                  phaseCapPres,
                                  dPhaseCapPres_dPhaseVolFrac ),
-  m_capPresKernelWrappers( capPresKernelWrappers )
+  m_capPresKernelWrappers( capPresKernelWrappers ),
+  m_inverseCapPresWrappers( inverseCapPresWrappers )
 {}
 
 TableCapillaryPressure::KernelWrapper
@@ -193,8 +238,10 @@ TableCapillaryPressure::createKernelWrapper()
 {
   createAllTableKernelWrappers();
   return KernelWrapper( m_capPresKernelWrappers,
+                        m_inverseCapPresWrappers,
                         m_phaseTypes,
                         m_phaseOrder,
+                        m_phaseTrappedVolFrac,
                         m_phaseCapPressure,
                         m_dPhaseCapPressure_dPhaseVolFrac );
 }
diff --git a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.hpp b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.hpp
index 739b9993083..f7b661a6090 100644
--- a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressure.hpp
@@ -55,8 +55,10 @@ class TableCapillaryPressure : public CapillaryPressureBase
 public:
 
     KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & capPresKernelWrappers,
+                   arrayView1d< TableFunction::KernelWrapper const > const & inverseCapPresWrappers,
                    arrayView1d< integer const > const & phaseTypes,
                    arrayView1d< integer const > const & phaseOrder,
+                   arrayView3d< real64, cappres::USD_CAPPRES > const & phaseTrapped,
                    arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPres,
                    arrayView4d< real64, cappres::USD_CAPPRES_DS > const & dPhaseCapPres_dPhaseVolFrac );
 
@@ -65,6 +67,12 @@ class TableCapillaryPressure : public CapillaryPressureBase
                   arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
                   arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
 
+    GEOS_HOST_DEVICE
+    void computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+                     arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+                     arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
+
+
     GEOS_HOST_DEVICE
     virtual void update( localIndex const k,
                          localIndex const q,
@@ -75,6 +83,7 @@ class TableCapillaryPressure : public CapillaryPressureBase
     /// Array of kernel wrappers for the capillary pressures
     /// Is of size 1 for two-phase flow, and of size 2 for three-phase flow
     arrayView1d< TableFunction::KernelWrapper const > const m_capPresKernelWrappers;
+    arrayView1d< TableFunction::KernelWrapper const > const m_inverseCapPresWrappers;
 
   };
 
@@ -91,6 +100,7 @@ class TableCapillaryPressure : public CapillaryPressureBase
     static constexpr char const * wettingIntermediateCapPresTableNameString() { return "wettingIntermediateCapPressureTableName"; }
     static constexpr char const * nonWettingIntermediateCapPresTableNameString() { return "nonWettingIntermediateCapPressureTableName"; }
     static constexpr char const * capPresWrappersString() { return "capPresWrappers"; }
+    static constexpr char const * inverseCapPresWrappersString() { return "inverseCapPresWrappers"; }
 
   };
 
@@ -116,6 +126,9 @@ class TableCapillaryPressure : public CapillaryPressureBase
 
   /// Capillary pressure kernel wrapper for the first pair (wetting-intermediate if NP=3, wetting-non-wetting otherwise)
   array1d< TableFunction::KernelWrapper > m_capPresKernelWrappers;
+  array1d< TableFunction::KernelWrapper > m_inverseCapPresWrappers;
+
+  std::vector< std::shared_ptr< TableFunction > > m_inverseTables;
 
 };
 
@@ -173,6 +186,37 @@ TableCapillaryPressure::KernelWrapper::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+TableCapillaryPressure::KernelWrapper::
+  computeInv( arraySlice1d< real64, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+              arraySlice1d< real64 const, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+              arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const
+{
+  LvArray::forValuesInSlice( dPhaseCapPres_dPhaseVolFrac, []( real64 & val ){ val = 0.0; } );
+
+  using PT = CapillaryPressureBase::PhaseType;
+  integer const ipWater = m_phaseOrder[PT::WATER];
+  integer const ipOil   = m_phaseOrder[PT::OIL];
+  integer const ipGas   = m_phaseOrder[PT::GAS];
+
+  GEOS_UNUSED_VAR( ipOil );
+
+  // put capillary pressure on the wetting phase
+  real64 capPresWater = phaseCapPres[ipWater];
+  array1d< real64 > input( 1 );
+  input[0] = capPresWater;
+  auto inputSlice = input.toSliceConst();
+
+  phaseVolFraction[ipWater] =
+    m_inverseCapPresWrappers[0].compute( inputSlice,
+                                         &(dPhaseCapPres_dPhaseVolFrac)[ipWater][ipWater] );
+
+  phaseVolFraction[ipGas] = 1.0 - phaseVolFraction[ipWater];
+
+}
+
+
 GEOS_HOST_DEVICE
 inline void
 TableCapillaryPressure::KernelWrapper::
diff --git a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHelpers.cpp b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHelpers.cpp
index 619e69a22db..d412260e7c5 100644
--- a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHelpers.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHelpers.cpp
@@ -130,18 +130,46 @@ void TableCapillaryPressureHelpers::populateMinPhaseVolumeFraction(
 }
 
 void
-TableCapillaryPressureHelpers::validateCapillaryPressureTable( geos::TableFunction const & capPresTable,
-                                                               geos::string const & fullConstitutiveName,
-                                                               bool const capPresMustBeIncreasing,
-                                                               geos::real64 & phaseMax, geos::real64 & phaseMin )
+TableCapillaryPressureHelpers::validateCapillaryPressureTable( const geos::TableFunction & capPresTable,
+                                                               const geos::string & fullConstitutiveName,
+                                                               const bool capPresMustBeIncreasing,
+                                                               geos::real64 & phaseMax,
+                                                               geos::real64 & phaseMin,
+                                                               geos::real64 & phaseCapPresMinEndPoint,
+                                                               geos::real64 & phaseCapPresMaxEndPoint )
 {
 
   TableCapillaryPressureHelpers::validateCapillaryPressureTable( capPresTable, fullConstitutiveName, capPresMustBeIncreasing );
   ArrayOfArraysView< real64 const > coords = capPresTable.getCoordinates();
   arraySlice1d< real64 const > phaseVolFrac = coords[0];
+    arrayView1d< real64 const > const capPres = capPresTable.getValues();
+
   phaseMin = phaseVolFrac[0];
+  phaseCapPresMinEndPoint = capPres[0];
   phaseMax = phaseVolFrac[phaseVolFrac.size()-1];
-}
+  phaseCapPresMaxEndPoint = capPres[phaseVolFrac.size()-1];
+
+
+      if(capPresMustBeIncreasing) {
+
+          for( localIndex i = 1; i < coords.sizeOfArray( 0 ); ++i ) {
+              if (isZero(capPres[i - 1]) && !isZero(capPres[i])) {
+                  phaseMin = phaseVolFrac[i - 1];
+                  phaseCapPresMinEndPoint = capPres[i - 1];
+              }
+          }
+      }
+      else
+      {
+          for( localIndex i = coords.sizeOfArray( 0 )-2; i>0; --i ) {
+              if (isZero(capPres[i + 1]) && !isZero(capPres[i])) {
+                  phaseMax = phaseVolFrac[i + 1];
+                  phaseCapPresMaxEndPoint = capPres[i + 1];
+              }
+          }
+
+      }
+  }
 
 
 } // namespace constitutive
diff --git a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHelpers.hpp b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHelpers.hpp
index a691637002c..276d8c3eb92 100644
--- a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHelpers.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHelpers.hpp
@@ -47,7 +47,9 @@ struct TableCapillaryPressureHelpers
                                        string const & fullConstitutiveName,
                                        bool const capPresMustBeIncreasing,
                                        real64 & phaseMax,
-                                       real64 & phaseMin );
+                                       real64 & phaseMin,
+                                       real64 & phaseCapPresMinEndPoint,
+                                       real64 & phaseCapPresMaxEndPoint );
 
   /**
    * @brief Populates the minimum phase volume fraction for each phase from the ends of the provided tables
diff --git a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHysteresis.cpp b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHysteresis.cpp
new file mode 100644
index 00000000000..3485f743c00
--- /dev/null
+++ b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHysteresis.cpp
@@ -0,0 +1,4004 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2018-2020 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2020 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2018-2020 TotalEnergies
+ * Copyright (c) 2019-     GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+
+#include "TableCapillaryPressureHysteresis.hpp"
+
+#include "constitutive/capillaryPressure/TableCapillaryPressureHelpers.hpp"
+#include "functions/FunctionManager.hpp"
+#include "constitutive/ConstitutiveManager.hpp"
+
+namespace geos {
+
+    using namespace dataRepository;
+
+    namespace constitutive {
+
+        TableCapillaryPressureHysteresis::TableCapillaryPressureHysteresis(const std::string &name,
+                                                                           dataRepository::Group *const parent)
+                : CapillaryPressureBase(name, parent) {
+
+            registerWrapper(viewKeyStruct::phaseHasHysteresisString(), &m_phaseHasHysteresis).
+                            setInputFlag(InputFlags::FALSE)
+                    .                         // will be deduced from tables
+                            setSizedFromParent(0);
+
+            registerWrapper(viewKeyStruct::landParameterString(), &m_landParam).
+                    setInputFlag(InputFlags::FALSE).                       // will be deduced from tables
+                    setSizedFromParent(0);
+
+            //2phase
+            registerWrapper(viewKeyStruct::drainageWettingNonWettingCapPresTableNameString(),
+                            &m_drainageWettingNonWettingCapPresTableName).
+                    setInputFlag(InputFlags::OPTIONAL).
+                    setDescription("Name of the drainage two-phase table for capillary pressure curve. \n"
+                                   "If you want to use 3-phase flow please use instead " +
+                                   string(viewKeyStruct::drainageWettingIntermediateCapPresTableNameString()) +
+                                   " and " +
+                                   string(viewKeyStruct::drainageNonWettingIntermediateCapPresTableNameString()) +
+                                   "to specify the tables names");
+            registerWrapper(viewKeyStruct::imbibitionWettingNonWettingCapPresTableNameString(),
+                            &m_imbibitionWettingNonWettingCapPresTableName).
+                    setInputFlag(InputFlags::OPTIONAL).
+                    setDescription("Name of the drainage two-phase table for capillary pressure curve. \n"
+                                   "If you want to use 3-phase flow please use instead " +
+                                   string(viewKeyStruct::imbibitionWettingIntermediateCapPresTableNameString()) +
+                                   " and " +
+                                   string(viewKeyStruct::imbibitionNonWettingIntermediateCapPresTableNameString()) +
+                                   "to specify the tables names");
+            //3phase
+            registerWrapper(viewKeyStruct::drainageWettingIntermediateCapPresTableNameString(),
+                            &m_drainageWettingIntermediateCapPresTableName).
+                    setInputFlag(InputFlags::OPTIONAL).
+                    setDescription(
+                    "Drainage wetting/intermediate (e.g. w/o) capillary pressure table name for the wetting phase.\n"
+                    "To neglect hysteresis on this phase, just use the same table name for the drainage and imbibition curves");
+            registerWrapper(viewKeyStruct::drainageNonWettingIntermediateCapPresTableNameString(),
+                            &m_drainageNonWettingIntermediateCapPresTableName).
+                    setInputFlag(InputFlags::OPTIONAL).
+                    setDescription(
+                    "Drainage non-wetting/intermediate (e.g. o/g) capillary pressure table name for the non-wetting phase.\n"
+                    "To neglect hysteresis on this phase, just use the same table name for the drainage and imbibition curves");
+            registerWrapper(viewKeyStruct::imbibitionWettingIntermediateCapPresTableNameString(),
+                            &m_imbibitionWettingIntermediateCapPresTableName).
+                    setInputFlag(InputFlags::OPTIONAL).
+                    setDescription("Imbibition wetting/intermediate (e.g. w/o) table name for the wetting phase.\n"
+                                   "To neglect hysteresis on this phase, just use the same table name for the drainage and imbibition curves");
+            registerWrapper(viewKeyStruct::imbibitionNonWettingIntermediateCapPresTableNameString(),
+                            &m_imbibitionNonWettingIntermediateCapPresTableName).
+                    setInputFlag(InputFlags::OPTIONAL).
+                    setDescription("Imbibition non-wetting/intermediate (e.g. o/g) table name for the wetting phase.\n"
+                                   "To neglect hysteresis on this phase, just use the same table name for the drainage and imbibition curves");
+
+            // kernels
+            //2p
+            registerWrapper(viewKeyStruct::wettingNonWettingCapillaryPressureKernelWrappersString(),
+                            &m_wettingNonWettingCapillaryPressureKernelWrappers)
+                    .setSizedFromParent(0).setRestartFlags(RestartFlags::NO_WRITE);
+            //3p
+            registerWrapper(viewKeyStruct::wettingIntermediateCapillaryPressureKernelWrappersString(),
+                            &m_wettingIntermediateCapillaryPressureKernelWrappers)
+                    .setSizedFromParent(0).setRestartFlags(RestartFlags::NO_WRITE);
+            registerWrapper(viewKeyStruct::nonWettingIntermediateCapillaryPressureKernelWrappersString(),
+                            &m_nonWettingIntermediateCapillaryPressureKernelWrappers)
+                    .setSizedFromParent(0).setRestartFlags(RestartFlags::NO_WRITE);
+
+
+            registerWrapper(viewKeyStruct::wettingCurveString(), &m_wettingCurve).
+                            setInputFlag(
+                            InputFlags::FALSE).         // will be deduced from tables
+                            setSizedFromParent(
+                            0)
+                    .setRestartFlags(RestartFlags::NO_WRITE);
+
+            registerWrapper(viewKeyStruct::nonWettingCurveString(), &m_nonWettingCurve).
+                            setInputFlag(
+                            InputFlags::FALSE).         // will be deduced from tables
+                            setSizedFromParent(
+                            0)
+                    .setRestartFlags(RestartFlags::NO_WRITE);
+
+            //Forwarded to KilloughHysteresis
+            registerWrapper(KilloughHysteresis::viewKeyStruct::jerauldParameterAString(), &m_jerauldParam_a).
+                    setInputFlag(InputFlags::OPTIONAL).
+                    setApplyDefaultValue(0.1).
+                    setDescription(
+                    "First parameter (modification parameter) introduced by Jerauld in the Land trapping model (see RTD documentation).");
+
+            registerWrapper(KilloughHysteresis::viewKeyStruct::jerauldParameterBString(), &m_jerauldParam_b).
+                    setInputFlag(InputFlags::OPTIONAL).
+                    setApplyDefaultValue(0.0).
+                    setDescription(
+                    "Second parameter (modification parameter) introduced by Jerauld in the Land trapping model (see RTD documentation).");
+
+
+            registerWrapper(KilloughHysteresis::viewKeyStruct::killoughCurvatureParameterPcString(),
+                            &m_killoughCurvatureParamCapPres).
+                    setInputFlag(
+                    InputFlags::OPTIONAL).
+                    setApplyDefaultValue(
+                    .1).
+                    setDescription(
+                    "Curvature parameter introduced by Killough for wetting-phase hysteresis (see RTD documentation).");
+
+            //misc
+            registerWrapper(viewKeyStruct::phaseIntermediateMinVolFractionString(), &m_phaseIntermediateMinVolFraction).
+                    setInputFlag(InputFlags::FALSE).setDescription("min vol fraction of intermediate if exist").
+                    // will be deduced from tables
+                    setSizedFromParent(0);
+
+            registerField< fields::cappres::mode >( &m_mode );
+
+
+            registerField< fields::cappres::phaseMaxHistoricalVolFraction >(
+                           &m_phaseMaxHistoricalVolFraction );
+            registerField< fields::cappres::phaseMinHistoricalVolFraction >(
+                           &m_phaseMinHistoricalVolFraction );
+            registerField< fields::cappres::phaseMode2PeakVolFraction >(
+                           &m_phaseMode2PeakVolFraction );
+
+        }
+
+/// usual utils
+
+        void TableCapillaryPressureHysteresis::postProcessInput() {
+
+            using TPP = ThreePhasePairPhaseType;
+
+            integer const numPhases = m_phaseNames.size();
+            GEOS_THROW_IF(numPhases != 2 && numPhases != 3,
+                           GEOS_FMT("{}: the expected number of fluid phases is either two, or three",
+                                     getFullName()),
+                           InputError);
+
+            m_phaseHasHysteresis.resize(2);
+
+            if (numPhases == 2) {
+                GEOS_THROW_IF(m_drainageWettingNonWettingCapPresTableName.empty(),
+                               GEOS_FMT(
+                                       "{}: for a two-phase flow simulation, we must use {} to specify the capillary pressure table for the drainage pair (wetting phase, non-wetting phase)",
+                                       getFullName(),
+                                       viewKeyStruct::drainageWettingNonWettingCapPresTableNameString()),
+                               InputError);
+
+
+                m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING] = (m_imbibitionWettingNonWettingCapPresTableName.empty() ||
+                                                                   m_imbibitionWettingNonWettingCapPresTableName ==
+                                                                   m_drainageWettingNonWettingCapPresTableName)
+                                                                  ? 0 : 1;
+                m_phaseHasHysteresis[TPP::INTERMEDIATE_NONWETTING] = m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING];
+
+
+            } else if (numPhases == 3) {
+
+
+                GEOS_THROW_IF(m_drainageWettingIntermediateCapPresTableName.empty() ||
+                               m_drainageNonWettingIntermediateCapPresTableName.empty(),
+                               GEOS_FMT(
+                                       "{}: for a three-phase flow simulation, we must use {} to specify the capillary pressure table "
+                                       "for the pair (wetting phase, intermediate phase), and {} to specify the capillary pressure table "
+                                       "for the pair (non-wetting phase, intermediate phase)",
+                                       getFullName(),
+                                       viewKeyStruct::drainageWettingIntermediateCapPresTableNameString(),
+                                       viewKeyStruct::drainageNonWettingIntermediateCapPresTableNameString()),
+                               InputError);
+
+                m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING] = (m_imbibitionWettingIntermediateCapPresTableName.empty() ||
+                                                                   m_imbibitionWettingIntermediateCapPresTableName ==
+                                                                   m_drainageWettingIntermediateCapPresTableName)
+                                                                  ? 0 : 1;
+
+                m_phaseHasHysteresis[TPP::INTERMEDIATE_NONWETTING] = (m_imbibitionNonWettingIntermediateCapPresTableName.empty() ||
+                                                                      m_imbibitionNonWettingIntermediateCapPresTableName ==
+                                                                      m_drainageNonWettingIntermediateCapPresTableName)
+                                                                     ? 0 : 1;
+            }
+            //Killough section
+            //TODO improve hard coded default
+            KilloughHysteresis::postProcessInput(m_jerauldParam_a, m_jerauldParam_b, 0,
+                                                 m_killoughCurvatureParamCapPres);
+
+            GEOS_THROW_IF(m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING] == 0 &&
+                           m_phaseHasHysteresis[TPP::INTERMEDIATE_NONWETTING] == 0,
+                           GEOS_FMT(
+                                   "{}: we must use {} (2-phase) / {} or {} (3-phase) to specify at least one imbibition relative permeability table",
+                                   getFullName(),
+                                   viewKeyStruct::imbibitionWettingNonWettingCapPresTableNameString(),
+                                   viewKeyStruct::imbibitionWettingIntermediateCapPresTableNameString(),
+                                   viewKeyStruct::imbibitionNonWettingIntermediateCapPresTableNameString()),
+                           InputError);
+
+        }
+
+        void TableCapillaryPressureHysteresis::initializePreSubGroups() {
+            CapillaryPressureBase::initializePreSubGroups();
+
+            integer const numPhases = m_phaseNames.size();
+            FunctionManager const &functionManager = FunctionManager::getInstance();
+
+            //equivalent to oil/gas - a.k.a two phase flow ordered by non wetting
+            bool const capPresMustBeIncreasing = (m_phaseOrder[PhaseType::WATER] < 0)
+                                                 ? true   // pc on the gas phase, function must be increasing
+                                                 : false; // pc on the water phase, function must be decreasing
+
+
+            // Step 1: check sanity of drainage tables
+            if (numPhases == 2) {
+
+                real64 drainageWettingPhaseMaxVolumeFraction, drainageWettingMinCapPres,
+                        drainageNonWettingPhaseMinVolumeFraction, drainageNonWettingMinCapPres,
+                        imbibitionWettingPhaseMaxVolumeFraction, imbibitionWettingMinCapPres,
+                        imbibitionNonWettingPhaseMinVolumeFraction, imbibitionNonWettingMinCapPres,
+                        wettingPhaseMinVolumeFraction, wettingMaxCapPres,
+                        nonWettingPhaseMaxVolumeFraction, nonWettingMaxCapPres;
+
+                {
+		  
+		  imbibitionNonWettingMinCapPres = 0.0; 
+
+                    GEOS_THROW_IF(!functionManager.hasGroup(m_drainageWettingNonWettingCapPresTableName),
+                                   GEOS_FMT("{}: the table function named {} could not be found",
+                                             getFullName(),
+                                             m_drainageWettingNonWettingCapPresTableName),
+                                   InputError);
+                    TableFunction const
+                            &capPresTable = functionManager.getGroup<TableFunction>(
+                            m_drainageWettingNonWettingCapPresTableName);
+
+                    //w/o  or  w/g pair
+                    if (!capPresMustBeIncreasing) {
+                        TableCapillaryPressureHelpers::validateCapillaryPressureTable(capPresTable, getFullName(),
+                                                                                      capPresMustBeIncreasing,
+                                                                                      drainageWettingPhaseMaxVolumeFraction,
+                                                                                      wettingPhaseMinVolumeFraction,
+                                                                                      drainageWettingMinCapPres,
+                                                                                      wettingMaxCapPres);
+
+                        drainageNonWettingPhaseMinVolumeFraction = 1. - drainageWettingPhaseMaxVolumeFraction;
+                        nonWettingPhaseMaxVolumeFraction = 1. - wettingPhaseMinVolumeFraction;
+
+                    } else { // o/g pair
+                        TableCapillaryPressureHelpers::validateCapillaryPressureTable(capPresTable, getFullName(),
+                                                                                      capPresMustBeIncreasing,
+                                                                                      nonWettingPhaseMaxVolumeFraction,
+                                                                                      drainageNonWettingPhaseMinVolumeFraction,
+                                                                                      nonWettingMaxCapPres,
+                                                                                      drainageNonWettingMinCapPres );
+
+                        drainageWettingPhaseMaxVolumeFraction = 1. - drainageNonWettingPhaseMinVolumeFraction;
+                        wettingPhaseMinVolumeFraction = 1. - nonWettingPhaseMaxVolumeFraction;
+                    }
+
+                }
+
+                {
+                    GEOS_THROW_IF(!functionManager.hasGroup(m_imbibitionWettingNonWettingCapPresTableName),
+                                   GEOS_FMT("{}: the table function named {} could not be found",
+                                             getFullName(),
+                                             m_imbibitionWettingNonWettingCapPresTableName),
+                                   InputError);
+                    TableFunction const
+                            &capPresTable = functionManager.getGroup<TableFunction>(
+                            m_imbibitionWettingNonWettingCapPresTableName);
+
+                    //w/o  or  w/g pair
+                    if (!capPresMustBeIncreasing) {
+                        TableCapillaryPressureHelpers::validateCapillaryPressureTable(capPresTable, getFullName(),
+                                                                                      capPresMustBeIncreasing,
+                                                                                      imbibitionWettingPhaseMaxVolumeFraction,
+                                                                                      wettingPhaseMinVolumeFraction,
+                                                                                      imbibitionWettingMinCapPres,
+                                                                                      wettingMaxCapPres);
+
+                        imbibitionNonWettingPhaseMinVolumeFraction = 1. - imbibitionWettingPhaseMaxVolumeFraction;
+                        nonWettingPhaseMaxVolumeFraction = 1. - wettingPhaseMinVolumeFraction;
+
+                    } else { // o/g pair
+                        TableCapillaryPressureHelpers::validateCapillaryPressureTable(capPresTable, getFullName(),
+                                                                                      capPresMustBeIncreasing,
+                                                                                      nonWettingPhaseMaxVolumeFraction,
+                                                                                      imbibitionNonWettingPhaseMinVolumeFraction,
+                                                                                      nonWettingMaxCapPres,
+                                                                                      imbibitionWettingMinCapPres );
+
+                        imbibitionWettingPhaseMaxVolumeFraction = 1. - imbibitionNonWettingPhaseMinVolumeFraction;
+                        wettingPhaseMinVolumeFraction = 1. - nonWettingPhaseMaxVolumeFraction;
+                    }
+                }
+
+                //constructing wetting/nonwetting curves
+
+                if(!capPresMustBeIncreasing) {
+                    m_wettingCurve.setPoints(
+                            {wettingPhaseMinVolumeFraction, wettingMaxCapPres},   // same as imbibition min
+                            {imbibitionWettingPhaseMaxVolumeFraction, imbibitionWettingMinCapPres},
+                            {drainageWettingPhaseMaxVolumeFraction, drainageWettingMinCapPres});
+                }
+                else {
+                    m_nonWettingCurve.setPoints(
+                            {nonWettingPhaseMaxVolumeFraction,nonWettingMaxCapPres},
+                            {imbibitionNonWettingPhaseMinVolumeFraction,imbibitionNonWettingMinCapPres},
+                            {drainageNonWettingPhaseMinVolumeFraction,drainageNonWettingMinCapPres}
+                            );
+                }
+
+            } else if (numPhases == 3) {
+
+	      real64 drainageWettingPhaseMaxVolumeFraction, drainageWettingMinCapPres,
+		drainageNonWettingPhaseMinVolumeFraction, drainageNonWettingMinCapPres,
+		imbibitionWettingPhaseMaxVolumeFraction, imbibitionWettingMinCapPres,
+		imbibitionNonWettingPhaseMinVolumeFraction, imbibitionNonWettingMinCapPres,
+		wettingPhaseMinVolumeFraction, wettingMaxCapPres,
+		nonWettingPhaseMaxVolumeFraction, nonWettingMaxCapPres;
+
+	      GEOS_UNUSED_VAR( drainageWettingMinCapPres );	      
+//define scope to avoid differentiate temp var (lazy)
+                {
+                    GEOS_THROW_IF(!functionManager.hasGroup(m_drainageWettingIntermediateCapPresTableName),
+                                   GEOS_FMT("{}: the table function named {} could not be found",
+                                             getFullName(),
+                                             m_drainageWettingIntermediateCapPresTableName),
+                                   InputError);
+                    TableFunction const
+                            &capPresTableWI = functionManager.getGroup<TableFunction>(
+                            m_drainageWettingIntermediateCapPresTableName);
+                    TableCapillaryPressureHelpers::validateCapillaryPressureTable(capPresTableWI, getFullName(), false,
+                                                                                  drainageWettingPhaseMaxVolumeFraction,
+                                                                                  wettingPhaseMinVolumeFraction,
+                                                                                  drainageNonWettingMinCapPres,
+                                                                                  wettingMaxCapPres);
+
+                    GEOS_THROW_IF(!functionManager.hasGroup(m_drainageNonWettingIntermediateCapPresTableName),
+                                   GEOS_FMT("{}: the table function named {} could not be found",
+                                             getFullName(),
+                                             m_drainageNonWettingIntermediateCapPresTableName),
+                                   InputError);
+                    TableFunction const &capPresTableNWI =
+                            functionManager.getGroup<TableFunction>(m_drainageNonWettingIntermediateCapPresTableName);
+                    TableCapillaryPressureHelpers::validateCapillaryPressureTable(capPresTableNWI, getFullName(), true,
+                                                                                  nonWettingPhaseMaxVolumeFraction,
+                                                                                  drainageNonWettingPhaseMinVolumeFraction,
+                                                                                  nonWettingMaxCapPres,
+                                                                                  drainageWettingPhaseMaxVolumeFraction
+                    );
+
+                    m_phaseIntermediateMinVolFraction =
+                            1.0 - drainageWettingPhaseMaxVolumeFraction - drainageWettingPhaseMaxVolumeFraction;
+                }
+
+                if (!m_imbibitionWettingIntermediateCapPresTableName.empty()) {
+
+                    GEOS_THROW_IF(!functionManager.hasGroup(m_imbibitionWettingIntermediateCapPresTableName),
+                                   GEOS_FMT("{}: the table function named {} could not be found",
+                                             getFullName(),
+                                             m_imbibitionWettingIntermediateCapPresTableName),
+                                   InputError);
+                    TableFunction const
+                            &capPresTableWI = functionManager.getGroup<TableFunction>(
+                            m_imbibitionWettingIntermediateCapPresTableName);
+                    TableCapillaryPressureHelpers::validateCapillaryPressureTable(capPresTableWI, getFullName(), false,
+                                                                                  imbibitionWettingPhaseMaxVolumeFraction,
+                                                                                  wettingPhaseMinVolumeFraction,
+                                                                                  imbibitionWettingMinCapPres,
+                                                                                  wettingMaxCapPres
+                                                                                  );
+
+
+                }
+
+                if (!m_imbibitionNonWettingIntermediateCapPresTableName.empty()) {
+
+                    GEOS_THROW_IF(!functionManager.hasGroup(m_imbibitionNonWettingIntermediateCapPresTableName),
+                                   GEOS_FMT("{}: the table function named {} could not be found",
+                                             getFullName(),
+                                             m_imbibitionNonWettingIntermediateCapPresTableName),
+                                   InputError);
+                    TableFunction const &capPresTableNWI =
+                            functionManager.getGroup<TableFunction>(m_imbibitionNonWettingIntermediateCapPresTableName);
+                    TableCapillaryPressureHelpers::validateCapillaryPressureTable(capPresTableNWI, getFullName(), true,
+                                                                                  nonWettingPhaseMaxVolumeFraction,
+                                                                                  imbibitionNonWettingPhaseMinVolumeFraction,
+                                                                                  nonWettingMaxCapPres,
+                                                                                  imbibitionNonWettingMinCapPres);
+
+
+                }
+            }
+
+            // Step 2: check the sanity btw drainage and imbibition
+            auto const eps = 1e-15;
+            if (numPhases == 2) {
+                //TODO weak make stronger
+                GEOS_THROW_IF(
+                        m_wettingCurve.isZero() && m_nonWettingCurve.isZero(),
+                        GEOS_FMT(
+                                "{}: Inconsistent data for capillary pressure hysteresis. No hysteresis curve is defined.",
+                                getFullName()),
+                        InputError);
+
+                GEOS_THROW_IF(
+                        !m_wettingCurve.isZero() && !m_nonWettingCurve.isZero(),
+                        GEOS_FMT(
+                                "{}: Inconsistent data for capillary pressure hysteresis. Both non wetting and wetting hysteresis curve are defined in two phase flow setting.",
+                                getFullName()),
+                        InputError);
+
+
+            } else if (numPhases == 3) {
+
+                GEOS_THROW_IF(std::fabs(m_wettingCurve.oppositeBoundPhaseVolFraction - (1. - m_nonWettingCurve.oppositeBoundPhaseVolFraction - m_phaseIntermediateMinVolFraction)) > eps,
+                               GEOS_FMT(
+                                       "{}: Inconsistent data for capillary pressure hysteresis. {}, {} and {} should sum up to 1.",
+                                       getFullName(), "Sw_min", "Snw_max", "Sinter_min"),
+                               InputError);
+                GEOS_THROW_IF(std::fabs(m_wettingCurve.drainageExtremaPhaseVolFraction - (1. - m_nonWettingCurve.drainageExtremaPhaseVolFraction - m_phaseIntermediateMinVolFraction)) > eps,
+                               GEOS_FMT(
+                                       "{}: Inconsistent data for capillary pressure hysteresis. {}, {} and {} should sum up to 1.",
+                                       getFullName(), "Sw_min", "Snw_max", "Sinter_min"),
+                               InputError);
+                GEOS_THROW_IF(std::fabs(m_wettingCurve.imbibitionExtremaPhaseVolFraction - (1. - m_nonWettingCurve.imbibitionExtremaPhaseVolFraction - m_phaseIntermediateMinVolFraction)) > eps,
+                               GEOS_FMT(
+                                       "{}: Inconsistent data for capillary pressure hysteresis. {}, {} and {} should sum up to 1.",
+                                       getFullName(), "Sw_min", "Snw_max", "Sinter_min"),
+                               InputError);
+
+            }
+
+
+            // Step 3: compute the Land coefficient
+            computeLandCoefficient();
+            
+
+
+            if (m_phaseMaxHistoricalVolFraction.size(1) == 0 && numPhases > 0) {
+                localIndex const currentSize = m_phaseMaxHistoricalVolFraction.size(0);
+                if (currentSize > 0) {
+                    m_phaseMaxHistoricalVolFraction.resize(currentSize, numPhases);
+                    m_phaseMinHistoricalVolFraction.resize(currentSize, numPhases);
+                    m_phaseMode2PeakVolFraction.resize(currentSize, numPhases);
+                    m_phaseMaxHistoricalVolFraction.setValues<parallelDevicePolicy<> >(0.0);
+                    m_phaseMinHistoricalVolFraction.setValues<parallelDevicePolicy<> >(1.0);
+                    m_phaseMode2PeakVolFraction.setValues<parallelDevicePolicy<> >(0.0);
+                }
+            }
+        }
+
+/// Land coeff (tb refactored out in KilloughHysteresis) and saved cvgd
+
+        void TableCapillaryPressureHysteresis::computeLandCoefficient() {
+            // For now, we keep two separate Land parameters for the wetting and non-wetting phases
+            // For two-phase flow, we make sure that they are equal
+            m_landParam.resize(2);
+
+            // Note: for simplicity, the notations are taken from IX documentation (although this breaks our phaseVolFrac naming convention)
+
+            // Step 1: Land parameter for the wetting phase
+
+            integer ipWetting, ipNonWetting;
+            std::tie(ipWetting, ipNonWetting) = phaseIndex(m_phaseOrder);
+
+            KilloughHysteresis::computeLandCoefficient( m_wettingCurve, m_landParam[ipWetting] );
+            KilloughHysteresis::computeLandCoefficient( m_nonWettingCurve, m_landParam[ipNonWetting] );
+
+        }
+
+/// common utils
+        void TableCapillaryPressureHysteresis::resizeFields(localIndex const size, localIndex const numPts) {
+            CapillaryPressureBase::resizeFields(size, numPts);
+
+            integer const numPhases = numFluidPhases();
+            
+
+
+            m_mode.resize(size);
+            
+            if (numPhases > 0) {
+                m_phaseMaxHistoricalVolFraction.resize(size, numPhases);
+                m_phaseMinHistoricalVolFraction.resize(size, numPhases);
+                m_phaseMode2PeakVolFraction.resize(size, numPhases);
+                m_phaseMaxHistoricalVolFraction.setValues<parallelDevicePolicy<> >(0.0);
+                m_phaseMinHistoricalVolFraction.setValues<parallelDevicePolicy<> >(1.0);
+                m_phaseMode2PeakVolFraction.setValues<parallelDevicePolicy<> >(0.0);
+            }
+
+
+        }
+
+        void TableCapillaryPressureHysteresis::saveConvergedPhaseVolFractionState(
+                arrayView2d<real64 const, compflow::USD_PHASE> const &phaseVolFraction) const {
+            CapillaryPressureBase::saveConvergedState();
+
+            arrayView2d<real64, compflow::USD_PHASE> phaseMaxHistoricalVolFraction = m_phaseMaxHistoricalVolFraction.toView();
+            arrayView2d<real64, compflow::USD_PHASE> phaseMinHistoricalVolFraction = m_phaseMinHistoricalVolFraction.toView();
+            arrayView2d<real64, compflow::USD_PHASE> phaseMode2PeakVolFraction = m_phaseMode2PeakVolFraction.toView();
+            arrayView1d<integer> mode_int = m_mode.toView();
+
+            localIndex const numElems = phaseVolFraction.size(0);
+            integer const numPhases = numFluidPhases();
+
+
+
+            using PT = CapillaryPressureBase::PhaseType;
+            arrayView1d<integer const> const phaseOrderView = phaseOrder();
+            integer const ipWater = phaseOrderView[PT::WATER];
+            integer const ipOil = phaseOrderView[PT::OIL];
+            integer const ipGas = phaseOrderView[PT::GAS];
+            
+            integer ipWetting = -1;
+            if (ipWater >= 0 && ipOil >= 0 && ipGas >= 0) {
+                ipWetting = ipWater;
+            } else if (ipWater < 0) {
+                ipWetting = ipOil;
+            } else if (ipOil < 0) {
+                ipWetting = ipWater;
+            } else if (ipGas < 0) {
+                ipWetting = ipWater;
+            }
+
+            forAll<parallelDevicePolicy<> >(numElems, [=] GEOS_HOST_DEVICE(localIndex const ei) {
+                for (integer ip = 0; ip < numPhases; ++ip) {
+                    phaseMaxHistoricalVolFraction[ei][ip] = LvArray::math::max(phaseVolFraction[ei][ip],
+                                                                               phaseMaxHistoricalVolFraction[ei][ip]);
+                    phaseMinHistoricalVolFraction[ei][ip] = LvArray::math::min(phaseVolFraction[ei][ip],
+                                                                               phaseMinHistoricalVolFraction[ei][ip]);
+                }
+                
+                if (ipWetting >= 0 && ipWetting < numPhases) {
+                    ModeIndexType const currentMode = static_cast<ModeIndexType>(mode_int[ei]);
+                    if (currentMode == ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                        real64 const currentS = phaseVolFraction[ei][ipWetting];
+                        if (currentS > phaseMode2PeakVolFraction[ei][ipWetting]) {
+                            phaseMode2PeakVolFraction[ei][ipWetting] = currentS;
+                        }
+                    } else if (currentMode != ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                        phaseMode2PeakVolFraction[ei][ipWetting] = 0.0;
+                    }
+                }
+            });
+
+        }
+
+        void
+        TableCapillaryPressureHysteresis::KernelWrapper::computeImbibitionWettingCapillaryPressure(
+                const arrayView1d<const TableFunction::KernelWrapper> &wettingKernelWapper,
+                const KilloughHysteresis::HysteresisCurve &wettingCurve,
+                const KilloughHysteresis::HysteresisCurve &nonWettingCurve, //discard if not needed
+                const geos::real64 &landParam,
+                const geos::real64 &phaseVolFraction,
+                const geos::real64 &phaseMinHistoricalVolFraction,
+                const geos::real64 &phaseMaxHistoricalVolFraction,
+                const geos::real64 &phaseMode2PeakVolFraction,
+                geos::real64 &phaseTrappedVolFrac,
+                geos::real64 &phaseCapPressure,
+                geos::real64 &dPhaseCapPressure_dPhaseVolFrac,
+                const ModeIndexType &mode) const {
+            GEOS_ASSERT(wettingCurve.isWetting());
+            real64 const S = phaseVolFraction;
+            real64 const Smxi = wettingCurve.imbibitionExtremaPhaseVolFraction;
+            real64 const Smxd = wettingCurve.drainageExtremaPhaseVolFraction;
+            real64 const Smin = wettingCurve.oppositeBoundPhaseVolFraction;
+            real64 const Smax = wettingCurve.drainageExtremaPhaseVolFraction;
+
+	    GEOS_UNUSED_VAR( Smxi, Smxd, phaseTrappedVolFrac );	      
+	    
+//  if( S <= Smin )
+//  {
+//    //below accessible range
+//    phaseCapPressure = CAP_INF;
+//    dPhaseCapPressure_dPhaseVolFrac = -CAP_INF_DERIV;
+//  }
+//  else if( S >= Smxd )
+//  {
+//    //above accessible range
+//    phaseCapPressure = -CAP_INF;
+//    dPhaseCapPressure_dPhaseVolFrac = -CAP_INF_DERIV;
+//  }
+//  else
+            {
+                //drainage to imbibition
+                real64 dpci_dS, dpcd_dS;
+                real64 const pci = wettingKernelWapper[ModeIndexType::IMBIBITION].compute(&S, &dpci_dS);
+                real64 const pcd = wettingKernelWapper[ModeIndexType::DRAINAGE].compute(&S, &dpcd_dS);
+                real64 const Somin = m_phaseIntermediateMinVolFraction;
+
+                real64 const E = m_killoughCurvatureParamCapPres;
+
+                //Step 2. compute F as in (EQ 34.15) F = (1/(Sw-Shy+E)-1/E) / (1/(Swma-Shy+E)-1/E)
+                //drainage to imbibition branch
+                if (mode == ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                    // DRAINAGE_TO_IMBIBITION: Shy should be minimum historical (where drainage started)
+                    real64 const Shy = (phaseMinHistoricalVolFraction > Smin) ? phaseMinHistoricalVolFraction : Smin;
+
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(nonWettingCurve,
+                                                                               Shy,
+                                                                               landParam,
+                                                                               m_jerauldParam_a,
+                                                                               m_jerauldParam_b,
+                                                                               Scrt);
+                    real64 const Swma = 1 - Scrt - Somin;
+                    real64 F = (1. / (S - Shy + E) - 1. / E) / (1. / (Swma - Shy + E) - 1. / E);
+                    //force bound
+                    F = LvArray::math::max(F, 0.0);
+                    F = LvArray::math::min(F, 1.0);
+
+                    //Step 3. Eventually assemble everything following (EQ. 34.14)
+                    phaseCapPressure = pcd + F * (pci - pcd);
+                    dPhaseCapPressure_dPhaseVolFrac = dpcd_dS + F * (dpci_dS - dpcd_dS);
+                }
+                    //imbibition to drainage
+                else if (mode == ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                    // IMBIBITION_TO_DRAINAGE: Shy should be maximum historical (where imbibition started)
+                    real64 const Shy = (phaseMaxHistoricalVolFraction < Smax) ? phaseMaxHistoricalVolFraction : Smax;
+
+                    // For IMBIBITION_TO_DRAINAGE, use the same formula structure as non-wetting phase
+                    // F = (1. / (S - Shy + E) - 1. / E) / (1. / (Swmin - Shy + E) - 1. / E)
+                    // This ensures F = 0 when S = Shy (high saturation) and F = 1 when S = Swmin (low saturation)
+                    // Minimum accessible wetting saturation = Somin (irreducible wetting saturation)
+                    // Use actual Somin (may be 0.0), the formula will handle negative values correctly
+                    real64 const Swmin = Somin;
+
+                    real64 const F_num = (1. / (S - Shy + E) - 1. / E);
+                    real64 const F_denom = (1. / (Swmin - Shy + E) - 1. / E);
+                    // Both numerator and denominator can be negative when Swmin < Shy - E
+                    // This is okay - negative/negative = positive F
+                    real64 F = F_num / F_denom;
+                    //force bound
+                    F = LvArray::math::max(F, 0.0);
+                    F = LvArray::math::min(F, 1.0);
+
+                    //Step 3. Eventually assemble everything following (EQ. 34.14)
+                    phaseCapPressure = pci + F * (pcd - pci);
+                    dPhaseCapPressure_dPhaseVolFrac = dpci_dS + F * (dpcd_dS - dpci_dS);
+                }
+                //imbibition to drainage from scanning curve (departing from DRAINAGE_TO_IMBIBITION)
+                else if (mode == ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                    // IMBIBITION_TO_DRAINAGE_FROM_SCANNING: Secondary drainage scanning curve
+                    // Based on Killough (1976) - solve quadratic for ghost departure point
+                    //
+                    // Nomenclature:
+                    // - Sw_star (S_star): second reversal saturation (turnaround point, peak reached during Mode 2)
+                    // - Sw_Hyst_imb (H): first reversal point (where imbibition started, departure from drainage)
+                    // - Sw_wr (Sw_wr): residual/connate wetting saturation
+                    // - x (Sw_star_Hyst_ghost): ghost departure point on imbibition curve (unknown, to be solved)
+                    //
+                    // Step 1: Identify reversal points
+                    // S_star is the turnaround point (peak reached during Mode 2)
+                    real64 S_star = phaseMode2PeakVolFraction;
+                    if (S_star < 1e-12 || S_star >= Smax - 1e-12) {
+                        // Use phaseMaxHistoricalVolFraction, but ensure it's between H and Smax
+                        real64 const H_temp = (phaseMinHistoricalVolFraction > Smin) ? phaseMinHistoricalVolFraction : Smin;
+                        if (phaseMaxHistoricalVolFraction > H_temp + 1e-12 && phaseMaxHistoricalVolFraction < Smax - 1e-12) {
+                            S_star = phaseMaxHistoricalVolFraction;
+                        } else {
+                            S_star = LvArray::math::max(H_temp + 0.1, LvArray::math::min(S, Smax - 0.01));
+                        }
+                    }
+                    
+                    real64 const H = (phaseMinHistoricalVolFraction > Smin) ? phaseMinHistoricalVolFraction : Smin;
+                    // Sw_wr: residual/connate wetting saturation - minimum saturation on drainage curve
+                    // For wetting phase, oppositeBoundPhaseVolFraction should be the minimum, but if it's 0,
+                    // we need to get the actual minimum from the drainage curve table
+                    // Since we can't easily access table coordinates from KernelWrapper, use Smin if > 0, otherwise try Somin
+                    real64 Sw_wr = Smin;
+                    if (Sw_wr < 1e-12) {
+                        Sw_wr = (Somin > 1e-12) ? Somin : 1e-6; // Small default to avoid division issues
+                    }
+                    
+                    // Step 2: Compute F_known from Mode 2 (imbibition scanning curve) at S_star
+                    // Mode 2 formula: F = (1 / (S - H + E) - 1 / E) / (1 / (Swma - H + E) - 1 / E)
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(nonWettingCurve,
+                                                                               H,
+                                                                               landParam,
+                                                                               m_jerauldParam_a,
+                                                                               m_jerauldParam_b,
+                                                                               Scrt);
+                    real64 const Swma = 1 - Scrt - Somin;
+                    real64 F_known = 0.0;
+                    if (S_star <= Swma + 1e-12) {
+                        real64 const F_num = (1. / (S_star - H + E) - 1. / E);
+                        real64 const F_denom = (1. / (Swma - H + E) - 1. / E);
+                        if (LvArray::math::abs(F_denom) > 1e-12) {
+                            F_known = F_num / F_denom;
+                        } else {
+                            F_known = (S_star > H) ? 1.0 : 0.0;
+                        }
+                    } else {
+                        // S_star > Swma: beyond Mode 2 range, use F_known = 0 (pure imbibition)
+                        F_known = 0.0;
+                    }
+                    F_known = LvArray::math::max(0.0, LvArray::math::min(1.0, F_known));
+                    
+                    // Step 3: Compute F_star_target = 1 - F_known (from Eq. A-6)
+                    real64 const F_star_target = 1.0 - F_known;
+                    
+                    // Step 4: Solve quadratic for x = Sw_star_Hyst_ghost
+                    // F* = [1/(x - S_star + E) - 1/E] / [1/(x - H + E) - 1/E] = F_star_target
+                    // Note: Denominator uses H (first reversal point), not Sw_wr, so curve rejoins drainage at H
+                    // Rearranging gives: (1-T)*x^2 + B*x + C = 0
+                    // where T = F_star_target, a = S_star, b = H, e = E
+                    real64 const a = S_star;
+                    real64 const b = H;  // Use H instead of Sw_wr so curve rejoins drainage at H
+                    real64 const e = E;
+                    real64 const T = F_star_target;
+                    
+                    real64 const coeff_A = (1.0 - T);
+                    real64 const coeff_B = -(1.0 - T) * (a + b - 2.0 * e) - (1.0 - T) * e;
+                    real64 const coeff_C = (1.0 - T) * (a - e) * (b - e)
+                                         - e * e * (1.0 + T)
+                                         - e * (T * a - b);
+                    
+                    real64 x = S_star;
+                    real64 discriminant = coeff_B * coeff_B - 4.0 * coeff_A * coeff_C;
+                    
+                    if (discriminant >= 0.0 && LvArray::math::abs(coeff_A) > 1e-14) {
+                        real64 sqrt_disc = LvArray::math::sqrt(discriminant);
+                        real64 x1 = (-coeff_B + sqrt_disc) / (2.0 * coeff_A);
+                        real64 x2 = (-coeff_B - sqrt_disc) / (2.0 * coeff_A);
+                        
+                        // Pick the physically meaningful root: x must be > S_star
+                        if (x1 > S_star - 1e-8 && x2 > S_star - 1e-8) {
+                            x = LvArray::math::min(x1, x2); // Take the closer one
+                        } else if (x1 > S_star - 1e-8) {
+                            x = x1;
+                        } else if (x2 > S_star - 1e-8) {
+                            x = x2;
+                        }
+                    }
+                    
+                    // Step 5: Compute F_star for current saturation S
+                    // F_star = [1/(x - S + E) - 1/E] / [1/(x - H + E) - 1/E]
+                    // When S = H, F_star = 1.0 (pure drainage), so curve rejoins drainage at H
+                    real64 F_star = 1.0;
+                    real64 F_star_num = (1. / (x - S + E) - 1. / E);
+                    real64 F_star_denom = (1. / (x - H + E) - 1. / E);
+                    if (LvArray::math::abs(F_star_denom) > 1e-12) {
+                        F_star = F_star_num / F_star_denom;
+                        F_star = LvArray::math::max(0.0, LvArray::math::min(1.0, F_star));
+                    }
+                    
+                    // Step 6: Compute Pc using Eq. A-5: P_c = P_c^Im + F* [P_c^Dr - P_c^Im]
+                    phaseCapPressure = pci + F_star * (pcd - pci);
+                    dPhaseCapPressure_dPhaseVolFrac = dpci_dS + F_star * (dpcd_dS - dpci_dS);
+                } else {
+                    GEOS_THROW(GEOS_FMT("{}: State is {}.Shouldnt be used in pure DRAINAGE or IMBIBITION.",
+                                          "TableCapillaryPressureHysteresis",
+                                          (mode == ModeIndexType::DRAINAGE) ? "DRAINAGE" : ((mode ==
+                                                                                             ModeIndexType::IMBIBITION)
+                                                                                            ? "IMBIBITION"
+                                                                                            : "UNKNOWN")),
+                                InputError);
+                }
+
+
+            }
+
+        }
+
+        void
+        TableCapillaryPressureHysteresis::KernelWrapper::computeImbibitionWettingCapillaryPressure(
+                const arrayView1d<const TableFunction::KernelWrapper> &wettingKernelWapper,
+                const KilloughHysteresis::HysteresisCurve &wettingCurve,
+                const geos::real64 &landParam,
+                const geos::real64 &phaseVolFraction,
+                const geos::real64 &phaseMinHistoricalVolFraction,
+                const geos::real64 &phaseMaxHistoricalVolFraction,
+                const geos::real64 &phaseMode2PeakVolFraction,
+                geos::real64 &phaseTrappedVolFrac,
+                geos::real64 &phaseCapPressure,
+                geos::real64 &dPhaseCapPressure_dPhaseVolFrac,
+                const ModeIndexType &mode) const {
+            GEOS_ASSERT(wettingCurve.isWetting());
+            real64 const S = phaseVolFraction;
+            real64 const Smxi = wettingCurve.imbibitionExtremaPhaseVolFraction;
+            real64 const Smxd = wettingCurve.drainageExtremaPhaseVolFraction;
+            real64 const Smin = wettingCurve.oppositeBoundPhaseVolFraction;
+            real64 const Smax = wettingCurve.drainageExtremaPhaseVolFraction;
+
+	    GEOS_UNUSED_VAR( Smxi, Smxd, phaseTrappedVolFrac );	      
+	    
+//  if( S <= Smin )
+//  {
+//    //below accessible range
+//    phaseCapPressure = CAP_INF;
+//    dPhaseCapPressure_dPhaseVolFrac = -CAP_INF_DERIV;
+//  }
+//  else if( S >= Smxd )
+//  {
+//    //above accessible range
+//    phaseCapPressure = -CAP_INF;
+//    dPhaseCapPressure_dPhaseVolFrac = -CAP_INF_DERIV;
+//  }
+//  else
+            {
+                //drainage to imbibition
+                real64 dpci_dS, dpcd_dS;
+                real64 const pci = wettingKernelWapper[ModeIndexType::IMBIBITION].compute(&S, &dpci_dS);
+                real64 const pcd = wettingKernelWapper[ModeIndexType::DRAINAGE].compute(&S, &dpcd_dS);
+
+                real64 const Somin = m_phaseIntermediateMinVolFraction;
+                real64 const E = m_killoughCurvatureParamCapPres;
+
+                //Step 2. compute F as in (EQ 34.15) F = (1/(Sw-Shy+E)-1/E) / (1/(Swma-Shy+E)-1/E)
+                //drainage to imbibition branch
+                if (mode == ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                    // DRAINAGE_TO_IMBIBITION: Shy should be minimum historical (where drainage started)
+                    real64 const Shy = (phaseMinHistoricalVolFraction > Smin) ? phaseMinHistoricalVolFraction : Smin;
+
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(wettingCurve,
+                                                                               Shy,
+                                                                               landParam,
+                                                                               m_jerauldParam_a,
+                                                                               m_jerauldParam_b,
+                                                                               Scrt);
+
+
+
+                    //should be the pore space accessible to the two wetting phase
+                    real64 const Swma = 1 - (1 -  Scrt);
+                    real64 F = (1. / (S - Shy + E) - 1. / E) / (1. / (Swma - Shy + E) - 1. / E);
+                    //force bound
+                    F = LvArray::math::max(F, 0.0);
+                    F = LvArray::math::min(F, 1.0);
+
+                    //Step 3. Eventually assemble everything following (EQ. 34.14)
+                    phaseCapPressure = pcd + F * (pci - pcd);
+                    dPhaseCapPressure_dPhaseVolFrac = dpcd_dS + F * (dpci_dS - dpcd_dS);
+                }
+                    //imbibition to drainage
+                else if (mode == ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                    // IMBIBITION_TO_DRAINAGE: Shy should be maximum historical (where imbibition started)
+                    real64 const Shy = (phaseMaxHistoricalVolFraction < Smax) ? phaseMaxHistoricalVolFraction : Smax;
+
+                    // For IMBIBITION_TO_DRAINAGE, use the same formula structure as non-wetting phase
+                    // F = (1. / (S - Shy + E) - 1. / E) / (1. / (Swmin - Shy + E) - 1. / E)
+                    // This ensures F = 0 when S = Shy (high saturation) and F = 1 when S = Swmin (low saturation)
+                    // For two-phase, use Smin as the minimum accessible wetting saturation
+                    // Use actual Smin (may be 0.0), the formula will handle negative values correctly
+                    real64 const Swmin = Smin;
+
+                    real64 const F_num = (1. / (S - Shy + E) - 1. / E);
+                    real64 const F_denom = (1. / (Swmin - Shy + E) - 1. / E);
+                    // Both numerator and denominator can be negative when Swmin < Shy - E
+                    // This is okay - negative/negative = positive F
+                    real64 F = F_num / F_denom;
+                    //force bound
+                    F = LvArray::math::max(F, 0.0);
+                    F = LvArray::math::min(F, 1.0);
+
+                    //Step 3. Eventually assemble everything following (EQ. 34.14)
+                    phaseCapPressure = pci + F * (pcd - pci);
+                    dPhaseCapPressure_dPhaseVolFrac = dpci_dS + F * (dpcd_dS - dpci_dS);
+                }
+                //imbibition to drainage from scanning curve (departing from DRAINAGE_TO_IMBIBITION)
+                else if (mode == ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                    // IMBIBITION_TO_DRAINAGE_FROM_SCANNING: Secondary drainage scanning curve
+                    // Based on Killough (1976) - solve quadratic for ghost departure point
+                    //
+                    // Nomenclature:
+                    // - Sw_star (S_star): second reversal saturation (turnaround point, peak reached during Mode 2)
+                    // - Sw_Hyst_imb (H): first reversal point (where imbibition started, departure from drainage)
+                    // - Sw_wr (Sw_wr): residual/connate wetting saturation
+                    // - x (Sw_star_Hyst_ghost): ghost departure point on imbibition curve (unknown, to be solved)
+                    //
+                    // Step 1: Identify reversal points
+                    // S_star is the turnaround point (peak reached during Mode 2)
+                    real64 S_star = phaseMode2PeakVolFraction;
+                    if (S_star < 1e-12 || S_star >= Smax - 1e-12) {
+                        // Use phaseMaxHistoricalVolFraction, but ensure it's between H and Smax
+                        real64 const H_temp = (phaseMinHistoricalVolFraction > Smin) ? phaseMinHistoricalVolFraction : Smin;
+                        if (phaseMaxHistoricalVolFraction > H_temp + 1e-12 && phaseMaxHistoricalVolFraction < Smax - 1e-12) {
+                            S_star = phaseMaxHistoricalVolFraction;
+                        } else {
+                            S_star = LvArray::math::max(H_temp + 0.1, LvArray::math::min(S, Smax - 0.01));
+                        }
+                    }
+                    
+                    real64 const H = (phaseMinHistoricalVolFraction > Smin) ? phaseMinHistoricalVolFraction : Smin;
+                    // Sw_wr: residual/connate wetting saturation - minimum saturation on drainage curve
+                    // For wetting phase, oppositeBoundPhaseVolFraction should be the minimum, but if it's 0,
+                    // we need to get the actual minimum from the drainage curve table
+                    // Since we can't easily access table coordinates from KernelWrapper, use Smin if > 0, otherwise try Somin
+                    real64 Sw_wr = Smin;
+                    if (Sw_wr < 1e-12) {
+                        Sw_wr = (Somin > 1e-12) ? Somin : 1e-6; // Small default to avoid division issues
+                    }
+                    
+                    // Step 2: Compute F_known from Mode 2 (imbibition scanning curve) at S_star
+                    // Mode 2 formula: F = (1 / (S - H + E) - 1 / E) / (1 / (Swma - H + E) - 1 / E)
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(wettingCurve,
+                                                                               H,
+                                                                               landParam,
+                                                                               m_jerauldParam_a,
+                                                                               m_jerauldParam_b,
+                                                                               Scrt);
+                    real64 const Swma = 1 - (1 - Scrt); // For two-phase, following existing Mode 2 pattern
+                    real64 F_known = 0.0;
+                    if (S_star <= Swma + 1e-12) {
+                        real64 const F_num = (1. / (S_star - H + E) - 1. / E);
+                        real64 const F_denom = (1. / (Swma - H + E) - 1. / E);
+                        if (LvArray::math::abs(F_denom) > 1e-12) {
+                            F_known = F_num / F_denom;
+                        } else {
+                            F_known = (S_star > H) ? 1.0 : 0.0;
+                        }
+                    } else {
+                        // S_star > Swma: beyond Mode 2 range, use F_known = 0 (pure imbibition)
+                        F_known = 0.0;
+                    }
+                    F_known = LvArray::math::max(0.0, LvArray::math::min(1.0, F_known));
+                    
+                    // Step 3: Compute F_star_target = 1 - F_known (from Eq. A-6)
+                    real64 const F_star_target = 1.0 - F_known;
+                    
+                    // Step 4: Solve quadratic for x = Sw_star_Hyst_ghost
+                    // F* = [1/(x - S_star + E) - 1/E] / [1/(x - H + E) - 1/E] = F_star_target
+                    // Note: Denominator uses H (first reversal point), not Sw_wr, so curve rejoins drainage at H
+                    // Rearranging gives: (1-T)*x^2 + B*x + C = 0
+                    // where T = F_star_target, a = S_star, b = H, e = E
+                    real64 const a = S_star;
+                    real64 const b = H;  // Use H instead of Sw_wr so curve rejoins drainage at H
+                    real64 const e = E;
+                    real64 const T = F_star_target;
+                    
+                    real64 const coeff_A = (1.0 - T);
+                    real64 const coeff_B = -(1.0 - T) * (a + b - 2.0 * e) - (1.0 - T) * e;
+                    real64 const coeff_C = (1.0 - T) * (a - e) * (b - e)
+                                         - e * e * (1.0 + T)
+                                         - e * (T * a - b);
+                    
+                    real64 x = S_star;
+                    real64 discriminant = coeff_B * coeff_B - 4.0 * coeff_A * coeff_C;
+                    
+                    if (discriminant >= 0.0 && LvArray::math::abs(coeff_A) > 1e-14) {
+                        real64 sqrt_disc = LvArray::math::sqrt(discriminant);
+                        real64 x1 = (-coeff_B + sqrt_disc) / (2.0 * coeff_A);
+                        real64 x2 = (-coeff_B - sqrt_disc) / (2.0 * coeff_A);
+                        
+                        // Pick the physically meaningful root: x must be > S_star
+                        if (x1 > S_star - 1e-8 && x2 > S_star - 1e-8) {
+                            x = LvArray::math::min(x1, x2); // Take the closer one
+                        } else if (x1 > S_star - 1e-8) {
+                            x = x1;
+                        } else if (x2 > S_star - 1e-8) {
+                            x = x2;
+                        }
+                    }
+                    
+                    // Step 5: Compute F_star for current saturation S
+                    // F_star = [1/(x - S + E) - 1/E] / [1/(x - H + E) - 1/E]
+                    // When S = H, F_star = 1.0 (pure drainage), so curve rejoins drainage at H
+                    real64 F_star = 1.0;
+                    real64 F_star_num = (1. / (x - S + E) - 1. / E);
+                    real64 F_star_denom = (1. / (x - H + E) - 1. / E);
+                    if (LvArray::math::abs(F_star_denom) > 1e-12) {
+                        F_star = F_star_num / F_star_denom;
+                        F_star = LvArray::math::max(0.0, LvArray::math::min(1.0, F_star));
+                    }
+                    
+                    // Step 6: Compute Pc using Eq. A-5: P_c = P_c^Im + F* [P_c^Dr - P_c^Im]
+                    phaseCapPressure = pci + F_star * (pcd - pci);
+                    dPhaseCapPressure_dPhaseVolFrac = dpci_dS + F_star * (dpcd_dS - dpci_dS);
+                } else {
+                    GEOS_THROW(GEOS_FMT("{}: State is {}.Shouldnt be used in pure DRAINAGE or IMBIBITION.",
+                                          "TableCapillaryPressureHysteresis",
+                                          (mode == ModeIndexType::DRAINAGE) ? "DRAINAGE" : ((mode ==
+                                                                                             ModeIndexType::IMBIBITION)
+                                                                                            ? "IMBIBITION"
+                                                                                            : "UNKNOWN")),
+                                InputError);
+                }
+
+
+            }
+
+        }
+        void TableCapillaryPressureHysteresis::KernelWrapper::computeTwoPhaseWetting(const geos::integer ipWetting,
+                                                                                     const geos::integer GEOS_UNUSED_PARAM( ipNonWetting ),
+                                                                                     const arraySlice1d<const geos::real64,
+                                                                                             compflow::USD_PHASE -
+                                                                                             1> &phaseVolFraction,
+                                                                                     const arraySlice1d<const geos::real64,
+                                                                                             compflow::USD_PHASE
+                                                                                             -
+                                                                                             1> &phaseMaxHistoricalVolFraction,
+                                                                                     const arraySlice1d<const geos::real64,
+                                                                                             compflow::USD_PHASE
+                                                                                             -
+                                                                                             1> &phaseMinHistoricalVolFraction,
+                                                                                     const arraySlice1d<geos::real64,
+                                                                                             relperm::USD_RELPERM
+                                                                                             - 2> &phaseTrappedVolFrac,
+                                                                                     arraySlice1d<geos::real64,
+                                                                                             relperm::USD_RELPERM
+                                                                                             -
+                                                                                             2> const &phaseCapPressure,
+                                                                                     arraySlice2d<geos::real64,
+                                                                                             relperm::USD_RELPERM_DS
+                                                                                             -
+                                                                                             2> const &dPhaseCapPressure_dPhaseVolFrac,
+                                                                                     ModeIndexType &mode,
+                                                                                     arraySlice1d<geos::real64,
+                                                                                             compflow::USD_PHASE - 1> &phaseMode2PeakVolFraction) const {
+            using TTP = ThreePhasePairPhaseType;
+
+            // Validate array sizes and indices before accessing
+            GEOS_ASSERT_MSG(ipWetting >= 0, "ipWetting must be non-negative");
+            GEOS_ASSERT_MSG(static_cast<integer>(phaseVolFraction.size()) > ipWetting,
+                        GEOS_FMT("phaseVolFraction array too small: size={}, ipWetting={}. "
+                                 "This usually means the arrays haven't been properly resized. "
+                                 "Ensure resizeFields() has been called before using the KernelWrapper.",
+                                 phaseVolFraction.size(), ipWetting));
+            GEOS_ASSERT_MSG(static_cast<integer>(phaseMaxHistoricalVolFraction.size()) > ipWetting,
+                        GEOS_FMT("phaseMaxHistoricalVolFraction array too small: size={}, ipWetting={}. "
+                                 "This usually means the arrays haven't been properly resized. "
+                                 "Ensure resizeFields() has been called before using the KernelWrapper.",
+                                 phaseMaxHistoricalVolFraction.size(), ipWetting));
+            GEOS_ASSERT_MSG(static_cast<integer>(phaseMinHistoricalVolFraction.size()) > ipWetting,
+                        GEOS_FMT("phaseMinHistoricalVolFraction array too small: size={}, ipWetting={}. "
+                                 "This usually means the arrays haven't been properly resized. "
+                                 "Ensure resizeFields() has been called before using the KernelWrapper.",
+                                 phaseMinHistoricalVolFraction.size(), ipWetting));
+            GEOS_ASSERT_MSG(static_cast<integer>(m_wettingNonWettingCapillaryPressureKernelWrappers.size()) >= 2,
+                        GEOS_FMT("m_wettingNonWettingCapillaryPressureKernelWrappers must have at least 2 elements, but got {}. "
+                                 "This usually means createAllTableKernelWrappers() failed to populate the arrays.",
+                                 m_wettingNonWettingCapillaryPressureKernelWrappers.size()));
+
+            // TEMPORARY: Disable scanning curves for testing convergence
+            // Define at function scope so it's accessible to both wetting and non-wetting phase code
+            constexpr bool ENABLE_SCANNING_CURVES = true;
+            
+            // TEMPORARY: Force IMBIBITION mode for testing (overrides normal mode determination)
+            constexpr bool FORCE_IMBIBITION_MODE = false;
+
+            // TEMPORARY: Enable/disable Mode 4 (IMBIBITION_TO_DRAINAGE_FROM_SCANNING)
+            // When false, the code stays in Mode 2 and does not transition to Mode 4
+            constexpr bool ENABLE_MODE4 = false;
+
+            // Determine mode based on saturation condition and flow direction
+            // Use DRAINAGE when saturation is at or below minimum historical
+            // Use scanning curves when above minimum, detecting direction of change
+            bool const useDrainage = FORCE_IMBIBITION_MODE ? false :
+                                     (!m_phaseHasHysteresis[TTP::INTERMEDIATE_WETTING] ||
+                                      phaseVolFraction[ipWetting] <= phaseMinHistoricalVolFraction[ipWetting] + flowReversalBuffer);
+            
+            //--- wetting  cap pressure -- W/O or W/G two phase flow
+            // Use drainage curve when S <= S_min
+            // Use scanning curves when S > S_min, but detect if we're in secondary drainage
+            // DEBUG: Print mode for capillary pressure
+            // printf("CapPressure: mode=%d, S_w=%.6e, S_min=%.6e, S_max=%.6e, hasHyst=%d\n",
+            //        static_cast<int>(mode),
+            //        phaseVolFraction[ipWetting],
+            //        phaseMinHistoricalVolFraction[ipWetting],
+            //        phaseMaxHistoricalVolFraction[ipWetting],
+            //        static_cast<int>(m_phaseHasHysteresis[TTP::INTERMEDIATE_WETTING]));
+            
+            if (useDrainage) {
+                // Use simple drainage curve (matching relative permeability)
+                mode = ModeIndexType::DRAINAGE;
+                phaseTrappedVolFrac[ipWetting] = LvArray::math::min(phaseVolFraction[ipWetting],
+                                                                    m_wettingCurve.oppositeBoundPhaseVolFraction);
+                // printf("CapPressure: Using DRAINAGE curve (arrayIndex=0)\n");
+                GEOS_ASSERT_MSG(static_cast<integer>(m_wettingNonWettingCapillaryPressureKernelWrappers.size()) > ModeIndexType::DRAINAGE,
+                                "Invalid array index for kernel wrapper access");
+                computeBoundCapillaryPressure(
+                        m_wettingNonWettingCapillaryPressureKernelWrappers[ModeIndexType::DRAINAGE],
+                        phaseVolFraction[ipWetting],
+                        phaseCapPressure[ipWetting],
+                        dPhaseCapPressure_dPhaseVolFrac[ipWetting][ipWetting]);
+            }
+            else {
+                // Use scanning curves - original conservative approach: only switch from pure states to scanning curves
+                // Scanning curve modes persist once set (no switching between DRAINAGE_TO_IMBIBITION and IMBIBITION_TO_DRAINAGE)
+                
+                // If mode is already set to pure IMBIBITION, use it directly (for Pc bounds computation)
+                if (mode == ModeIndexType::IMBIBITION) {
+                    // Force pure imbibition mode - use the imbibition table directly
+                    phaseTrappedVolFrac[ipWetting] = LvArray::math::min(phaseVolFraction[ipWetting],
+                                                                        m_wettingCurve.oppositeBoundPhaseVolFraction);
+                    GEOS_ASSERT_MSG(static_cast<integer>(m_wettingNonWettingCapillaryPressureKernelWrappers.size()) > ModeIndexType::IMBIBITION,
+                                    "Invalid array index for kernel wrapper access");
+                    computeBoundCapillaryPressure(
+                            m_wettingNonWettingCapillaryPressureKernelWrappers[ModeIndexType::IMBIBITION],
+                            phaseVolFraction[ipWetting],
+                            phaseCapPressure[ipWetting],
+                            dPhaseCapPressure_dPhaseVolFrac[ipWetting][ipWetting]);
+                    return; // Exit early, don't use scanning curves
+                }
+                
+                // If FORCE_IMBIBITION_MODE is enabled, override mode to IMBIBITION
+                if (FORCE_IMBIBITION_MODE) {
+                    mode = ModeIndexType::IMBIBITION;
+                }
+                
+                // If scanning curves are disabled, reset any scanning curve modes back to pure modes
+                if (!ENABLE_SCANNING_CURVES) {
+                    if (mode == ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                        mode == ModeIndexType::IMBIBITION_TO_DRAINAGE ||
+                        mode == ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                        // Reset to pure drainage or imbibition based on saturation
+                        if (FORCE_IMBIBITION_MODE) {
+                            mode = ModeIndexType::IMBIBITION;
+                        } else {
+                            real64 const Smin = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                            real64 const Smax = m_wettingCurve.drainageExtremaPhaseVolFraction;
+                            real64 const Shy_min = (phaseMinHistoricalVolFraction[ipWetting] > Smin) ? 
+                                                  phaseMinHistoricalVolFraction[ipWetting] : Smin;
+                            real64 const Shy_max = (phaseMaxHistoricalVolFraction[ipWetting] < Smax) ? 
+                                                  phaseMaxHistoricalVolFraction[ipWetting] : Smax;
+                            real64 const currentS = phaseVolFraction[ipWetting];
+                            
+                            if (currentS <= Shy_min + flowReversalBuffer) {
+                                mode = ModeIndexType::DRAINAGE;
+                            } else if (currentS >= Shy_max - flowReversalBuffer) {
+                                mode = ModeIndexType::IMBIBITION;
+                            } else {
+                                // Default to drainage if in between
+                                mode = ModeIndexType::DRAINAGE;
+                            }
+                        }
+                    }
+                }
+                
+                bool justSwitchedToMode2 = false;
+                if (ENABLE_SCANNING_CURVES && (mode == ModeIndexType::DRAINAGE || mode == ModeIndexType::IMBIBITION)) {
+                    // Transitioning from a pure state to a scanning curve.
+                    // The previous mode tells us the direction of the reversal:
+                    //   - From DRAINAGE: saturation is now increasing → DRAINAGE_TO_IMBIBITION (Mode 2)
+                    //   - From IMBIBITION: saturation is now decreasing → IMBIBITION_TO_DRAINAGE (Mode 3)
+                    if (mode == ModeIndexType::DRAINAGE) {
+                mode = ModeIndexType::DRAINAGE_TO_IMBIBITION;
+                        justSwitchedToMode2 = true;
+                    } else {
+                        mode = ModeIndexType::IMBIBITION_TO_DRAINAGE;
+                        // Reset Mode 2 peak when leaving imbibition
+                        if (phaseMode2PeakVolFraction[ipWetting] > 0.0) {
+                            phaseMode2PeakVolFraction[ipWetting] = 0.0;
+                        }
+                    }
+                }
+                // Mode 2 peak is now tracked explicitly at end of timestep in saveConvergedPhaseVolFractionState()
+                // No need to update it during Newton iterations - use constant value from previous timestep
+                // This prevents oscillations during Newton solve from affecting the peak value
+                // Check for transition from DRAINAGE_TO_IMBIBITION to drainage (departing from scanning curve)
+                // Mode 4: Switch when saturation decreases from the peak reached during Mode 2
+                // In Mode 2, saturation increases from Shy_min (reversal point) towards Mode2_peak
+                // Once saturation starts decreasing from Mode2_peak by at least 1e-4, switch to Mode 4
+                // IMPORTANT: Only check for Mode 4 if we were already in Mode 2 (not just switched from Mode 0)
+                // This prevents immediate Mode 0 -> Mode 2 -> Mode 4 transition within a single Newton iteration
+                // TEMPORARY: Disable scanning curves for testing convergence
+                if (ENABLE_MODE4 && ENABLE_SCANNING_CURVES && mode == ModeIndexType::DRAINAGE_TO_IMBIBITION && !justSwitchedToMode2) {
+                    real64 const currentS = phaseVolFraction[ipWetting];
+                    real64 const Mode2_peak = phaseMode2PeakVolFraction[ipWetting];
+                    // Use same approach as other mode switches: small buffer + mode persistence
+                    // Similar to Mode 0 -> Mode 2: use flowReversalBuffer (1e-12) for consistency
+                    // Mode 4 will persist once set, preventing oscillation-induced switching
+                    // However, we need a slightly larger buffer than 1e-12 because:
+                    // 1. The peak is a dynamic value that was just reached
+                    // 2. Saturation can oscillate around the peak during Newton iterations
+                    // Use a relative buffer: 0.01% of the peak value, with a minimum of 1e-4
+                    // This is still much smaller than before but provides some protection against numerical noise
+                    real64 const relativeBuffer = 0.0001 * Mode2_peak; // 0.01% of peak
+                    real64 const absoluteBuffer = 1e-4; // Minimum absolute buffer (same as original)
+                    real64 const decreaseBuffer = LvArray::math::max(relativeBuffer, absoluteBuffer);
+                    // Valid range for Mode 4 switching: between min and max historical saturations
+                    real64 const Smin = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                    real64 const Smax = m_wettingCurve.drainageExtremaPhaseVolFraction;
+                    real64 const S_test_min = (phaseMinHistoricalVolFraction[ipWetting] > Smin) ? 
+                                             phaseMinHistoricalVolFraction[ipWetting] : Smin;
+                    real64 const S_test_max = (phaseMaxHistoricalVolFraction[ipWetting] < Smax) ? 
+                                             phaseMaxHistoricalVolFraction[ipWetting] : Smax;
+                    
+                    // Check: saturation must have decreased from the Mode 2 peak
+                    // Only switch to Mode 4 if currentS < Mode2_peak - decreaseBuffer
+                    // Also ensure Mode2_peak is valid (non-zero, meaning we've tracked a peak)
+                    // And current saturation is within valid historical range
+                    // Once Mode 4 is set, it persists (like Mode 2), preventing oscillation-induced switching
+                    bool saturationHasDecreased = (Mode2_peak > 0.0 && currentS < Mode2_peak - decreaseBuffer);
+                    
+                    if (saturationHasDecreased &&
+                        currentS >= S_test_min &&
+                        currentS <= S_test_max) {
+                        mode = ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING;
+                    }
+                    // Otherwise, keep Mode 2 (saturation still increasing or hasn't decreased enough from peak)
+                    // Mode 2 persists once set, similar to how Mode 0 persists when S <= S_min + flowReversalBuffer
+                }
+                // IMBIBITION_TO_DRAINAGE_FROM_SCANNING mode persists once set
+                
+                // If scanning curves are disabled, use pure drainage/imbibition curves
+                if (!ENABLE_SCANNING_CURVES && 
+                    (mode == ModeIndexType::DRAINAGE || mode == ModeIndexType::IMBIBITION)) {
+                    // Use pure drainage or imbibition curve
+                    phaseTrappedVolFrac[ipWetting] = LvArray::math::min(phaseVolFraction[ipWetting],
+                                                                        m_wettingCurve.oppositeBoundPhaseVolFraction);
+                    GEOS_ASSERT_MSG(static_cast<integer>(m_wettingNonWettingCapillaryPressureKernelWrappers.size()) > mode,
+                                    "Invalid array index for kernel wrapper access");
+                    computeBoundCapillaryPressure(
+                            m_wettingNonWettingCapillaryPressureKernelWrappers[mode],
+                            phaseVolFraction[ipWetting],
+                            phaseCapPressure[ipWetting],
+                            dPhaseCapPressure_dPhaseVolFrac[ipWetting][ipWetting]);
+                } else {
+                    // Use scanning curves
+                    // printf("CapPressure: Using scanning curve (mode=%d)\n", static_cast<int>(mode));
+                computeImbibitionWettingCapillaryPressure(m_wettingNonWettingCapillaryPressureKernelWrappers,
+                                                          m_wettingCurve,
+                                                          m_landParam[ipWetting],
+                                                          phaseVolFraction[ipWetting],
+                                                          phaseMinHistoricalVolFraction[ipWetting],
+                                                              phaseMaxHistoricalVolFraction[ipWetting],
+                                                              phaseMode2PeakVolFraction[ipWetting],
+                                                          phaseTrappedVolFrac[ipWetting],
+                                                          phaseCapPressure[ipWetting],
+                                                          dPhaseCapPressure_dPhaseVolFrac[ipWetting][ipWetting],
+                                                          mode);
+                }
+            }
+
+// trapped vol fraction
+            if (mode == ModeIndexType::DRAINAGE || mode == ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                mode == ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+
+
+
+                    real64 const Smin = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                    real64 const Shy = (phaseMinHistoricalVolFraction[ipWetting] < Smin)
+                                       ? phaseMinHistoricalVolFraction[ipWetting]
+                                       : Smin;
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, Shy,
+                                                                               m_landParam[ipWetting],
+                                                                               m_jerauldParam_a,
+                                                                               m_jerauldParam_b,
+                                                                               Scrt);
+                phaseTrappedVolFrac[ipWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipWetting]);
+
+
+                //keep the same Land coeff as two phase only
+                KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve.toNonWetting(), Shy,
+                                                                           m_landParam[ipWetting],
+                                                                           m_jerauldParam_a,
+                                                                           m_jerauldParam_b,
+                                                                           Scrt);
+                phaseTrappedVolFrac[ipWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipWetting]);
+
+
+
+
+            }
+            else if (mode == ModeIndexType::IMBIBITION || mode == ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+
+                    real64 const Smax = m_wettingCurve.imbibitionExtremaPhaseVolFraction;
+                    real64 const Shy = (phaseMaxHistoricalVolFraction[ipWetting] < Smax)
+                                       ? phaseMaxHistoricalVolFraction[ipWetting]
+                                       : Smax;
+                    real64 Scrt = 0.0;
+                    //TODO (jacques) check if still accurate
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve,
+                                                                               Shy,
+                                                                               m_landParam[ipWetting],
+                                                                               m_jerauldParam_a,
+                                                                               m_jerauldParam_b,
+                                                                               Scrt);
+
+                    phaseTrappedVolFrac[ipWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipWetting]);
+
+                //keep the same Land coeff as two phase only
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve.toNonWetting(), Shy,
+                                                                           m_landParam[ipWetting],
+                                                                           m_jerauldParam_a,
+                                                                           m_jerauldParam_b,
+                                                                           Scrt);
+                phaseTrappedVolFrac[ipWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipWetting]);
+
+            }
+
+        }
+
+        void TableCapillaryPressureHysteresis::KernelWrapper::computeTwoPhaseNonWetting(const geos::integer ipWetting,
+                                                                                        const geos::integer ipNonWetting,
+                                                                                        const arraySlice1d<const geos::real64,
+                                                                                                compflow::USD_PHASE -
+                                                                                                1> &phaseVolFraction,
+                                                                                        const arraySlice1d<const geos::real64,
+                                                                                                compflow::USD_PHASE
+                                                                                                -
+                                                                                                1> &phaseMaxHistoricalVolFraction,
+                                                                                        const arraySlice1d<const geos::real64,
+                                                                                                compflow::USD_PHASE
+                                                                                                -
+                                                                                                1> &phaseMinHistoricalVolFraction,
+                                                                                        const arraySlice1d<geos::real64,
+                                                                                                relperm::USD_RELPERM
+                                                                                                -
+                                                                                                2> &phaseTrappedVolFrac,
+                                                                                        arraySlice1d<geos::real64,
+                                                                                                relperm::USD_RELPERM
+                                                                                                -
+                                                                                                2> const &phaseCapPressure,
+                                                                                        arraySlice2d<geos::real64,
+                                                                                                relperm::USD_RELPERM_DS
+                                                                                                -
+                                                                                                2> const &dPhaseCapPressure_dPhaseVolFrac,
+                                                                                        ModeIndexType &mode) const {
+            using TTP = ThreePhasePairPhaseType;
+            
+            // TEMPORARY: Disable scanning curves for testing convergence
+            // Define at function scope so it's accessible throughout this function
+            constexpr bool ENABLE_SCANNING_CURVES = true;
+            
+            // TEMPORARY: Force IMBIBITION mode for testing (overrides normal mode determination)
+            constexpr bool FORCE_IMBIBITION_MODE = false;
+
+            //update state
+            // TODO check if we can get rid of  DRAINAGE_TO_IMBIBITION && IMBIBITION_TO_DRAINAGE
+            if (mode == ModeIndexType::DRAINAGE_TO_IMBIBITION &&
+                phaseVolFraction[ipNonWetting] >= phaseMaxHistoricalVolFraction[ipNonWetting] + flowReversalBuffer)
+                mode = ModeIndexType::DRAINAGE;
+            if (mode == ModeIndexType::IMBIBITION_TO_DRAINAGE &&
+                phaseVolFraction[ipWetting] <= phaseMinHistoricalVolFraction[ipNonWetting] + flowReversalBuffer)
+                mode = ModeIndexType::IMBIBITION;
+
+
+
+            
+            // If scanning curves are disabled, reset any scanning curve modes back to pure modes
+            if (!ENABLE_SCANNING_CURVES) {
+                if (mode == ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                    mode == ModeIndexType::IMBIBITION_TO_DRAINAGE ||
+                    mode == ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                    // Reset to pure drainage or imbibition based on saturation
+                    if (FORCE_IMBIBITION_MODE) {
+                        mode = ModeIndexType::IMBIBITION;
+                    } else {
+                        if (phaseVolFraction[ipNonWetting] <= phaseMinHistoricalVolFraction[ipNonWetting] + flowReversalBuffer) {
+                            mode = ModeIndexType::DRAINAGE;
+                        } else if (phaseVolFraction[ipNonWetting] >= phaseMaxHistoricalVolFraction[ipNonWetting] - flowReversalBuffer) {
+                            mode = ModeIndexType::IMBIBITION;
+                        } else {
+                            // Default to drainage if in between
+                            mode = ModeIndexType::DRAINAGE;
+                        }
+                    }
+                }
+            }
+            
+            // Force IMBIBITION mode if flag is set (overrides all other logic)
+            if (FORCE_IMBIBITION_MODE) {
+                mode = ModeIndexType::IMBIBITION;
+            }
+            
+            if (ENABLE_SCANNING_CURVES && (mode == ModeIndexType::DRAINAGE || mode == ModeIndexType::IMBIBITION)) {
+                // Handle transitions from pure states to scanning curves
+                // If current saturation is significantly above min historical, we're in imbibition
+                if (phaseVolFraction[ipNonWetting] > phaseMinHistoricalVolFraction[ipNonWetting] + flowReversalBuffer) {
+                    if (mode == ModeIndexType::DRAINAGE) {
+                        mode = ModeIndexType::DRAINAGE_TO_IMBIBITION;
+                    }
+                }
+                // If current saturation is significantly below max historical, we're in drainage
+                else if (phaseVolFraction[ipNonWetting] < phaseMaxHistoricalVolFraction[ipNonWetting] - flowReversalBuffer) {
+                    if (mode == ModeIndexType::IMBIBITION) {
+                        mode = ModeIndexType::IMBIBITION_TO_DRAINAGE;
+                    }
+                }
+            }
+            // Mode 4 switching is only implemented for wetting phase, not for non-wetting phase
+            // Scanning curve modes persist - no switching between DRAINAGE_TO_IMBIBITION and IMBIBITION_TO_DRAINAGE
+
+            // Use simple drainage/imbibition curves when:
+            // 1. No hysteresis enabled, OR
+            // 2. We're in pure DRAINAGE mode (use drainage curve), OR
+            // 3. We're in pure IMBIBITION mode (use imbibition curve)
+            // Use scanning curves only during transitions (DRAINAGE_TO_IMBIBITION or IMBIBITION_TO_DRAINAGE)
+            if (!m_phaseHasHysteresis[TTP::INTERMEDIATE_NONWETTING] ||
+                mode == ModeIndexType::DRAINAGE ||
+                mode == ModeIndexType::IMBIBITION) {
+                phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(phaseVolFraction[ipNonWetting],
+                                                                       (mode == ModeIndexType::DRAINAGE)
+                                                                       ? m_nonWettingCurve.drainageExtremaPhaseVolFraction
+                                                                       : m_nonWettingCurve.imbibitionExtremaPhaseVolFraction);
+                // Ensure mode is a valid array index (0 or 1)
+                integer const arrayIndex = (mode == ModeIndexType::DRAINAGE) ? ModeIndexType::DRAINAGE : ModeIndexType::IMBIBITION;
+                GEOS_ASSERT_MSG(arrayIndex >= 0 && arrayIndex < static_cast<integer>(m_wettingNonWettingCapillaryPressureKernelWrappers.size()),
+                                "Invalid array index for kernel wrapper access");
+                computeBoundCapillaryPressure(
+                        m_wettingNonWettingCapillaryPressureKernelWrappers[arrayIndex],
+                        phaseVolFraction[ipNonWetting],
+                        phaseCapPressure[ipNonWetting],
+                        dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting]);
+                // when pc is on the gas phase, we need to multiply user input by -1
+                // because CompositionalMultiphaseFVM does: pres_gas = pres_oil - pc_og, so we need a negative pc_og
+                phaseCapPressure[ipNonWetting] *= -1;
+                dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting] *= -1;
+
+            } else {
+                // We're in a transition state (DRAINAGE_TO_IMBIBITION or IMBIBITION_TO_DRAINAGE)
+                // Use scanning curves (unless disabled)
+                if (!ENABLE_SCANNING_CURVES) {
+                    // Scanning curves disabled - use pure drainage/imbibition based on current mode
+                    // This should not happen if reset logic worked correctly, but handle it anyway
+                    if (mode == ModeIndexType::DRAINAGE || mode == ModeIndexType::IMBIBITION) {
+                        phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(phaseVolFraction[ipNonWetting],
+                                                                              (mode == ModeIndexType::DRAINAGE)
+                                                                              ? m_nonWettingCurve.drainageExtremaPhaseVolFraction
+                                                                              : m_nonWettingCurve.imbibitionExtremaPhaseVolFraction);
+                        integer const arrayIndex = (mode == ModeIndexType::DRAINAGE) ? ModeIndexType::DRAINAGE : ModeIndexType::IMBIBITION;
+                        GEOS_ASSERT_MSG(arrayIndex >= 0 && arrayIndex < static_cast<integer>(m_wettingNonWettingCapillaryPressureKernelWrappers.size()),
+                                        "Invalid array index for kernel wrapper access");
+                        computeBoundCapillaryPressure(
+                                m_wettingNonWettingCapillaryPressureKernelWrappers[arrayIndex],
+                                phaseVolFraction[ipNonWetting],
+                                phaseCapPressure[ipNonWetting],
+                                dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting]);
+                        phaseCapPressure[ipNonWetting] *= -1;
+                        dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting] *= -1;
+                    } else {
+                        mode = ModeIndexType::DRAINAGE;
+                        phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(phaseVolFraction[ipNonWetting],
+                                                                              m_nonWettingCurve.drainageExtremaPhaseVolFraction);
+                        computeBoundCapillaryPressure(
+                                m_wettingNonWettingCapillaryPressureKernelWrappers[ModeIndexType::DRAINAGE],
+                                phaseVolFraction[ipNonWetting],
+                                phaseCapPressure[ipNonWetting],
+                                dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting]);
+                        phaseCapPressure[ipNonWetting] *= -1;
+                        dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting] *= -1;
+                    }
+                } else {
+                // Use scanning curves
+
+                computeImbibitionNonWettingCapillaryPressure(m_wettingNonWettingCapillaryPressureKernelWrappers,
+                                                             m_nonWettingCurve,
+                                                             m_landParam[ipNonWetting],
+                                                             phaseVolFraction[ipNonWetting],
+                                                             phaseMaxHistoricalVolFraction[ipNonWetting],
+                                                             phaseTrappedVolFrac[ipNonWetting],
+                                                             phaseCapPressure[ipNonWetting],
+                                                             dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting],
+                                                             mode);
+
+                // when pc is on the gas phase, we need to multiply user input by -1
+                // because CompositionalMultiphaseFVM does: pres_gas = pres_oil - pc_og, so we need a negative pc_og
+                phaseCapPressure[ipNonWetting] *= -1;
+                dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting] *= -1;
+                }
+            }
+
+// trapped vol fraction
+            if (mode == ModeIndexType::DRAINAGE || mode == ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                mode == ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+
+                {
+                    real64 const Smax = m_nonWettingCurve.oppositeBoundPhaseVolFraction;
+                    real64 const Shy = (phaseMaxHistoricalVolFraction[ipNonWetting] > Smax)
+                                       ? phaseMaxHistoricalVolFraction[ipNonWetting]
+                                       : Smax;
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_nonWettingCurve, Shy,
+                                                                               m_landParam[ipNonWetting],
+                                                                               m_jerauldParam_a, m_jerauldParam_b,
+                                                                               Scrt);
+                    phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipNonWetting]);
+
+                    //keep the same Land coeff as two phase only
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_nonWettingCurve.toWetting(), Shy,
+                                                                               m_landParam[ipNonWetting],
+                                                                               m_jerauldParam_a, m_jerauldParam_b,
+                                                                               Scrt);
+                    phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipNonWetting]);
+                }
+            } else if (mode == ModeIndexType::IMBIBITION || mode == ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+
+                {
+                    real64 const Smin = m_nonWettingCurve.imbibitionExtremaPhaseVolFraction;;
+                    real64 const Shy = (phaseMinHistoricalVolFraction[ipNonWetting] > Smin)
+                                       ? phaseMinHistoricalVolFraction[ipNonWetting]
+                                       : Smin;
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_nonWettingCurve, Shy,
+                                                                               m_landParam[ipNonWetting],
+                                                                               m_jerauldParam_a, m_jerauldParam_b,
+                                                                               Scrt);
+                    phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipNonWetting]);
+
+                    //keep the same Land coeff as two phase only
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_nonWettingCurve.toWetting(), Shy,
+                                                                               m_landParam[ipNonWetting],
+                                                                               m_jerauldParam_a, m_jerauldParam_b,
+                                                                               Scrt);
+                    phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipNonWetting]);
+                }
+            }
+
+
+        }
+
+        void TableCapillaryPressureHysteresis::KernelWrapper::computeThreePhase(const geos::integer ipWetting,
+                                                                                const geos::integer GEOS_UNUSED_PARAM( ipInter ),
+                                                                                const geos::integer ipNonWetting,
+                                                                                const arraySlice1d<const geos::real64,
+                                                                                        compflow::USD_PHASE -
+                                                                                        1> &phaseVolFraction,
+                                                                                const arraySlice1d<const geos::real64,
+                                                                                        compflow::USD_PHASE
+                                                                                        -
+                                                                                        1> &phaseMaxHistoricalVolFraction,
+                                                                                const arraySlice1d<const geos::real64,
+                                                                                        compflow::USD_PHASE
+                                                                                        -
+                                                                                        1> &phaseMinHistoricalVolFraction,
+                                                                                const arraySlice1d<geos::real64,
+                                                                                        relperm::USD_RELPERM
+                                                                                        - 2> &phaseTrappedVolFrac,
+                                                                                const arraySlice1d<geos::real64,
+                                                                                        relperm::USD_RELPERM -
+                                                                                        2> &phaseCapPressure,
+                                                                                const arraySlice2d<geos::real64,
+                                                                                        relperm::USD_RELPERM_DS
+                                                                                        -
+                                                                                        2> &dPhaseCapPressure_dPhaseVolFrac,
+                                                                                ModeIndexType &mode,
+                                                                                arraySlice1d<geos::real64,
+                                                                                        compflow::USD_PHASE
+                                                                                        -
+                                                                                        1> &phaseMode2PeakVolFraction) const {
+
+
+            LvArray::forValuesInSlice(dPhaseCapPressure_dPhaseVolFrac, [](real64 &val) { val = 0.0; });
+            using TTP = ThreePhasePairPhaseType;
+
+            // -- wetting curve if drainage only
+            constexpr bool ENABLE_COMPUTE_BRANCH_DEBUG = false;
+            bool usePureCurve = !m_phaseHasHysteresis[TTP::INTERMEDIATE_WETTING] ||
+                (mode == ModeIndexType::DRAINAGE &&
+                 phaseVolFraction[ipWetting] <= phaseMinHistoricalVolFraction[ipWetting] + flowReversalBuffer) ||
+                (mode == ModeIndexType::IMBIBITION &&
+                 phaseVolFraction[ipWetting] >= phaseMaxHistoricalVolFraction[ipWetting] + flowReversalBuffer);
+            
+            if constexpr (ENABLE_COMPUTE_BRANCH_DEBUG) {
+                if (mode == ModeIndexType::DRAINAGE || mode == ModeIndexType::IMBIBITION) {
+                    std::cout << "[COMPUTE_BRANCH_DEBUG] Two-phase wetting, mode=" << (mode == ModeIndexType::DRAINAGE ? "DRAINAGE" : "IMBIBITION")
+                              << ", S=" << phaseVolFraction[ipWetting]
+                              << ", S_min=" << phaseMinHistoricalVolFraction[ipWetting]
+                              << ", S_max=" << phaseMaxHistoricalVolFraction[ipWetting]
+                              << ", usePureCurve=" << (usePureCurve ? "true" : "false")
+                              << ", hasHysteresis=" << m_phaseHasHysteresis[TTP::INTERMEDIATE_WETTING] << std::endl;
+                }
+            }
+            
+            if (usePureCurve) {
+                // water-oil capillary pressure
+                phaseTrappedVolFrac[ipWetting] = LvArray::math::min(phaseVolFraction[ipWetting],
+                                                                    m_wettingCurve.oppositeBoundPhaseVolFraction);
+                constexpr bool ENABLE_COMPUTE_TABLE_DEBUG = false;
+                real64 S_before = phaseVolFraction[ipWetting];
+                real64 dPc_dS_before = dPhaseCapPressure_dPhaseVolFrac[ipWetting][ipWetting];
+                integer const tableIndex = static_cast<integer>(mode);
+                if constexpr (ENABLE_COMPUTE_TABLE_DEBUG) {
+                  std::cout << "[COMPUTE_TABLE_DEBUG_TCH] Forward table lookup: mode=" << (mode == ModeIndexType::DRAINAGE ? "DRAINAGE" : "IMBIBITION")
+                            << ", tableIndex=" << tableIndex
+                            << ", S=" << S_before 
+                            << ", wrapper.size()=" << m_wettingIntermediateCapillaryPressureKernelWrappers.size() << std::endl;
+                }
+                phaseCapPressure[ipWetting] =
+                        m_wettingIntermediateCapillaryPressureKernelWrappers[mode].compute(
+                                &(phaseVolFraction)[ipWetting],
+                                &(dPhaseCapPressure_dPhaseVolFrac)[ipWetting][ipWetting]);
+                real64 dPc_dS_after = dPhaseCapPressure_dPhaseVolFrac[ipWetting][ipWetting];
+                if constexpr (ENABLE_COMPUTE_TABLE_DEBUG) {
+                  std::cout << "[COMPUTE_TABLE_DEBUG_TCH] After table.compute: Pc=" << phaseCapPressure[ipWetting] 
+                            << ", dPc_dS_before=" << dPc_dS_before 
+                            << ", dPc_dS_after=" << dPc_dS_after << std::endl;
+                }
+            } else {
+                // We're in a scanning curve state - preserve the mode if already set, otherwise determine from position
+                if (mode != ModeIndexType::DRAINAGE_TO_IMBIBITION && 
+                    mode != ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                    // Starting from a pure state - determine initial scanning curve direction
+                mode = (mode == ModeIndexType::DRAINAGE) ? ModeIndexType::DRAINAGE_TO_IMBIBITION
+                                                         : ModeIndexType::IMBIBITION_TO_DRAINAGE;
+                }
+                computeImbibitionWettingCapillaryPressure(m_wettingIntermediateCapillaryPressureKernelWrappers,
+                                                          m_wettingCurve,
+                                                          m_nonWettingCurve,
+                                                          m_landParam[ipWetting],
+                                                          phaseVolFraction[ipWetting],
+                                                          phaseMinHistoricalVolFraction[ipWetting],
+                                                          phaseMaxHistoricalVolFraction[ipWetting],
+                                                          phaseMode2PeakVolFraction[ipWetting],
+                                                          phaseTrappedVolFrac[ipWetting],
+                                                          phaseCapPressure[ipWetting],
+                                                          dPhaseCapPressure_dPhaseVolFrac[ipWetting][ipWetting],
+                                                          mode);
+
+
+            }
+
+
+            // -- non-wetting cure if drainage only
+            // gas-oil capillary pressure
+            if (!m_phaseHasHysteresis[TTP::INTERMEDIATE_NONWETTING] ||
+                (mode == ModeIndexType::DRAINAGE &&
+                 phaseVolFraction[ipNonWetting] >= phaseMaxHistoricalVolFraction[ipNonWetting] + flowReversalBuffer) ||
+                (mode == ModeIndexType::IMBIBITION &&
+                 phaseVolFraction[ipNonWetting] <= phaseMinHistoricalVolFraction[ipNonWetting] + flowReversalBuffer)) {
+                phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(phaseVolFraction[ipNonWetting],
+                                                                       (mode == ModeIndexType::DRAINAGE)
+                                                                       ? m_nonWettingCurve.drainageExtremaPhaseVolFraction
+                                                                       : m_nonWettingCurve.imbibitionExtremaPhaseVolFraction);
+                phaseCapPressure[ipNonWetting] =
+                        m_nonWettingIntermediateCapillaryPressureKernelWrappers[mode].compute(
+                                &(phaseVolFraction)[ipNonWetting],
+                                &(dPhaseCapPressure_dPhaseVolFrac)[ipNonWetting][ipNonWetting]);
+
+
+                // when pc is on the gas phase, we need to multiply user input by -1
+                // because CompositionalMultiphaseFVM does: pres_gas = pres_oil - pc_og, so we need a negative pc_og
+                phaseCapPressure[ipNonWetting] *= -1;
+                dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting] *= -1;
+            } else {
+                // We're in a scanning curve state - preserve the mode if already set, otherwise determine from position
+                if (mode != ModeIndexType::DRAINAGE_TO_IMBIBITION && 
+                    mode != ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                    // Starting from a pure state - determine initial scanning curve direction
+                mode = (mode == ModeIndexType::DRAINAGE) ? ModeIndexType::DRAINAGE_TO_IMBIBITION
+                                                         : ModeIndexType::IMBIBITION_TO_DRAINAGE;
+                }
+
+                computeImbibitionNonWettingCapillaryPressure(m_nonWettingIntermediateCapillaryPressureKernelWrappers,
+                                                             m_nonWettingCurve,
+                                                             m_wettingCurve,
+                                                             m_landParam[ipNonWetting],
+                                                             phaseVolFraction[ipNonWetting],
+                                                             phaseMinHistoricalVolFraction[ipNonWetting],
+                                                             phaseTrappedVolFrac[ipNonWetting],
+                                                             phaseCapPressure[ipNonWetting],
+                                                             dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting],
+                                                             mode);
+                // when pc is on the gas phase, we need to multiply user input by -1
+                // because CompositionalMultiphaseFVM does: pres_gas = pres_oil - pc_og, so we need a negative pc_og
+                phaseCapPressure[ipNonWetting] *= -1;
+                dPhaseCapPressure_dPhaseVolFrac[ipNonWetting][ipNonWetting] *= -1;
+
+                //update trapped fraction
+                if (mode == ModeIndexType::DRAINAGE || mode == ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                    mode == ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+
+
+                    {
+                        real64 const Smin = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                        real64 const Shy = (phaseMinHistoricalVolFraction[ipWetting] < Smin)
+                                           ? phaseMinHistoricalVolFraction[ipWetting]
+                                           : Smin;
+                        real64 Scrt = 0.0;
+                        KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, Shy,
+                                                                                   m_landParam[ipWetting],
+                                                                                   m_jerauldParam_a, m_jerauldParam_b,
+                                                                                   Scrt);
+                        phaseTrappedVolFrac[ipWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipWetting]);
+                    }
+
+                    {
+                        real64 const Smax = m_nonWettingCurve.oppositeBoundPhaseVolFraction;
+                        real64 const Shy = (phaseMaxHistoricalVolFraction[ipNonWetting] > Smax)
+                                           ? phaseMaxHistoricalVolFraction[ipNonWetting]
+                                           : Smax;
+                        real64 Scrt = 0.0;
+                        KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_nonWettingCurve, Shy,
+                                                                                   m_landParam[ipNonWetting],
+                                                                                   m_jerauldParam_a, m_jerauldParam_b,
+                                                                                   Scrt);
+                        phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipNonWetting]);
+                    }
+                } else if (mode == ModeIndexType::IMBIBITION || mode == ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                    {
+                        real64 const Smax = m_wettingCurve.imbibitionExtremaPhaseVolFraction;
+                        real64 const Shy = (phaseMaxHistoricalVolFraction[ipWetting] < Smax)
+                                           ? phaseMaxHistoricalVolFraction[ipWetting]
+                                           : Smax;
+                        real64 Scrt = 0.0;
+                        KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, Shy,
+                                                                                   m_landParam[ipWetting],
+                                                                                   m_jerauldParam_a, m_jerauldParam_b,
+                                                                                   Scrt);
+                        phaseTrappedVolFrac[ipWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipWetting]);
+                    }
+
+                    {
+                        real64 const Smin = m_nonWettingCurve.imbibitionExtremaPhaseVolFraction;;
+                        real64 const Shy = (phaseMinHistoricalVolFraction[ipNonWetting] > Smin)
+                                           ? phaseMinHistoricalVolFraction[ipNonWetting]
+                                           : Smin;
+                        real64 Scrt = 0.0;
+                        KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_nonWettingCurve, Shy,
+                                                                                   m_landParam[ipNonWetting],
+                                                                                   m_jerauldParam_a, m_jerauldParam_b,
+                                                                                   Scrt);
+                        phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min(Scrt, phaseVolFraction[ipNonWetting]);
+                    }
+                }
+
+
+            }
+
+
+        }
+
+
+        void
+        TableCapillaryPressureHysteresis::KernelWrapper::computeImbibitionNonWettingCapillaryPressure(
+                const arrayView1d<const TableFunction::KernelWrapper> &nonWettingKernelWrapper,
+                const KilloughHysteresis::HysteresisCurve &nonWettingCurve,
+                const KilloughHysteresis::HysteresisCurve &wettingCurve,
+                const geos::real64 &landParam,
+                const geos::real64 &phaseVolFraction,
+                const geos::real64 &phaseMaxHistoricalVolFraction,
+                geos::real64 &phaseTrappedVolFrac,
+                geos::real64 &phaseCapPressure,
+                geos::real64 &dPhaseCapPressure_dPhaseVolFrac,
+                const ModeIndexType &mode) const {
+            GEOS_ASSERT(!nonWettingCurve.isWetting());
+            real64 const S = phaseVolFraction;
+            real64 const Smii = nonWettingCurve.imbibitionExtremaPhaseVolFraction;
+            real64 const Smid = nonWettingCurve.drainageExtremaPhaseVolFraction;
+            real64 const Smax = nonWettingCurve.oppositeBoundPhaseVolFraction;
+
+	    GEOS_UNUSED_VAR( Smii, Smid );
+	    
+//  if( S >= Smax )
+//  {
+//    //above accessible range
+//    phaseCapPressure = CAP_INF;
+//    dPhaseCapPressure_dPhaseVolFrac = CAP_INF_DERIV;
+//  }
+//  else if( S <= Smid )
+//  {
+//    //below accessible range
+//    phaseCapPressure = -CAP_INF;
+//    dPhaseCapPressure_dPhaseVolFrac = CAP_INF_DERIV;
+//  }
+//  else
+            {
+                //drainage to imbibition
+                real64 dpci_dS, dpcd_dS;
+                real64 const pci = nonWettingKernelWrapper[ModeIndexType::IMBIBITION].compute(&S, &dpci_dS);
+                real64 const pcd = nonWettingKernelWrapper[ModeIndexType::DRAINAGE].compute(&S, &dpcd_dS);
+
+                // Step 1: get the trapped from wetting data
+                real64 const Shy = (phaseMaxHistoricalVolFraction < Smax) ? phaseMaxHistoricalVolFraction : Smax;
+
+                //drainage to imbibition
+                if (mode == ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(nonWettingCurve, Shy, landParam,
+                                                                               m_jerauldParam_a, m_jerauldParam_b,
+                                                                               Scrt);
+
+                    real64 const E = m_killoughCurvatureParamCapPres;
+
+                    //Set 2. compute F as in (EQ 34.21) F = (1/(Shy-S+E)-1/E) / (1/(Shy - Sgcr +E)-1/E)
+                    real64 F = (1. / (Shy - S + E) - 1. / E) / (1. / (Shy - Scrt + E) - 1. / E);
+                    //force bound
+                    F = LvArray::math::max(F, 0.0);
+                    F = LvArray::math::min(F, 1.0);
+
+                    //Step 3. compute dF_dS
+                    real64 dF_dS = (1. / (S * S)) / (1. / (Shy - Scrt + E) - 1. / E);
+
+                    //Step 4. Eventually assemble everything following (EQ. 34.20)
+                    phaseCapPressure = pcd + F * (pci - pcd);
+                    dPhaseCapPressure_dPhaseVolFrac = dpci_dS + F * (dpci_dS - dpcd_dS);
+                    dPhaseCapPressure_dPhaseVolFrac += dF_dS * (pci - pcd);
+
+                    //update trapped fraction
+                    phaseTrappedVolFrac = LvArray::math::min(Scrt, S);
+
+                }
+                    //imbibition to drainage
+                else if (mode == ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(wettingCurve, Shy, landParam,
+                                                                               m_jerauldParam_a, m_jerauldParam_b,
+                                                                               Scrt);
+                    real64 Sgma = 1. - Scrt - m_phaseIntermediateMinVolFraction;
+
+                    real64 const E = m_killoughCurvatureParamCapPres;
+
+                    //Set 2. compute F as in (EQ 34.21) F = (1/(Shy-S+E)-1/E) / (1/(Shy - Sgcr +E)-1/E)
+                    real64 F = (1. / (S - Shy + E) - 1. / E) / (1. / (Sgma - Shy + E) - 1. / E);
+                    //force bound
+                    F = LvArray::math::max(F, 0.0);
+                    F = LvArray::math::min(F, 1.0);
+
+                    //Step 3. compute dF_dS
+                    real64 dF_dS = (-1. / (S * S)) / (1. / (Shy - Scrt + E) - 1. / E);
+
+                    //Step 4. Eventually assemble everything following (EQ. 34.20)
+                    phaseCapPressure = pci + F * (pcd - pci);
+                    dPhaseCapPressure_dPhaseVolFrac = dpcd_dS + F * (dpcd_dS - dpci_dS);
+                    dPhaseCapPressure_dPhaseVolFrac += dF_dS * (pcd - pci);
+                } else {
+                    GEOS_THROW(GEOS_FMT("{}: State is {}.Shouldnt be used in pure DRAINAGE or IMBIBITION.",
+                                          "TableCapillaryPressureHysteresis",
+                                          (mode == ModeIndexType::DRAINAGE) ? "DRAINAGE" : ((mode ==
+                                                                                             ModeIndexType::IMBIBITION)
+                                                                                            ? "IMBIBITION"
+                                                                                            : "UNKNOWN")),
+                                InputError);
+                }
+
+
+            }
+        }
+
+
+        void
+        TableCapillaryPressureHysteresis::KernelWrapper::computeImbibitionNonWettingCapillaryPressure(
+                const arrayView1d<const TableFunction::KernelWrapper> &nonWettingKernelWrapper,
+                const KilloughHysteresis::HysteresisCurve &nonWettingCurve,
+                const geos::real64 &landParam,
+                const geos::real64 &phaseVolFraction,
+                const geos::real64 &phaseMaxHistoricalVolFraction,
+                geos::real64 &phaseTrappedVolFrac,
+                geos::real64 &phaseCapPressure,
+                geos::real64 &dPhaseCapPressure_dPhaseVolFrac,
+                const ModeIndexType &mode) const {
+
+            GEOS_ASSERT(!nonWettingCurve.isWetting());
+            real64 const S = phaseVolFraction;
+            real64 const Smii = nonWettingCurve.imbibitionExtremaPhaseVolFraction;
+            real64 const Smid = nonWettingCurve.drainageExtremaPhaseVolFraction;
+            real64 const Smax = nonWettingCurve.oppositeBoundPhaseVolFraction;
+
+	    GEOS_UNUSED_VAR( Smii, Smid );
+	    
+//  if( S >= Smax )
+//  {
+//    //above accessible range
+//    phaseCapPressure = CAP_INF;
+//    dPhaseCapPressure_dPhaseVolFrac = CAP_INF_DERIV;
+//  }
+//  else if( S <= Smid )
+//  {
+//    //below accessible range
+//    phaseCapPressure = -CAP_INF;
+//    dPhaseCapPressure_dPhaseVolFrac = CAP_INF_DERIV;
+//  }
+//  else
+            {
+                //drainage to imbibition
+                real64 dpci_dS, dpcd_dS;
+                real64 const pci = nonWettingKernelWrapper[ModeIndexType::IMBIBITION].compute(&S, &dpci_dS);
+                real64 const pcd = nonWettingKernelWrapper[ModeIndexType::DRAINAGE].compute(&S, &dpcd_dS);
+
+                // Step 1: get the trapped from wetting data
+                real64 const Shy = (phaseMaxHistoricalVolFraction < Smax) ? phaseMaxHistoricalVolFraction : Smax;
+
+                //drainage to imbibition
+                if (mode == ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(nonWettingCurve, Shy, landParam,
+                                                                               m_jerauldParam_a, m_jerauldParam_b,
+                                                                               Scrt);
+
+                    real64 const E = m_killoughCurvatureParamCapPres;
+
+                    //Set 2. compute F as in (EQ 34.21) F = (1/(Shy-S+E)-1/E) / (1/(Shy - Sgcr +E)-1/E)
+                    real64 F = (1. / (Shy - S + E) - 1. / E) / (1. / (Shy - Scrt + E) - 1. / E);
+                    //force bound
+                    F = LvArray::math::max(F, 0.0);
+                    F = LvArray::math::min(F, 1.0);
+
+                    //Step 3. compute dF_dS
+                    real64 dF_dS = (1. / (S * S)) / (1. / (Shy - Scrt + E) - 1. / E);
+
+                    //Step 4. Eventually assemble everything following (EQ. 34.20)
+                    phaseCapPressure = pcd + F * (pci - pcd);
+                    dPhaseCapPressure_dPhaseVolFrac = dpci_dS + F * (dpci_dS - dpcd_dS);
+                    dPhaseCapPressure_dPhaseVolFrac += dF_dS * (pci - pcd);
+
+                    //update trapped fraction
+                    phaseTrappedVolFrac = LvArray::math::min(Scrt, S);
+
+                }
+                    //imbibition to drainage
+                else if (mode == ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                    real64 Scrt = 0.0;
+                    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(nonWettingCurve, Shy, landParam,
+                                                                               m_jerauldParam_a, m_jerauldParam_b,
+                                                                               Scrt);
+                    real64 Sgma = 1. - (1. - Scrt);
+
+                    real64 const E = m_killoughCurvatureParamCapPres;
+
+                    //Set 2. compute F as in (EQ 34.21) F = (1/(Shy-S+E)-1/E) / (1/(Shy - Sgcr +E)-1/E)
+                    real64 F = (1. / (S - Shy + E) - 1. / E) / (1. / (Sgma - Shy + E) - 1. / E);
+                    //force bound
+                    F = LvArray::math::max(F, 0.0);
+                    F = LvArray::math::min(F, 1.0);
+
+                    //Step 3. compute dF_dS
+                    real64 dF_dS = (-1. / (S * S)) / (1. / (Shy - Scrt + E) - 1. / E);
+
+                    //Step 4. Eventually assemble everything following (EQ. 34.20)
+                    phaseCapPressure = pci + F * (pcd - pci);
+                    dPhaseCapPressure_dPhaseVolFrac = dpcd_dS + F * (dpcd_dS - dpci_dS);
+                    dPhaseCapPressure_dPhaseVolFrac += dF_dS * (pcd - pci);
+                } else {
+                    GEOS_THROW(GEOS_FMT("{}: State is {}.Shouldnt be used in pure DRAINAGE or IMBIBITION.",
+                                          "TableCapillaryPressureHysteresis",
+                                          (mode == ModeIndexType::DRAINAGE) ? "DRAINAGE" : ((mode ==
+                                                                                             ModeIndexType::IMBIBITION)
+                                                                                            ? "IMBIBITION"
+                                                                                            : "UNKNOWN")),
+                                InputError);
+                }
+
+
+            }
+        }
+
+
+        void TableCapillaryPressureHysteresis::KernelWrapper::computeBoundCapillaryPressure(
+                const TableFunction::KernelWrapper &drainageRelpermWrapper,
+                const geos::real64 &phaseVolFraction,
+                geos::real64 &phaseCapPressure,
+                geos::real64 &dPhaseCapPressure_dPhaseVolFrac) const {
+            phaseCapPressure = drainageRelpermWrapper.compute(&phaseVolFraction,
+                                                              &dPhaseCapPressure_dPhaseVolFrac);
+        }
+
+        /// Helper function to compute Pc(S) for given S, mode, and historical values
+        /// Used for Newton-Raphson inversion in computeInv
+        GEOS_HOST_DEVICE
+        inline real64 TableCapillaryPressureHysteresis::KernelWrapper::computeCapillaryPressureForSaturation(
+                real64 const S,
+                fields::cappres::ModeIndexType const &mode,
+                integer const ipPhase,
+                real64 const &phaseMinHistoricalVolFraction,
+                real64 const &phaseMaxHistoricalVolFraction,
+                real64 const &phaseMode2PeakVolFraction,
+                arrayView1d<TableFunction::KernelWrapper const> const &capPresKernelWrappers,
+                KilloughHysteresis::HysteresisCurve const &wettingCurve,
+                KilloughHysteresis::HysteresisCurve const &nonWettingCurve,
+                real64 const &landParam,
+                real64 const &phaseIntermediateMinVolFraction,
+                real64 const &killoughCurvatureParam,
+                real64 const &jerauldParam_a,
+                real64 const &jerauldParam_b,
+                bool const isWettingPhase,
+                real64 const precomputedScrt,
+                real64 const precomputedDenomF,
+                real64 const precomputedShy) const
+        {
+            GEOS_UNUSED_VAR( ipPhase, landParam, jerauldParam_a, jerauldParam_b );
+            real64 pc = 0.0;
+            real64 dpc_dS = 0.0;
+            
+            // For pure drainage or imbibition modes, use the table directly
+            if (mode == fields::cappres::ModeIndexType::DRAINAGE || mode == fields::cappres::ModeIndexType::IMBIBITION) {
+                integer const arrayIndex = (mode == fields::cappres::ModeIndexType::DRAINAGE) ? fields::cappres::ModeIndexType::DRAINAGE : fields::cappres::ModeIndexType::IMBIBITION;
+                if (arrayIndex < static_cast<integer>(capPresKernelWrappers.size())) {
+                    constexpr bool ENABLE_COMPUTE_PC_DEBUG = false;
+                    if constexpr (ENABLE_COMPUTE_PC_DEBUG) {
+                      std::cout << "[COMPUTE_PC_DEBUG] computeCapillaryPressureForSaturation: mode=" 
+                                << (mode == fields::cappres::ModeIndexType::DRAINAGE ? "DRAINAGE" : "IMBIBITION")
+                                << ", arrayIndex=" << arrayIndex 
+                                << ", S=" << S 
+                                << ", capPresKernelWrappers.size()=" << capPresKernelWrappers.size() << std::endl;
+                    }
+                    pc = capPresKernelWrappers[arrayIndex].compute(&S, &dpc_dS);
+                    if constexpr (ENABLE_COMPUTE_PC_DEBUG) {
+                      std::cout << "[COMPUTE_PC_DEBUG] After table.compute: pc=" << pc << ", dpc_dS=" << dpc_dS << std::endl;
+                    }
+                }
+            }
+            // For scanning curves (DRAINAGE_TO_IMBIBITION or IMBIBITION_TO_DRAINAGE)
+            else {
+                // Precomputed values should be provided by caller (from computeFlux before local_solver)
+                // If not provided, fall back to drainage curve to avoid calling computeTrappedCriticalPhaseVolFraction
+                if (precomputedScrt < 0.0) {
+                    // Precomputed values not provided - return drainage curve value
+                    real64 const arrayIndex = fields::cappres::ModeIndexType::DRAINAGE;
+                    if (arrayIndex < static_cast<integer>(capPresKernelWrappers.size())) {
+                        pc = capPresKernelWrappers[arrayIndex].compute(&S, &dpc_dS);
+                    }
+                    return pc;
+                }
+                
+                real64 dpci_dS, dpcd_dS;
+                real64 const pci = capPresKernelWrappers[fields::cappres::ModeIndexType::IMBIBITION].compute(&S, &dpci_dS);
+                real64 const pcd = capPresKernelWrappers[fields::cappres::ModeIndexType::DRAINAGE].compute(&S, &dpcd_dS);
+                
+                real64 const E = killoughCurvatureParam;
+                
+                if (isWettingPhase) {
+                    real64 const Smin = wettingCurve.oppositeBoundPhaseVolFraction;
+                    real64 const Smax = wettingCurve.drainageExtremaPhaseVolFraction;
+                    
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                        // DRAINAGE_TO_IMBIBITION: transitioning from drainage (low S) to imbibition (high S)
+                        // Shy should be the minimum historical saturation (where drainage started)
+                    real64 const Shy = (precomputedShy >= 0.0) ? precomputedShy : 
+                                      ((phaseMinHistoricalVolFraction > Smin) ? phaseMinHistoricalVolFraction : Smin);
+                    
+                        // Use precomputed value - should have been computed before local_solver
+                        real64 const Scrt = precomputedScrt;
+                        // For wetting curve, Scrt IS the max wetting saturation (Swma = Scrt)
+                        // This matches the forward compute: Swma = 1 - (1 - Scrt) = Scrt
+                        real64 const Swma = 1 - (1 - Scrt);
+                        real64 denomF = precomputedDenomF;
+                        if (LvArray::math::abs(precomputedDenomF) < 1e-15) {
+                            denomF = (1. / (Swma - Shy + E) - 1. / E);
+                        }
+                        // Guard against division by zero
+                        real64 F = 0.0;
+                        if (LvArray::math::abs(denomF) >= 1e-15) {
+                            real64 const F_num = (1. / (S - Shy + E) - 1. / E);
+                            F = F_num / denomF;
+                        }
+                        F = LvArray::math::max(F, 0.0);
+                        F = LvArray::math::min(F, 1.0);
+                        
+                        pc = pcd + F * (pci - pcd);
+                        dpc_dS = dpcd_dS + F * (dpci_dS - dpcd_dS);
+                    }
+                    else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                        // IMBIBITION_TO_DRAINAGE: transitioning from imbibition (high S) to drainage (low S)
+                        // Shy should be the maximum historical saturation (where imbibition started)
+                        real64 const Shy = (precomputedShy >= 0.0) ? precomputedShy : 
+                                          ((phaseMaxHistoricalVolFraction < Smax) ? phaseMaxHistoricalVolFraction : Smax);
+                        
+                        // Use precomputed value - should have been computed before local_solver
+                        real64 const Scrt = precomputedScrt;
+                        
+                        real64 denomF = precomputedDenomF;
+                        if (LvArray::math::abs(precomputedDenomF) < 1e-15) {
+                            denomF = (1. / (Shy - Scrt + E) - 1. / E);
+                        }
+                        // Guard against division by zero
+                        real64 F = 0.0;
+                        if (LvArray::math::abs(denomF) >= 1e-15) {
+                            real64 const F_num = (1. / (Shy - S + E) - 1. / E);
+                            F = F_num / denomF;
+                        }
+                        F = LvArray::math::max(F, 0.0);
+                        F = LvArray::math::min(F, 1.0);
+                        
+                        pc = pci + F * (pcd - pci);
+                        dpc_dS = dpci_dS + F * (dpcd_dS - dpci_dS);
+                    }
+                    else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                        // IMBIBITION_TO_DRAINAGE_FROM_SCANNING: Secondary drainage scanning curve (Mode 4)
+                        // Based on Killough (1976) - solve quadratic for ghost departure point
+                        real64 const H = (phaseMinHistoricalVolFraction > Smin) ? phaseMinHistoricalVolFraction : Smin;
+                        real64 S_star = phaseMode2PeakVolFraction;
+                        if (S_star < 1e-12 || S_star >= Smax - 1e-12) {
+                            if (phaseMaxHistoricalVolFraction > H + 1e-12 && phaseMaxHistoricalVolFraction < Smax - 1e-12) {
+                                S_star = phaseMaxHistoricalVolFraction;
+                            } else {
+                                S_star = LvArray::math::max(H + 0.1, LvArray::math::min(S, Smax - 0.01));
+                            }
+                        }
+                        
+                        // Compute F_known from Mode 2 at S_star
+                        real64 const Scrt = precomputedScrt;
+                        // For wetting curve, Scrt IS the max wetting saturation (Swma = Scrt)
+                        real64 const Swma = 1 - (1 - Scrt);
+                        real64 F_known = 0.0;
+                        if (S_star <= Swma + 1e-12) {
+                            real64 const F_num = (1. / (S_star - H + E) - 1. / E);
+                            real64 const F_denom = (1. / (Swma - H + E) - 1. / E);
+                            if (LvArray::math::abs(F_denom) > 1e-12) {
+                                F_known = F_num / F_denom;
+                            }
+                        }
+                        F_known = LvArray::math::max(0.0, LvArray::math::min(1.0, F_known));
+                        
+                        // F_star_target = 1 - F_known
+                        real64 const F_star_target = 1.0 - F_known;
+                        
+                        // Solve quadratic for x (ghost departure point)
+                        real64 const a = S_star;
+                        real64 const b = H;  // Use H so curve rejoins drainage at H
+                        real64 const T = F_star_target;
+                        real64 const coeff_A = (1.0 - T);
+                        real64 const coeff_B = -(1.0 - T) * (a + b - 2.0 * E) - (1.0 - T) * E;
+                        real64 const coeff_C = (1.0 - T) * (a - E) * (b - E)
+                                             - E * E * (1.0 + T)
+                                             - E * (T * a - b);
+                        
+                        real64 x = S_star;
+                        real64 discriminant = coeff_B * coeff_B - 4.0 * coeff_A * coeff_C;
+                        if (discriminant >= 0.0 && LvArray::math::abs(coeff_A) > 1e-14) {
+                            real64 sqrt_disc = LvArray::math::sqrt(discriminant);
+                            real64 x1 = (-coeff_B + sqrt_disc) / (2.0 * coeff_A);
+                            real64 x2 = (-coeff_B - sqrt_disc) / (2.0 * coeff_A);
+                            if (x1 > S_star - 1e-8 && x2 > S_star - 1e-8) {
+                                x = LvArray::math::min(x1, x2);
+                            } else if (x1 > S_star - 1e-8) {
+                                x = x1;
+                            } else if (x2 > S_star - 1e-8) {
+                                x = x2;
+                            }
+                        }
+                        
+                        // Compute F_star: F_star = [1/(x - S + E) - 1/E] / [1/(x - H + E) - 1/E]
+                        real64 F_star = 1.0;
+                        real64 const F_star_num = (1. / (x - S + E) - 1. / E);
+                        real64 const F_star_denom = (1. / (x - H + E) - 1. / E);
+                        if (LvArray::math::abs(F_star_denom) > 1e-12) {
+                            F_star = F_star_num / F_star_denom;
+                            F_star = LvArray::math::max(0.0, LvArray::math::min(1.0, F_star));
+                        }
+                        
+                        // Pc = Pc_Im + F_star * (Pc_Dr - Pc_Im)
+                        pc = pci + F_star * (pcd - pci);
+                        dpc_dS = dpci_dS + F_star * (dpcd_dS - dpci_dS);
+                    }
+                }
+                else {
+                    // Non-wetting phase
+                    real64 const Smax = nonWettingCurve.oppositeBoundPhaseVolFraction;
+                    real64 const Shy = (precomputedShy >= 0.0) ? precomputedShy :
+                                      ((phaseMaxHistoricalVolFraction < Smax) ? phaseMaxHistoricalVolFraction : Smax);
+                    
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                        // Use precomputed value - should have been computed before local_solver
+                        real64 const Scrt = precomputedScrt;
+                        
+                        real64 denomF = precomputedDenomF;
+                        if (LvArray::math::abs(precomputedDenomF) < 1e-15) {
+                            denomF = (1. / (Shy - Scrt + E) - 1. / E);
+                        }
+                        // Guard against division by zero
+                        real64 F = 0.0;
+                        if (LvArray::math::abs(denomF) >= 1e-15) {
+                            real64 const F_num = (1. / (Shy - S + E) - 1. / E);
+                            F = F_num / denomF;
+                        }
+                        F = LvArray::math::max(F, 0.0);
+                        F = LvArray::math::min(F, 1.0);
+                        
+                        pc = pcd + F * (pci - pcd);
+                        dpc_dS = dpci_dS + F * (dpci_dS - dpcd_dS);
+                        // Note: there's also a dF/dS term in the non-wetting case, but for inversion we approximate
+                    }
+                    else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                        // Use precomputed value - should have been computed before local_solver
+                        real64 const Scrt = precomputedScrt;
+                        real64 const Sgma = 1. - Scrt - phaseIntermediateMinVolFraction;
+                        
+                        real64 denomF = precomputedDenomF;
+                        if (LvArray::math::abs(precomputedDenomF) < 1e-15) {
+                            denomF = (1. / (Sgma - Shy + E) - 1. / E);
+                        }
+                        // Guard against division by zero
+                        real64 F = 0.0;
+                        if (LvArray::math::abs(denomF) >= 1e-15) {
+                            real64 const F_num = (1. / (S - Shy + E) - 1. / E);
+                            F = F_num / denomF;
+                        }
+                        F = LvArray::math::max(F, 0.0);
+                        F = LvArray::math::min(F, 1.0);
+                        
+                        pc = pci + F * (pcd - pci);
+                        dpc_dS = dpcd_dS + F * (dpcd_dS - dpci_dS);
+                        // Note: there's also a dF/dS term in the non-wetting case, but for inversion we approximate
+                    }
+                }
+            }
+            
+            return pc;
+        }
+
+        void
+        TableCapillaryPressureHysteresis::KernelWrapper::computeInv(
+                arraySlice1d<real64, compflow::USD_PHASE - 1> const &phaseVolFraction,
+                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseMaxHistoricalVolFraction,
+                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseMinHistoricalVolFraction,
+                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseMode2PeakVolFraction,
+                arraySlice1d<real64 const, cappres::USD_CAPPRES - 2> const &phaseTrappedVolFrac,
+                arraySlice1d<real64 const, cappres::USD_CAPPRES - 2> const &phaseCapPressure,
+                arraySlice2d<real64, cappres::USD_CAPPRES_DS - 2> const &dPhaseCapPressure_dPhaseVolFrac,
+                fields::cappres::ModeIndexType const &mode) const
+        {
+            GEOS_UNUSED_VAR( phaseTrappedVolFrac );
+            LvArray::forValuesInSlice(dPhaseCapPressure_dPhaseVolFrac, [](real64 &val) { val = 0.0; });
+
+            constexpr bool ENABLE_COMPUTEINV_PATH_DEBUG = false;
+            if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+              std::cout << "[COMPUTEINV_PATH] Entry to computeInv(), mode=" 
+                        << (mode == fields::cappres::ModeIndexType::DRAINAGE ? "DRAINAGE" : 
+                            mode == fields::cappres::ModeIndexType::IMBIBITION ? "IMBIBITION" : "SCANNING") << std::endl;
+            }
+
+            using PT = CapillaryPressureBase::PhaseType;
+            integer const ipWater = (PT::WATER < m_phaseOrder.size()) ? m_phaseOrder[PT::WATER] : -1;
+            integer const ipOil = (PT::OIL < m_phaseOrder.size()) ? m_phaseOrder[PT::OIL] : -1;
+            integer const ipGas = (PT::GAS < m_phaseOrder.size()) ? m_phaseOrder[PT::GAS] : -1;
+            
+            if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+              std::cout << "[COMPUTEINV_PATH] Phase indices: ipWater=" << ipWater 
+                        << ", ipOil=" << ipOil << ", ipGas=" << ipGas << std::endl;
+              std::cout << "[COMPUTEINV_PATH] After phase indices calculation, continuing..." << std::endl;
+            }
+
+            constexpr real64 tol = 1e-9;
+            constexpr integer maxIter = 20;
+            constexpr real64 minS = 0.0;
+            constexpr real64 maxS = 1.0;
+
+            // Determine which phase pairs need inversion
+            if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+              std::cout << "[COMPUTEINV_PATH] Checking phase combination..." << std::endl;
+              std::cout << "[COMPUTEINV_PATH] ipWater=" << ipWater << ", ipOil=" << ipOil << ", ipGas=" << ipGas << std::endl;
+              bool isThreePhase = (ipWater >= 0 && ipOil >= 0 && ipGas >= 0);
+              std::cout << "[COMPUTEINV_PATH] Three-phase condition: " << (isThreePhase ? "TRUE" : "FALSE") << std::endl;
+              std::cout << "[COMPUTEINV_PATH] About to check three-phase if statement..." << std::endl;
+            }
+            if (ipWater >= 0 && ipOil >= 0 && ipGas >= 0) {
+                if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                  std::cout << "[COMPUTEINV_PATH] Taking THREE-PHASE path" << std::endl;
+                }
+                // Three-phase: invert wetting and non-wetting capillary pressures
+                
+                // 1. Invert wetting phase (water-oil capillary pressure)
+                constexpr real64 pcEpsilon = 1e-10;
+                constexpr bool ENABLE_INVERSE_TABLE_DEBUG = false;
+                if (ipWater >= 0 && LvArray::math::abs(phaseCapPressure[ipWater]) > pcEpsilon) {
+                    // For pure DRAINAGE or IMBIBITION modes, use direct table lookup (analytical inverse)
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE || mode == fields::cappres::ModeIndexType::IMBIBITION) {
+                        integer const arrayIndex = (mode == fields::cappres::ModeIndexType::DRAINAGE) ? 0 : 1;
+                        array1d<real64> input(1);
+                        input[0] = phaseCapPressure[ipWater];
+                        auto inputSlice = input.toSliceConst();
+                        
+                        if constexpr (ENABLE_INVERSE_TABLE_DEBUG) {
+                          real64 S_before = phaseVolFraction[ipWater];
+                          real64 dS_dPc_before = dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater];
+                          std::cout << "[INVERSE_TABLE_DEBUG] Cell1 (water), mode=" << (mode == fields::cappres::ModeIndexType::DRAINAGE ? "DRAINAGE" : "IMBIBITION") 
+                                    << ", arrayIndex=" << arrayIndex << std::endl;
+                          std::cout << "  Input Pc=" << input[0] << std::endl;
+                          std::cout << "  S before inverse table=" << S_before << std::endl;
+                          std::cout << "  dS_dPc before inverse table=" << dS_dPc_before << std::endl;
+                        }
+                        
+                        // Match TableCapillaryPressure exactly: pass derivative pointer directly to inverse table
+                        // Note: The inverse table returns dS/dPc, but we store it directly like TableCapillaryPressure does
+                        // The local solver will call compute() afterwards to get the correct dPc/dS derivative
+                        phaseVolFraction[ipWater] = m_inverseWettingIntermediateCapillaryPressureKernelWrappers[arrayIndex].compute(
+                                inputSlice, &dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater]);
+                        
+                        if constexpr (ENABLE_INVERSE_TABLE_DEBUG) {
+                          real64 S_after = phaseVolFraction[ipWater];
+                          real64 dS_dPc_after = dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater];
+                          std::cout << "  S after inverse table=" << S_after << std::endl;
+                          std::cout << "  dS_dPc after inverse table=" << dS_dPc_after << std::endl;
+                        }
+                        
+                        phaseVolFraction[ipOil] = 1.0 - phaseVolFraction[ipWater] - phaseVolFraction[ipGas];
+                        // Direct lookup complete, skip Newton-Raphson
+                    } else {
+                        // For scanning curves, use analytical inverse if possible, otherwise Newton-Raphson
+                        // TEMPORARY: Flag to enable analytical inverse for scanning curves
+                        constexpr bool USE_ANALYTICAL_INVERSE_SCANNING = true;
+                        
+                    real64 S_guess = phaseMaxHistoricalVolFraction[ipWater];
+                    if (S_guess <= phaseMinHistoricalVolFraction[ipWater] || S_guess < minS || S_guess > maxS) {
+                        // Fall back to drainage/imbibition curve evaluation if available
+                        real64 const Smin = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                        real64 const Smax = m_wettingCurve.drainageExtremaPhaseVolFraction;
+                        S_guess = 0.5 * (Smin + Smax);
+                        S_guess = LvArray::math::max(S_guess, minS);
+                        S_guess = LvArray::math::min(S_guess, maxS);
+                    }
+                    
+                    // Precompute fixed parameters for scanning curves (these don't change during Newton-Raphson)
+                    real64 precomputedScrt_water = -1.0;
+                    real64 precomputedDenomF_water = 0.0;
+                    real64 precomputedShy_water = -1.0;
+                    
+                    // Precompute for scanning curves (Mode 2, Mode 3, or Mode 4)
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                        mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE ||
+                        mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                        real64 const Smin = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                        real64 const Smax = m_wettingCurve.drainageExtremaPhaseVolFraction;
+                        real64 const E = m_killoughCurvatureParamCapPres;
+                        
+                        if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                            // DRAINAGE_TO_IMBIBITION: Shy should be minimum historical (where drainage started)
+                            precomputedShy_water = (phaseMinHistoricalVolFraction[ipWater] > Smin) ? 
+                                                  phaseMinHistoricalVolFraction[ipWater] : Smin;
+                            
+                            // Compute Scrt for DRAINAGE_TO_IMBIBITION scanning curve (wetting phase)
+                            real64 Scrt = 0.0;
+                            KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, precomputedShy_water,
+                                                                                       m_landParam[ipWater],
+                                                                                       m_jerauldParam_a, m_jerauldParam_b,
+                                                                                       Scrt);
+                            precomputedScrt_water = Scrt;
+                            // For wetting curve, Scrt IS the max wetting saturation (Swma = Scrt)
+                            real64 const Swma = 1. - (1. - Scrt);
+                            // Compute denomF for DRAINAGE_TO_IMBIBITION: denomF = (1. / (Swma - Shy + E) - 1. / E)
+                            precomputedDenomF_water = (1. / (Swma - precomputedShy_water + E) - 1. / E);
+                        }
+                        else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                            // IMBIBITION_TO_DRAINAGE: Shy should be maximum historical (where imbibition started)
+                            precomputedShy_water = (phaseMaxHistoricalVolFraction[ipWater] < Smax) ? 
+                                                  phaseMaxHistoricalVolFraction[ipWater] : Smax;
+                            
+                            // Compute Scrt for IMBIBITION_TO_DRAINAGE scanning curve (wetting phase)
+                            real64 Scrt = 0.0;
+                            KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, precomputedShy_water,
+                                                                                       m_landParam[ipWater],
+                                                                                       m_jerauldParam_a, m_jerauldParam_b,
+                                                                                       Scrt);
+                            precomputedScrt_water = Scrt;
+                            // Compute denomF for IMBIBITION_TO_DRAINAGE: denomF = (1. / (Shy - Scrt + E) - 1. / E)
+                            precomputedDenomF_water = (1. / (precomputedShy_water - Scrt + E) - 1. / E);
+                        }
+                        else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                            // Mode 4: IMBIBITION_TO_DRAINAGE_FROM_SCANNING
+                            // H (first reversal point) should be minimum historical (where imbibition started)
+                            // This is used to compute Scrt for Mode 4
+                            real64 const H = (phaseMinHistoricalVolFraction[ipWater] > Smin) ? 
+                                           phaseMinHistoricalVolFraction[ipWater] : Smin;
+                            
+                            // Compute Scrt for Mode 4 based on H (first reversal point)
+                            real64 Scrt = 0.0;
+                            KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, H,
+                                                                                       m_landParam[ipWater],
+                                                                                       m_jerauldParam_a, m_jerauldParam_b,
+                                                                                       Scrt);
+                            precomputedScrt_water = Scrt;
+                            // For Mode 4, precomputedShy is not used in the same way, but set it to H for consistency
+                            precomputedShy_water = H;
+                            // denomF is not used for Mode 4 (it solves quadratic instead), but set to 0 to indicate it's not applicable
+                            precomputedDenomF_water = 0.0;
+                        }
+                    }
+                    
+                    real64 S = S_guess;
+                    
+                    // Try analytical inverse for scanning curves if enabled
+                    if (USE_ANALYTICAL_INVERSE_SCANNING) {
+                        // Use inverse tables to get bounds: S_dr(Pc) and S_im(Pc)
+                        array1d<real64> input_dr(1), input_im(1);
+                        input_dr[0] = phaseCapPressure[ipWater];
+                        input_im[0] = phaseCapPressure[ipWater];
+                        auto inputSlice_dr = input_dr.toSliceConst();
+                        auto inputSlice_im = input_im.toSliceConst();
+                        
+                        real64 dS_dPc_dr = 0.0, dS_dPc_im = 0.0;
+                        real64 S_dr = m_inverseWettingIntermediateCapillaryPressureKernelWrappers[ModeIndexType::DRAINAGE].compute(
+                            inputSlice_dr, &dS_dPc_dr);
+                        real64 S_im = m_inverseWettingIntermediateCapillaryPressureKernelWrappers[ModeIndexType::IMBIBITION].compute(
+                            inputSlice_im, &dS_dPc_im);
+                        
+                        // Clamp to valid range
+                        S_dr = LvArray::math::max(minS, LvArray::math::min(maxS, S_dr));
+                        S_im = LvArray::math::max(minS, LvArray::math::min(maxS, S_im));
+                        
+                        // For scanning curves, S is between S_dr and S_im (order depends on mode)
+                        real64 S_low = LvArray::math::min(S_dr, S_im);
+                        real64 S_high = LvArray::math::max(S_dr, S_im);
+                        
+                        // Use analytical inverse based on F(S) formula
+                        real64 const E = m_killoughCurvatureParamCapPres;
+                        real64 const Pc_target = phaseCapPressure[ipWater];
+                        
+                        if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                            // DRAINAGE_TO_IMBIBITION: Pc = Pc_dr(S) + F(S) * [Pc_im(S) - Pc_dr(S)]
+                            // F(S) = (1. / (S - Shy + E) - 1. / E) / denomF
+                            // Rearranging: S = Shy - E + 1 / (F(S) * denomF + 1/E)
+                            real64 const Shy = precomputedShy_water;
+                            real64 const denomF = precomputedDenomF_water;
+                            
+                            // Initial guess: interpolate between S_dr and S_im
+                            S = 0.5 * (S_low + S_high);
+                            
+                            // Fixed-point iteration using analytical F(S) formula
+                            for (integer iter = 0; iter < 10; ++iter) {
+                                // Compute F(S) from current S
+                                real64 F_S = (1. / (S - Shy + E) - 1. / E) / denomF;
+                                F_S = LvArray::math::max(0.0, LvArray::math::min(1.0, F_S));
+                                
+                                // Compute Pc(S) to check convergence
+                                real64 pc_computed = this->computeCapillaryPressureForSaturation(
+                                    S, mode, ipWater,
+                                    phaseMinHistoricalVolFraction[ipWater],
+                                    phaseMaxHistoricalVolFraction[ipWater],
+                                    phaseMode2PeakVolFraction[ipWater],
+                                    m_wettingIntermediateCapillaryPressureKernelWrappers,
+                                    m_wettingCurve,
+                                    m_nonWettingCurve,
+                                    m_landParam[ipWater],
+                                    m_phaseIntermediateMinVolFraction,
+                                    m_killoughCurvatureParamCapPres,
+                                    m_jerauldParam_a,
+                                    m_jerauldParam_b,
+                                    true, // isWettingPhase
+                                    precomputedScrt_water,
+                                    precomputedDenomF_water,
+                                    precomputedShy_water);
+                                
+                                if (LvArray::math::abs(pc_computed - Pc_target) < tol) {
+                                    break;
+                                }
+                                
+                                real64 denom_F = F_S * denomF + 1. / E;
+                                if (LvArray::math::abs(denom_F) > 1e-12) {
+                                    real64 S_new = Shy - E + 1. / denom_F;
+                                    S_new = LvArray::math::max(S_low, LvArray::math::min(S_high, S_new));
+                                    S = S_new;
+                                } else {
+                                    // Fall back to interpolation if denominator is too small
+                                    S = 0.5 * (S + 0.5 * (S_low + S_high));
+                                }
+                            }
+                        }
+                        else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                            // IMBIBITION_TO_DRAINAGE: Pc = Pc_im(S) + F(S) * [Pc_dr(S) - Pc_im(S)]
+                            // F(S) = (1. / (S - Shy + E) - 1. / E) / denomF
+                            real64 const Shy = precomputedShy_water;
+                            real64 const denomF = precomputedDenomF_water;
+                            
+                            S = 0.5 * (S_low + S_high);
+                            
+                            for (integer iter = 0; iter < 10; ++iter) {
+                                real64 F_S = (1. / (S - Shy + E) - 1. / E) / denomF;
+                                F_S = LvArray::math::max(0.0, LvArray::math::min(1.0, F_S));
+                                
+                                real64 pc_computed = this->computeCapillaryPressureForSaturation(
+                                    S, mode, ipWater,
+                                    phaseMinHistoricalVolFraction[ipWater],
+                                    phaseMaxHistoricalVolFraction[ipWater],
+                                    phaseMode2PeakVolFraction[ipWater],
+                                    m_wettingIntermediateCapillaryPressureKernelWrappers,
+                                    m_wettingCurve,
+                                    m_nonWettingCurve,
+                                    m_landParam[ipWater],
+                                    m_phaseIntermediateMinVolFraction,
+                                    m_killoughCurvatureParamCapPres,
+                                    m_jerauldParam_a,
+                                    m_jerauldParam_b,
+                                    true, // isWettingPhase
+                                    precomputedScrt_water,
+                                    precomputedDenomF_water,
+                                    precomputedShy_water);
+                                
+                                if (LvArray::math::abs(pc_computed - Pc_target) < tol) {
+                                    break;
+                                }
+                                
+                                real64 denom_F = F_S * denomF + 1. / E;
+                                if (LvArray::math::abs(denom_F) > 1e-12) {
+                                    real64 S_new = Shy - E + 1. / denom_F;
+                                    S_new = LvArray::math::max(S_low, LvArray::math::min(S_high, S_new));
+                                    S = S_new;
+                                } else {
+                                    S = 0.5 * (S + 0.5 * (S_low + S_high));
+                                }
+                            }
+                        }
+                        // For IMBIBITION_TO_DRAINAGE_FROM_SCANNING, fall through to Newton-Raphson (more complex F_star formula)
+                    }
+                    
+                    real64 pc_check = this->computeCapillaryPressureForSaturation(
+                        S, mode, ipWater,
+                        phaseMinHistoricalVolFraction[ipWater],
+                        phaseMaxHistoricalVolFraction[ipWater],
+                        phaseMode2PeakVolFraction[ipWater],
+                        m_wettingIntermediateCapillaryPressureKernelWrappers,
+                        m_wettingCurve,
+                        m_nonWettingCurve,
+                        m_landParam[ipWater],
+                        m_phaseIntermediateMinVolFraction,
+                        m_killoughCurvatureParamCapPres,
+                        m_jerauldParam_a,
+                        m_jerauldParam_b,
+                        true, // isWettingPhase
+                        precomputedScrt_water,
+                        precomputedDenomF_water,
+                        precomputedShy_water);
+                    
+                    bool needs_newton = (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) ||
+                                       (LvArray::math::abs(pc_check - phaseCapPressure[ipWater]) >= tol);
+                    
+                    if (needs_newton) {
+                        real64 residual_prev = 1e30;
+                    
+                    for (integer iter = 0; iter < maxIter; ++iter) {
+                        // Compute Pc(S) using the helper function
+                        real64 pc_computed = this->computeCapillaryPressureForSaturation(
+                            S, mode, ipWater,
+                            phaseMinHistoricalVolFraction[ipWater],
+                            phaseMaxHistoricalVolFraction[ipWater],
+                                phaseMode2PeakVolFraction[ipWater],
+                            m_wettingIntermediateCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipWater],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            true, // isWettingPhase
+                            precomputedScrt_water,
+                            precomputedDenomF_water,
+                            precomputedShy_water);
+                        
+                        real64 residual = pc_computed - phaseCapPressure[ipWater];
+                        
+                        if (LvArray::math::abs(residual) < tol) {
+                            break;
+                        }
+                        
+                        // Compute derivative dPc/dS using adaptive finite difference
+                        // Use relative step size to handle different scales
+                        real64 const dS = LvArray::math::max(1e-8, 1e-6 * LvArray::math::max(LvArray::math::abs(S), 1e-6));
+                        real64 S_pert = S + dS;
+                        if (S_pert > maxS) {
+                            S_pert = LvArray::math::max(S - dS, minS);
+                        }
+                        
+                        real64 const pc_pert = this->computeCapillaryPressureForSaturation(
+                            S_pert, mode, ipWater,
+                            phaseMinHistoricalVolFraction[ipWater],
+                            phaseMaxHistoricalVolFraction[ipWater],
+                            phaseMode2PeakVolFraction[ipWater],
+                            m_wettingIntermediateCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipWater],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            true, // isWettingPhase
+                            precomputedScrt_water,
+                            precomputedDenomF_water,
+                            precomputedShy_water);
+                        
+                        real64 const dpc_dS = (pc_pert - pc_computed) / (S_pert - S);
+                        
+                        if (LvArray::math::abs(dpc_dS) > 1e-12) {
+                            real64 const newtonStep = -residual / dpc_dS;
+                            real64 const maxStep = 0.1; // Limit step size to prevent overshooting
+                            real64 const step = LvArray::math::max(-maxStep, LvArray::math::min(maxStep, newtonStep));
+                            
+                            real64 S_new = S + step;
+                            
+                            // Line search: if residual increases, reduce step
+                            if (iter > 0 && LvArray::math::abs(residual) > LvArray::math::abs(residual_prev)) {
+                                // Backtrack: use smaller step
+                                S_new = S + 0.5 * step;
+                            }
+                            
+                            // Clamp to valid range
+                            S_new = LvArray::math::max(S_new, minS);
+                            S_new = LvArray::math::min(S_new, maxS);
+                            
+                            if (LvArray::math::abs(S_new - S) < 1e-10 && 
+                                (S_new <= minS + 1e-10 || S_new >= maxS - 1e-10)) {
+                                // Use bisection between current guess and boundary
+                                S_new = 0.5 * (S + (S_new <= minS + 1e-10 ? minS : maxS));
+                            }
+                            
+                            residual_prev = residual;
+                            S = S_new;
+                        } else {
+                            // If derivative is zero or very small, use bisection
+                            real64 const S_low = LvArray::math::max(S - 0.1, minS);
+                            real64 const S_high = LvArray::math::min(S + 0.1, maxS);
+                            S = 0.5 * (S_low + S_high);
+                            S = LvArray::math::max(S, minS);
+                            S = LvArray::math::min(S, maxS);
+                        }
+                    }
+                    
+                    phaseVolFraction[ipWater] = S;
+                    phaseVolFraction[ipOil] = 1.0 - S - phaseVolFraction[ipGas];
+                    
+                    // Compute derivative at final S
+                    real64 dpc_dS_final = 0.0;
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE || mode == fields::cappres::ModeIndexType::IMBIBITION) {
+                        integer const arrayIndex = (mode == fields::cappres::ModeIndexType::DRAINAGE) ? fields::cappres::ModeIndexType::DRAINAGE : fields::cappres::ModeIndexType::IMBIBITION;
+                        m_wettingIntermediateCapillaryPressureKernelWrappers[arrayIndex].compute(&S, &dpc_dS_final);
+                    } else {
+                        // For scanning curves, compute derivative using finite difference
+                        real64 const dS_final = 1e-6;
+                        real64 const S_pert_final = LvArray::math::min(S + dS_final, maxS);
+                        real64 const pc_final = this->computeCapillaryPressureForSaturation(
+                            S, mode, ipWater,
+                            phaseMinHistoricalVolFraction[ipWater],
+                            phaseMaxHistoricalVolFraction[ipWater],
+                            phaseMode2PeakVolFraction[ipWater],
+                            m_wettingIntermediateCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipWater],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            true, // isWettingPhase
+                            precomputedScrt_water,
+                            precomputedDenomF_water,
+                            precomputedShy_water);
+                        real64 const pc_pert_final = this->computeCapillaryPressureForSaturation(
+                            S_pert_final, mode, ipWater,
+                            phaseMinHistoricalVolFraction[ipWater],
+                            phaseMaxHistoricalVolFraction[ipWater],
+                            phaseMode2PeakVolFraction[ipWater],
+                            m_wettingIntermediateCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipWater],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            true, // isWettingPhase
+                            precomputedScrt_water,
+                            precomputedDenomF_water,
+                            precomputedShy_water);
+                        dpc_dS_final = (pc_pert_final - pc_final) / dS_final;
+                    }
+                    dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater] = dpc_dS_final;
+                    } // End else block for scanning curves
+                }
+                } // Close if (ipWater >= 0) block
+                
+                // 2. Invert non-wetting phase (gas-oil capillary pressure)
+                if (ipGas >= 0 && LvArray::math::abs(phaseCapPressure[ipGas]) > pcEpsilon) {
+                    // For pure DRAINAGE or IMBIBITION modes, use direct table lookup (analytical inverse)
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE || mode == fields::cappres::ModeIndexType::IMBIBITION) {
+                        integer const arrayIndex = (mode == fields::cappres::ModeIndexType::DRAINAGE) ? 0 : 1;
+                        array1d<real64> input(1);
+                        input[0] = phaseCapPressure[ipGas];
+                        auto inputSlice = input.toSliceConst();
+                        
+                        if constexpr (ENABLE_INVERSE_TABLE_DEBUG) {
+                          real64 S_before = phaseVolFraction[ipGas];
+                          real64 dS_dPc_before = dPhaseCapPressure_dPhaseVolFrac[ipGas][ipGas];
+                          std::cout << "[INVERSE_TABLE_DEBUG] Cell2 (gas), mode=" << (mode == fields::cappres::ModeIndexType::DRAINAGE ? "DRAINAGE" : "IMBIBITION") 
+                                    << ", arrayIndex=" << arrayIndex << std::endl;
+                          std::cout << "  Input Pc=" << input[0] << std::endl;
+                          std::cout << "  S before inverse table=" << S_before << std::endl;
+                          std::cout << "  dS_dPc before inverse table=" << dS_dPc_before << std::endl;
+                        }
+                        
+                        // Match TableCapillaryPressure exactly: pass derivative pointer directly to inverse table
+                        // Note: The inverse table returns dS/dPc, but we store it directly like TableCapillaryPressure does
+                        // The local solver will call compute() afterwards to get the correct dPc/dS derivative
+                        phaseVolFraction[ipGas] = m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers[arrayIndex].compute(
+                                inputSlice, &dPhaseCapPressure_dPhaseVolFrac[ipGas][ipGas]);
+                        
+                        if constexpr (ENABLE_INVERSE_TABLE_DEBUG) {
+                          real64 S_after = phaseVolFraction[ipGas];
+                          real64 dS_dPc_after = dPhaseCapPressure_dPhaseVolFrac[ipGas][ipGas];
+                          std::cout << "  S after inverse table=" << S_after << std::endl;
+                          std::cout << "  dS_dPc after inverse table=" << dS_dPc_after << std::endl;
+                        }
+                        
+                        if (ipWater >= 0 && ipOil >= 0) {
+                            phaseVolFraction[ipOil] = 1.0 - phaseVolFraction[ipWater] - phaseVolFraction[ipGas];
+                        }
+                        // Direct lookup complete, skip Newton-Raphson
+                    } else {
+                        // For scanning curves, use Newton-Raphson
+                    // Note: For non-wetting phase, the capillary pressure is typically negative
+                    // and the relationship may be inverted (increasing Pc with decreasing S)
+                    real64 S_guess = phaseMaxHistoricalVolFraction[ipGas];
+                    if (S_guess <= phaseMinHistoricalVolFraction[ipGas] || S_guess < minS || S_guess > maxS) {
+                        real64 const Smin = m_nonWettingCurve.imbibitionExtremaPhaseVolFraction;
+                        real64 const Smax = m_nonWettingCurve.drainageExtremaPhaseVolFraction;
+                        S_guess = 0.5 * (Smin + Smax);
+                        S_guess = LvArray::math::max(S_guess, minS);
+                        S_guess = LvArray::math::min(S_guess, maxS);
+                    }
+                    
+                    // Precompute fixed parameters for scanning curves (these don't change during Newton-Raphson)
+                    real64 precomputedScrt_gas = -1.0;
+                    real64 precomputedDenomF_gas = 0.0;
+                    real64 precomputedShy_gas = -1.0;
+                    
+                    // Only precompute for scanning curves (DRAINAGE_TO_IMBIBITION or IMBIBITION_TO_DRAINAGE)
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                        mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                        real64 const Smax = m_nonWettingCurve.oppositeBoundPhaseVolFraction;
+                        precomputedShy_gas = (phaseMaxHistoricalVolFraction[ipGas] < Smax) ? 
+                                            phaseMaxHistoricalVolFraction[ipGas] : Smax;
+                        real64 const E = m_killoughCurvatureParamCapPres;
+                        
+                        if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                            // Compute Scrt for DRAINAGE_TO_IMBIBITION scanning curve
+                            real64 Scrt = 0.0;
+                            KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_nonWettingCurve, precomputedShy_gas,
+                                                                                       m_landParam[ipGas],
+                                                                                       m_jerauldParam_a, m_jerauldParam_b,
+                                                                                       Scrt);
+                            precomputedScrt_gas = Scrt;
+                            // Compute denomF for DRAINAGE_TO_IMBIBITION: denomF = (1. / (Shy - Scrt + E) - 1. / E)
+                            precomputedDenomF_gas = (1. / (precomputedShy_gas - Scrt + E) - 1. / E);
+                        }
+                        else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                            // Compute Scrt for IMBIBITION_TO_DRAINAGE scanning curve
+                            real64 Scrt = 0.0;
+                            KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, precomputedShy_gas,
+                                                                                       m_landParam[ipGas],
+                                                                                       m_jerauldParam_a, m_jerauldParam_b,
+                                                                                       Scrt);
+                            precomputedScrt_gas = Scrt;
+                            real64 const Sgma = 1. - Scrt - m_phaseIntermediateMinVolFraction;
+                            // Compute denomF for IMBIBITION_TO_DRAINAGE: denomF = (1. / (Sgma - Shy + E) - 1. / E)
+                            precomputedDenomF_gas = (1. / (Sgma - precomputedShy_gas + E) - 1. / E);
+                        }
+                    }
+                    
+                    real64 S = S_guess;
+                    real64 residual_prev = 1e30;
+                    
+                    for (integer iter = 0; iter < maxIter; ++iter) {
+                        real64 pc_computed = this->computeCapillaryPressureForSaturation(
+                            S, mode, ipGas,
+                            phaseMinHistoricalVolFraction[ipGas],
+                            phaseMaxHistoricalVolFraction[ipGas],
+                            phaseMode2PeakVolFraction[ipGas],
+                            m_nonWettingIntermediateCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipGas],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            false, // isWettingPhase = false
+                            precomputedScrt_gas,
+                            precomputedDenomF_gas,
+                            precomputedShy_gas);
+                        
+                        // For non-wetting phase, capillary pressure is typically multiplied by -1
+                        // Check which sign to use based on the input
+                        real64 residual = pc_computed - phaseCapPressure[ipGas];
+                        
+                        if (LvArray::math::abs(residual) < tol) {
+                            break;
+                        }
+                        
+                        // Compute derivative dPc/dS using adaptive finite difference
+                        real64 const dS = LvArray::math::max(1e-8, 1e-6 * LvArray::math::max(LvArray::math::abs(S), 1e-6));
+                        real64 S_pert = S + dS;
+                        if (S_pert > maxS) {
+                            S_pert = LvArray::math::max(S - dS, minS);
+                        }
+                        
+                        real64 const pc_pert = this->computeCapillaryPressureForSaturation(
+                            S_pert, mode, ipGas,
+                            phaseMinHistoricalVolFraction[ipGas],
+                            phaseMaxHistoricalVolFraction[ipGas],
+                            phaseMode2PeakVolFraction[ipGas],
+                            m_nonWettingIntermediateCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipGas],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            false, // isWettingPhase = false
+                            precomputedScrt_gas,
+                            precomputedDenomF_gas,
+                            precomputedShy_gas);
+                        
+                        real64 const dpc_dS = (pc_pert - pc_computed) / (S_pert - S);
+                        
+                        if (LvArray::math::abs(dpc_dS) > 1e-12) {
+                            real64 const newtonStep = -residual / dpc_dS;
+                            real64 const maxStep = 0.1; // Limit step size to prevent overshooting
+                            real64 const step = LvArray::math::max(-maxStep, LvArray::math::min(maxStep, newtonStep));
+                            
+                            real64 S_new = S + step;
+                            
+                            // Line search: if residual increases, reduce step
+                            if (iter > 0 && LvArray::math::abs(residual) > LvArray::math::abs(residual_prev)) {
+                                // Backtrack: use smaller step
+                                S_new = S + 0.5 * step;
+                            }
+                            
+                            // Clamp to valid range
+                            S_new = LvArray::math::max(S_new, minS);
+                            S_new = LvArray::math::min(S_new, maxS);
+                            
+                            if (LvArray::math::abs(S_new - S) < 1e-10 && 
+                                (S_new <= minS + 1e-10 || S_new >= maxS - 1e-10)) {
+                                // Use bisection between current guess and boundary
+                                S_new = 0.5 * (S + (S_new <= minS + 1e-10 ? minS : maxS));
+                            }
+                            
+                            residual_prev = residual;
+                            S = S_new;
+                        } else {
+                            // If derivative is zero or very small, use bisection
+                            real64 const S_low = LvArray::math::max(S - 0.1, minS);
+                            real64 const S_high = LvArray::math::min(S + 0.1, maxS);
+                            S = 0.5 * (S_low + S_high);
+                            S = LvArray::math::max(S, minS);
+                            S = LvArray::math::min(S, maxS);
+                        }
+                    }
+                    
+                    phaseVolFraction[ipGas] = S;
+                    
+                    if (ipWater >= 0 && ipOil >= 0) {
+                        phaseVolFraction[ipOil] = 1.0 - phaseVolFraction[ipWater] - phaseVolFraction[ipGas];
+                        phaseVolFraction[ipOil] = LvArray::math::max(phaseVolFraction[ipOil], 0.0);
+                        phaseVolFraction[ipOil] = LvArray::math::min(phaseVolFraction[ipOil], 1.0);
+                    }
+                    
+                    // Compute derivative at final S
+                    real64 dpc_dS_final = 0.0;
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE || mode == fields::cappres::ModeIndexType::IMBIBITION) {
+                        integer const arrayIndex = (mode == fields::cappres::ModeIndexType::DRAINAGE) ? fields::cappres::ModeIndexType::DRAINAGE : fields::cappres::ModeIndexType::IMBIBITION;
+                        m_nonWettingIntermediateCapillaryPressureKernelWrappers[arrayIndex].compute(&S, &dpc_dS_final);
+                    } else {
+                        // For scanning curves, compute derivative using finite difference
+                        real64 const dS_final = 1e-6;
+                        real64 const S_pert_final = LvArray::math::min(S + dS_final, maxS);
+                        real64 const pc_final = this->computeCapillaryPressureForSaturation(
+                            S, mode, ipGas,
+                            phaseMinHistoricalVolFraction[ipGas],
+                            phaseMaxHistoricalVolFraction[ipGas],
+                            phaseMode2PeakVolFraction[ipGas],
+                            m_nonWettingIntermediateCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipGas],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            false, // isWettingPhase = false
+                            precomputedScrt_gas,
+                            precomputedDenomF_gas,
+                            precomputedShy_gas);
+                        real64 const pc_pert_final = this->computeCapillaryPressureForSaturation(
+                            S_pert_final, mode, ipGas,
+                            phaseMinHistoricalVolFraction[ipGas],
+                            phaseMaxHistoricalVolFraction[ipGas],
+                            phaseMode2PeakVolFraction[ipGas],
+                            m_nonWettingIntermediateCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipGas],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            false, // isWettingPhase = false
+                            precomputedScrt_gas,
+                            precomputedDenomF_gas,
+                            precomputedShy_gas);
+                        dpc_dS_final = (pc_pert_final - pc_final) / dS_final;
+                    }
+                    dPhaseCapPressure_dPhaseVolFrac[ipGas][ipGas] = dpc_dS_final;
+                    } // End else block for scanning curves
+                }
+            }
+            // CRITICAL: Add debug right after three-phase block to see if we reach here
+            if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+              std::cout << "[COMPUTEINV_PATH] *** AFTER three-phase block, before else-if checks ***" << std::endl;
+              std::cout << "[COMPUTEINV_PATH] ipWater=" << ipWater << ", ipOil=" << ipOil << ", ipGas=" << ipGas << std::endl;
+              std::cout << "[COMPUTEINV_PATH] Three-phase block was SKIPPED (condition was false)" << std::endl;
+              std::cout << "[COMPUTEINV_PATH] About to check if (ipWater < 0)..." << std::endl;
+            }
+            if (ipWater < 0) {
+                if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                  std::cout << "[COMPUTEINV_PATH] *** TAKING ipWater < 0 path (oil-gas) ***" << std::endl;
+                  std::cout << "[COMPUTEINV_PATH] This should NOT happen with ipWater=0!" << std::endl;
+                }
+                if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                  std::cout << "[COMPUTEINV_PATH] After three-phase block, checking else-if conditions..." << std::endl;
+                  std::cout << "[COMPUTEINV_PATH] ipWater=" << ipWater << ", condition (ipWater < 0)=" << (ipWater < 0 ? "TRUE" : "FALSE") << std::endl;
+                  std::cout << "[COMPUTEINV_PATH] *** TAKING ipWater < 0 path (oil-gas) ***" << std::endl;
+                  std::cout << "[COMPUTEINV_PATH] This should NOT happen with ipWater=0!" << std::endl;
+                }
+                if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                  std::cout << "[COMPUTEINV_PATH] *** TAKING ipWater < 0 path (oil-gas) ***" << std::endl;
+                  std::cout << "[COMPUTEINV_PATH] This should NOT happen with ipWater=0!" << std::endl;
+                }
+                // Two-phase: oil-gas (non-wetting phase)
+                // Similar to above but simpler
+                constexpr real64 pcEpsilon_gas = 1e-10;
+                if (ipGas >= 0 && LvArray::math::abs(phaseCapPressure[ipGas]) > pcEpsilon_gas) {
+                    // For pure DRAINAGE or IMBIBITION modes, use direct table lookup (analytical inverse)
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE || mode == fields::cappres::ModeIndexType::IMBIBITION) {
+                        integer const arrayIndex = (mode == fields::cappres::ModeIndexType::DRAINAGE) ? 0 : 1;
+                        array1d<real64> input(1);
+                        input[0] = phaseCapPressure[ipGas];
+                        auto inputSlice = input.toSliceConst();
+                        // Match TableCapillaryPressure: no clamping, let the table handle bounds
+                        phaseVolFraction[ipGas] = m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers[arrayIndex].compute(
+                                inputSlice, &dPhaseCapPressure_dPhaseVolFrac[ipGas][ipGas]);
+                        if (ipOil >= 0) {
+                            phaseVolFraction[ipOil] = 1.0 - phaseVolFraction[ipGas];
+                        }
+                        // Direct lookup complete, skip Newton-Raphson
+                    } else {
+                        // For scanning curves, use Newton-Raphson
+                    real64 S_guess = phaseMaxHistoricalVolFraction[ipGas];
+                    if (S_guess < minS || S_guess > maxS) {
+                        S_guess = 0.5;
+                    }
+                    
+                    // Precompute fixed parameters for scanning curves (these don't change during Newton-Raphson)
+                    real64 precomputedScrt_gas = -1.0;
+                    real64 precomputedDenomF_gas = 0.0;
+                    real64 precomputedShy_gas = -1.0;
+                    
+                    // Only precompute for scanning curves (DRAINAGE_TO_IMBIBITION or IMBIBITION_TO_DRAINAGE)
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                        mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                        real64 const Smax = m_nonWettingCurve.oppositeBoundPhaseVolFraction;
+                        precomputedShy_gas = (phaseMaxHistoricalVolFraction[ipGas] < Smax) ? 
+                                            phaseMaxHistoricalVolFraction[ipGas] : Smax;
+                        real64 const E = m_killoughCurvatureParamCapPres;
+                        
+                        if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                            // Compute Scrt for DRAINAGE_TO_IMBIBITION scanning curve
+                            real64 Scrt = 0.0;
+                            KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_nonWettingCurve, precomputedShy_gas,
+                                                                                       m_landParam[ipGas],
+                                                                                       m_jerauldParam_a, m_jerauldParam_b,
+                                                                                       Scrt);
+                            precomputedScrt_gas = Scrt;
+                            // Compute denomF for DRAINAGE_TO_IMBIBITION: denomF = (1. / (Shy - Scrt + E) - 1. / E)
+                            precomputedDenomF_gas = (1. / (precomputedShy_gas - Scrt + E) - 1. / E);
+                        }
+                        else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                            // Compute Scrt for IMBIBITION_TO_DRAINAGE scanning curve
+                            real64 Scrt = 0.0;
+                            KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, precomputedShy_gas,
+                                                                                       m_landParam[ipGas],
+                                                                                       m_jerauldParam_a, m_jerauldParam_b,
+                                                                                       Scrt);
+                            precomputedScrt_gas = Scrt;
+                            real64 const Sgma = 1. - Scrt - m_phaseIntermediateMinVolFraction;
+                            // Compute denomF for IMBIBITION_TO_DRAINAGE: denomF = (1. / (Sgma - Shy + E) - 1. / E)
+                            precomputedDenomF_gas = (1. / (Sgma - precomputedShy_gas + E) - 1. / E);
+                        }
+                    }
+                    
+                    real64 S = S_guess;
+                    for (integer iter = 0; iter < maxIter; ++iter) {
+                        real64 pc_computed = this->computeCapillaryPressureForSaturation(
+                            S, mode, ipGas,
+                            phaseMinHistoricalVolFraction[ipGas],
+                            phaseMaxHistoricalVolFraction[ipGas],
+                            phaseMode2PeakVolFraction[ipGas],
+                            m_wettingNonWettingCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipGas],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            false, // isWettingPhase = false
+                            precomputedScrt_gas,
+                            precomputedDenomF_gas,
+                            precomputedShy_gas);
+                        
+                        real64 residual = pc_computed - phaseCapPressure[ipGas];
+                        
+                        if (LvArray::math::abs(residual) < tol) {
+                            break;
+                        }
+                        
+                        real64 const dS = 1e-6;
+                        real64 const S_pert = LvArray::math::min(S + dS, maxS);
+                        real64 const pc_pert = this->computeCapillaryPressureForSaturation(
+                            S_pert, mode, ipGas,
+                            phaseMinHistoricalVolFraction[ipGas],
+                            phaseMaxHistoricalVolFraction[ipGas],
+                            phaseMode2PeakVolFraction[ipGas],
+                            m_wettingNonWettingCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipGas],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            false, // isWettingPhase = false
+                            precomputedScrt_gas,
+                            precomputedDenomF_gas,
+                            precomputedShy_gas);
+                        
+                        real64 const dpc_dS = (pc_pert - pc_computed) / dS;
+                        
+                        if (LvArray::math::abs(dpc_dS) > 1e-12) {
+                            S = S - residual / dpc_dS;
+                            S = LvArray::math::max(S, minS);
+                            S = LvArray::math::min(S, maxS);
+                        } else {
+                            S = S - residual * 1e-6;
+                            S = LvArray::math::max(S, minS);
+                            S = LvArray::math::min(S, maxS);
+                        }
+                    }
+                    
+                    phaseVolFraction[ipGas] = S;
+                    if (ipOil >= 0) {
+                        phaseVolFraction[ipOil] = 1.0 - S;
+                    }
+                    } // End else block for scanning curves
+                }
+            }
+            else {
+                if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                  std::cout << "[COMPUTEINV_PATH] *** REACHED TWO-PHASE path (else block) ***" << std::endl;
+                  std::cout << "[COMPUTEINV_PATH] ipWater=" << ipWater << ", ipOil=" << ipOil << ", ipGas=" << ipGas << std::endl;
+                  std::cout << "[COMPUTEINV_PATH] About to check if (ipWater >= 0)" << std::endl;
+                  std::cout << "[COMPUTEINV_PATH] This is the path that should work for Mode 0 (DRAINAGE)!" << std::endl;
+                }
+                // Two-phase: water-oil or water-gas (wetting phase)
+                // Copy exact pattern from TableCapillaryPressure::computeInv
+                if (ipWater >= 0) {
+                    if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                      std::cout << "[COMPUTEINV_PATH] Two-phase: ipWater >= 0, entering water phase block" << std::endl;
+                      std::cout << "[COMPUTEINV_PATH] About to check mode: mode=" << static_cast<int>(mode) 
+                                << ", DRAINAGE=" << static_cast<int>(fields::cappres::ModeIndexType::DRAINAGE)
+                                << ", IMBIBITION=" << static_cast<int>(fields::cappres::ModeIndexType::IMBIBITION) << std::endl;
+                    }
+                    // For pure DRAINAGE or IMBIBITION modes, use direct table lookup (analytical inverse)
+                    // CRITICAL DEBUG: Check if mode condition is actually true
+                    bool isDrainage = (mode == fields::cappres::ModeIndexType::DRAINAGE);
+                    bool isImbibition = (mode == fields::cappres::ModeIndexType::IMBIBITION);
+                    bool isPureMode = (isDrainage || isImbibition);
+                    if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                      std::cout << "[COMPUTEINV_PATH] Mode condition check:" << std::endl;
+                      std::cout << "[COMPUTEINV_PATH]   mode (as int)=" << static_cast<int>(mode) << std::endl;
+                      std::cout << "[COMPUTEINV_PATH]   DRAINAGE (as int)=" << static_cast<int>(fields::cappres::ModeIndexType::DRAINAGE) << std::endl;
+                      std::cout << "[COMPUTEINV_PATH]   IMBIBITION (as int)=" << static_cast<int>(fields::cappres::ModeIndexType::IMBIBITION) << std::endl;
+                      std::cout << "[COMPUTEINV_PATH]   isDrainage=" << (isDrainage ? "TRUE" : "FALSE") << std::endl;
+                      std::cout << "[COMPUTEINV_PATH]   isImbibition=" << (isImbibition ? "TRUE" : "FALSE") << std::endl;
+                      std::cout << "[COMPUTEINV_PATH]   isPureMode (DRAINAGE || IMBIBITION)=" << (isPureMode ? "TRUE" : "FALSE") << std::endl;
+                    }
+                    if (isPureMode) {
+                        if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                          std::cout << "[COMPUTEINV_PATH] Using pure DRAINAGE/IMBIBITION path (same as working case)" << std::endl;
+                          std::cout << "[COMPUTEINV_PATH] mode=" << (mode == fields::cappres::ModeIndexType::DRAINAGE ? "DRAINAGE" : "IMBIBITION") << std::endl;
+                        }
+                        integer const arrayIndex = (mode == fields::cappres::ModeIndexType::DRAINAGE) ? 0 : 1;
+                        if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                          std::cout << "[COMPUTEINV_PATH] arrayIndex=" << arrayIndex << std::endl;
+                        }
+                        
+                        // Match TableCapillaryPressure exactly (but skip the forward table call which passes Pc instead of S)
+                        real64 capPresWater = phaseCapPressure[ipWater];
+                        if constexpr (ENABLE_COMPUTEINV_PATH_DEBUG) {
+                          std::cout << "[COMPUTEINV_PATH] Input Pc=" << capPresWater << std::endl;
+                          std::cout << "[COMPUTEINV_PATH] phaseVolFraction[ipWater] before=" << phaseVolFraction[ipWater] << std::endl;
+                        }
+                        array1d<real64> input(1);
+                        input[0] = capPresWater;
+                        auto inputSlice = input.toSliceConst();
+                        
+                        constexpr bool ENABLE_COMPUTEINV_DEBUG = false;
+                        if (ENABLE_COMPUTEINV_DEBUG) {
+                            std::cout << "[COMPUTEINV_DEBUG] Two-phase, mode=" << (mode == fields::cappres::ModeIndexType::DRAINAGE ? "DRAINAGE" : "IMBIBITION") 
+                                      << ", arrayIndex=" << arrayIndex << std::endl;
+                            std::cout << "[COMPUTEINV_DEBUG] Input Pc=" << capPresWater << std::endl;
+                            std::cout << "[COMPUTEINV_DEBUG] Derivative before call=" << dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater] << std::endl;
+                        }
+                        
+                        // Use only the inverse table call (the forward table call in TableCapillaryPressure passes Pc instead of S, which is incorrect)
+                        // The derivative array is already zeroed at the start of computeInv
+                        // real64 dS_dPc_before = dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater];
+                        real64 S_before_inv = phaseVolFraction[ipWater];
+                        if (ENABLE_COMPUTEINV_DEBUG) {
+                            std::cout << "[COMPUTEINV_DEBUG] Two-phase DRAINAGE/IMBIBITION: Before inverse table call" << std::endl;
+                            std::cout << "  S_before=" << S_before_inv << std::endl;
+                            std::cout << "  Pc_input=" << capPresWater << std::endl;
+                            std::cout << "  arrayIndex=" << arrayIndex << std::endl;
+                            std::cout << "  inputSlice[0]=" << inputSlice[0] << std::endl;
+                            std::cout << "  wrapper.size()=" << m_inverseWettingNonWettingCapillaryPressureKernelWrappers.size() << std::endl;
+                        }
+                        real64 S_returned = m_inverseWettingNonWettingCapillaryPressureKernelWrappers[arrayIndex].compute(
+                                inputSlice,
+                                &(dPhaseCapPressure_dPhaseVolFrac)[ipWater][ipWater]);
+                        phaseVolFraction[ipWater] = S_returned;
+                        real64 dS_dPc_after = dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater];
+                        real64 S_after_inv = phaseVolFraction[ipWater];
+                        
+                        if (ENABLE_COMPUTEINV_DEBUG) {
+                            std::cout << "[COMPUTEINV_DEBUG] After inverse table call:" << std::endl;
+                            std::cout << "  S_returned=" << S_returned << std::endl;
+                            std::cout << "  S_after=" << S_after_inv << std::endl;
+                            std::cout << "  dS_dPc_after=" << dS_dPc_after << std::endl;
+                            if (std::abs(S_after_inv) < 1e-10 && capPresWater > 3000 && capPresWater < 100000) {
+                                std::cout << "[COMPUTEINV_DEBUG] ERROR: Pc=" << capPresWater 
+                                          << " is within valid range but inverse table returned S=0!" << std::endl;
+                                std::cout << "[COMPUTEINV_DEBUG] This will cause zero Jacobian and Pc_int won't update!" << std::endl;
+                            }
+                        }
+                        
+                        // Set non-wetting phase - match TableCapillaryPressure
+                        if (ipGas >= 0) {
+                            phaseVolFraction[ipGas] = 1.0 - phaseVolFraction[ipWater];
+                        } else if (ipOil >= 0) {
+                            phaseVolFraction[ipOil] = 1.0 - phaseVolFraction[ipWater];
+                        }
+                        // Direct lookup complete, skip Newton-Raphson
+                    } else {
+                        constexpr bool ENABLE_TWOPHASE_SCANNINGINV_DEBUG = false;
+                        
+                        // For scanning curves, use Newton-Raphson
+                    real64 S_guess = phaseMaxHistoricalVolFraction[ipWater];
+                    if (S_guess < minS || S_guess > maxS) {
+                        real64 const Smin = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                        real64 const Smax = m_wettingCurve.drainageExtremaPhaseVolFraction;
+                        S_guess = 0.5 * (Smin + Smax);
+                        S_guess = LvArray::math::max(S_guess, minS);
+                        S_guess = LvArray::math::min(S_guess, maxS);
+                    }
+                        if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                            std::cout << "[2P_SCAN_INV] Mode=" << static_cast<int>(mode)
+                                      << ", Pc_target=" << phaseCapPressure[ipWater]
+                                      << ", S_guess=" << S_guess
+                                      << ", S_minHist=" << phaseMinHistoricalVolFraction[ipWater]
+                                      << ", S_maxHist=" << phaseMaxHistoricalVolFraction[ipWater]
+                                      << ", Smin_curve=" << m_wettingCurve.oppositeBoundPhaseVolFraction
+                                      << ", Smax_curve=" << m_wettingCurve.drainageExtremaPhaseVolFraction
+                                      << std::endl;
+                    }
+                    
+                    // Precompute fixed parameters for scanning curves (these don't change during Newton-Raphson)
+                    real64 precomputedScrt_water = -1.0;
+                    real64 precomputedDenomF_water = 0.0;
+                    real64 precomputedShy_water = -1.0;
+                    
+                        // Precompute for scanning curves (Mode 2, Mode 3, or Mode 4)
+                    if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION || 
+                            mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE ||
+                            mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                        real64 const Smin = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                            real64 const Smax = m_wettingCurve.drainageExtremaPhaseVolFraction;
+                        real64 const E = m_killoughCurvatureParamCapPres;
+                        
+                        if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                                // DRAINAGE_TO_IMBIBITION: Shy should be minimum historical (where drainage started)
+                                precomputedShy_water = (phaseMinHistoricalVolFraction[ipWater] > Smin) ? 
+                                                      phaseMinHistoricalVolFraction[ipWater] : Smin;
+                                
+                                // Compute Scrt for DRAINAGE_TO_IMBIBITION scanning curve (wetting phase)
+                                real64 Scrt = 0.0;
+                                KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, precomputedShy_water,
+                                                                                           m_landParam[ipWater],
+                                                                                           m_jerauldParam_a, m_jerauldParam_b,
+                                                                                           Scrt);
+                                precomputedScrt_water = Scrt;
+                                // For wetting curve, Scrt IS the max wetting saturation (Swma = Scrt)
+                                real64 const Swma = 1. - (1. - Scrt);
+                                // Compute denomF for DRAINAGE_TO_IMBIBITION: denomF = (1. / (Swma - Shy + E) - 1. / E)
+                                precomputedDenomF_water = (1. / (Swma - precomputedShy_water + E) - 1. / E);
+                        }
+                        else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                                // IMBIBITION_TO_DRAINAGE: Shy should be maximum historical (where imbibition started)
+                                precomputedShy_water = (phaseMaxHistoricalVolFraction[ipWater] < Smax) ? 
+                                                      phaseMaxHistoricalVolFraction[ipWater] : Smax;
+                                
+                                // Compute Scrt for IMBIBITION_TO_DRAINAGE scanning curve (wetting phase)
+                                real64 Scrt = 0.0;
+                                KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, precomputedShy_water,
+                                                                                           m_landParam[ipWater],
+                                                                                           m_jerauldParam_a, m_jerauldParam_b,
+                                                                                           Scrt);
+                                precomputedScrt_water = Scrt;
+                                // Compute denomF for IMBIBITION_TO_DRAINAGE: denomF = (1. / (Shy - Scrt + E) - 1. / E)
+                                precomputedDenomF_water = (1. / (precomputedShy_water - Scrt + E) - 1. / E);
+                            }
+                            else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                                // Mode 4: IMBIBITION_TO_DRAINAGE_FROM_SCANNING
+                                // H (first reversal point) should be minimum historical (where imbibition started)
+                                // This is used to compute Scrt for Mode 4
+                                real64 const H = (phaseMinHistoricalVolFraction[ipWater] > Smin) ? 
+                                               phaseMinHistoricalVolFraction[ipWater] : Smin;
+                                
+                                // Compute Scrt for Mode 4 based on H (first reversal point)
+                                real64 Scrt = 0.0;
+                                KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(m_wettingCurve, H,
+                                                                                           m_landParam[ipWater],
+                                                                                           m_jerauldParam_a, m_jerauldParam_b,
+                                                                                           Scrt);
+                                precomputedScrt_water = Scrt;
+                                // For Mode 4, precomputedShy is not used in the same way, but set it to H for consistency
+                                precomputedShy_water = H;
+                                // denomF is not used for Mode 4 (it solves quadratic instead), but set to 0 to indicate it's not applicable
+                            precomputedDenomF_water = 0.0;
+                        }
+                    }
+                    
+                        if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                            std::cout << "[2P_SCAN_INV] Precomputed: Shy=" << precomputedShy_water
+                                      << ", Scrt=" << precomputedScrt_water
+                                      << ", denomF=" << precomputedDenomF_water
+                                      << ", E=" << m_killoughCurvatureParamCapPres
+                                      << ", Somin=" << m_phaseIntermediateMinVolFraction
+                                      << std::endl;
+                            // Evaluate Pc at a few points to see the curve shape
+                            real64 const S_lo = precomputedShy_water;
+                            // For wetting curve, Scrt IS the max wetting saturation (Swma = Scrt)
+                            real64 const Swma = 1. - (1. - precomputedScrt_water);
+                            std::cout << "[2P_SCAN_INV] Shy=" << S_lo << ", Swma=" << Swma << std::endl;
+                            for (int probe = 0; probe <= 5; ++probe) {
+                                real64 S_probe = S_lo + (Swma - S_lo) * probe / 5.0;
+                                S_probe = LvArray::math::max(minS, LvArray::math::min(maxS, S_probe));
+                                real64 pc_probe = this->computeCapillaryPressureForSaturation(
+                                    S_probe, mode, ipWater,
+                                    phaseMinHistoricalVolFraction[ipWater],
+                                    phaseMaxHistoricalVolFraction[ipWater],
+                                    phaseMode2PeakVolFraction[ipWater],
+                                    m_wettingNonWettingCapillaryPressureKernelWrappers,
+                                    m_wettingCurve, m_nonWettingCurve,
+                                    m_landParam[ipWater],
+                                    m_phaseIntermediateMinVolFraction,
+                                    m_killoughCurvatureParamCapPres,
+                                    m_jerauldParam_a, m_jerauldParam_b,
+                                    true, precomputedScrt_water, precomputedDenomF_water, precomputedShy_water);
+                                std::cout << "[2P_SCAN_INV]   S=" << S_probe << " -> Pc=" << pc_probe << std::endl;
+                            }
+                        }
+                        
+                        real64 S_lo_bracket, S_hi_bracket;
+                        real64 Swma_debug = -1.0;
+                        bool degenerateBracket = false;
+                        if (mode == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION) {
+                            // Mode 2: scanning curve valid in [Shy, Swma]
+                            // For wetting curve, Scrt IS the max wetting saturation (Swma = Scrt)
+                            real64 const Swma = 1. - (1. - precomputedScrt_water);
+                            Swma_debug = Swma;
+                            S_lo_bracket = precomputedShy_water;
+                            S_hi_bracket = Swma;
+                            // Guard: if Swma <= Shy, the scanning curve has no valid range (degenerate case).
+                            // Fall back to returning S = Shy directly.
+                            if (Swma <= precomputedShy_water + 1e-12) {
+                                degenerateBracket = true;
+                            }
+                        }
+                        else if (mode == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE) {
+                            // Mode 3: scanning curve valid in [Scrt_end, Shy]
+                            S_lo_bracket = precomputedScrt_water;
+                            S_hi_bracket = precomputedShy_water;
+                            // Guard: if Shy <= Scrt, degenerate case
+                            if (precomputedShy_water <= precomputedScrt_water + 1e-12) {
+                                degenerateBracket = true;
+                            }
+                        }
+                        else {
+                            array1d<real64> input_inv(1);
+                            input_inv[0] = phaseCapPressure[ipWater];
+                            auto inputSlice_inv = input_inv.toSliceConst();
+                            
+                            real64 dS_dPc_dr_unused = 0.0, dS_dPc_im_unused = 0.0;
+                            real64 S_dr = m_inverseWettingNonWettingCapillaryPressureKernelWrappers[ModeIndexType::DRAINAGE].compute(
+                                inputSlice_inv, &dS_dPc_dr_unused);
+                            real64 S_im = m_inverseWettingNonWettingCapillaryPressureKernelWrappers[ModeIndexType::IMBIBITION].compute(
+                                inputSlice_inv, &dS_dPc_im_unused);
+                            S_dr = LvArray::math::max(minS, LvArray::math::min(maxS, S_dr));
+                            S_im = LvArray::math::max(minS, LvArray::math::min(maxS, S_im));
+                            S_lo_bracket = LvArray::math::min(S_dr, S_im);
+                            S_hi_bracket = LvArray::math::max(S_dr, S_im);
+                        }
+                        
+                        S_lo_bracket = LvArray::math::max(minS, S_lo_bracket);
+                        S_hi_bracket = LvArray::math::min(maxS, S_hi_bracket);
+                        
+                        // Ensure S_lo <= S_hi (safety: swap if somehow still inverted after clamping)
+                        if (S_lo_bracket > S_hi_bracket) {
+                            real64 tmp = S_lo_bracket;
+                            S_lo_bracket = S_hi_bracket;
+                            S_hi_bracket = tmp;
+                        }
+                        
+                        if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                            std::cout << "[2P_SCAN_INV] Bracket: S_lo=" << S_lo_bracket 
+                                      << ", S_hi=" << S_hi_bracket 
+                                      << ", Shy=" << precomputedShy_water 
+                                      << ", Swma=" << Swma_debug
+                                      << ", Scrt=" << precomputedScrt_water
+                                      << (degenerateBracket ? " DEGENERATE" : "")
+                                      << std::endl;
+                        }
+                        
+                        // Handle degenerate bracket: if Swma <= Shy (Mode 2) or Shy <= Scrt (Mode 3),
+                        // the scanning curve has no valid range. Return S = Shy (the departure point).
+                        // The Killough formula at S=Shy gives F=0, so Pc = Pc_dr(Shy), which is consistent
+                        // with the drainage curve at that point.
+                        real64 const Pc_target = phaseCapPressure[ipWater];
+                        
+                        if (degenerateBracket) {
+                            // Return S = Shy (departure point).
+                            // The Killough formula at Shy gives F=0, so Pc = Pc_dr(Shy), consistent with drainage.
+                            phaseVolFraction[ipWater] = precomputedShy_water;
+                            if (ipGas >= 0) {
+                                phaseVolFraction[ipGas] = 1.0 - precomputedShy_water;
+                            } else if (ipOil >= 0) {
+                                phaseVolFraction[ipOil] = 1.0 - precomputedShy_water;
+                            }
+                            // Use drainage table derivative at Shy → dS/dPc = 1/(dPc/dS)
+                            real64 dpc_dS_shy = 0.0;
+                            m_wettingNonWettingCapillaryPressureKernelWrappers[ModeIndexType::DRAINAGE].compute(
+                                &precomputedShy_water, &dpc_dS_shy );
+                            if (LvArray::math::abs(dpc_dS_shy) > 1e-14) {
+                                dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater] = 1.0 / dpc_dS_shy;
+                            } else {
+                                dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater] = 0.0;
+                            }
+                            constexpr bool ENABLE_SCANINV_SUMMARY_DEGEN = false;
+                            if constexpr (ENABLE_SCANINV_SUMMARY_DEGEN) {
+                                std::cout << "[SCAN_INV] mode=" << static_cast<int>(mode)
+                                          << " Pc_tgt=" << Pc_target
+                                          << " Shy=" << precomputedShy_water
+                                          << " S=" << precomputedShy_water
+                                          << " dS/dPc=" << dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater]
+                                          << " DEGENERATE_BRACKET"
+                                          << std::endl;
+                            }
+                        }
+                        
+                        if (!degenerateBracket) {
+                        // Step 2: Evaluate Pc at bracket endpoints to determine sign of residual
+                        
+                        // Helper macro-like inline evaluation (avoids lambda for GEOS_HOST_DEVICE compatibility)
+                        #define EVAL_SCANNING_PC(S_eval) \
+                            this->computeCapillaryPressureForSaturation( \
+                                (S_eval), mode, ipWater, \
+                                phaseMinHistoricalVolFraction[ipWater], \
+                                phaseMaxHistoricalVolFraction[ipWater], \
+                                phaseMode2PeakVolFraction[ipWater], \
+                                m_wettingNonWettingCapillaryPressureKernelWrappers, \
+                                m_wettingCurve, m_nonWettingCurve, \
+                                m_landParam[ipWater], \
+                                m_phaseIntermediateMinVolFraction, \
+                                m_killoughCurvatureParamCapPres, \
+                                m_jerauldParam_a, m_jerauldParam_b, \
+                                true, \
+                                precomputedScrt_water, \
+                                precomputedDenomF_water, \
+                                precomputedShy_water)
+                        
+                        real64 Pc_lo = EVAL_SCANNING_PC(S_lo_bracket);
+                        real64 Pc_hi = EVAL_SCANNING_PC(S_hi_bracket);
+                        real64 res_lo = Pc_lo - Pc_target;
+                        real64 res_hi = Pc_hi - Pc_target;
+                        
+                        if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                            std::cout << "[2P_SCAN_INV] Pc_target=" << Pc_target
+                                      << ", Pc_lo=" << Pc_lo << " (res=" << res_lo << ")"
+                                      << ", Pc_hi=" << Pc_hi << " (res=" << res_hi << ")" << std::endl;
+                        }
+                        
+                        // Early return: if the root is already at a bracket endpoint
+                        // (i.e., Pc_target ≈ Pc_scan(Shy) or Pc_target ≈ Pc_scan(Swma)),
+                        // return that endpoint directly. This avoids the bisection sign-test
+                        // bug where res_lo ≈ 0 causes the update rule `residual * res_lo < 0`
+                        // to take the wrong branch (0 * negative = 0, NOT < 0), pushing the
+                        // bracket away from the root and converging to garbage.
+                        bool skipBisection = false;
+                        real64 S = 0.5 * (S_lo_bracket + S_hi_bracket); // default midpoint
+                        
+                        if (LvArray::math::abs(res_lo) < tol) {
+                            S = S_lo_bracket;
+                            skipBisection = true;
+                            if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                                std::cout << "[2P_SCAN_INV] Root at lower bracket endpoint: S=" << S
+                                          << ", res_lo=" << res_lo << std::endl;
+                            }
+                        } else if (LvArray::math::abs(res_hi) < tol) {
+                            S = S_hi_bracket;
+                            skipBisection = true;
+                            if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                                std::cout << "[2P_SCAN_INV] Root at upper bracket endpoint: S=" << S
+                                          << ", res_hi=" << res_hi << std::endl;
+                            }
+                        }
+                        
+                        if (!skipBisection) {
+                        // Ensure bracket contains the root (res_lo and res_hi should have opposite signs)
+                        // If not, Pc_target is at the boundary of the scanning curve.
+                        // Clamp to the nearest endpoint (don't expand outside valid range).
+                        if (res_lo * res_hi > 0) {
+                            // Root not bracketed — Pc_target is at or beyond scanning curve boundary
+                            // Return the endpoint with the smallest residual
+                            if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                                std::cout << "[2P_SCAN_INV] Root not bracketed: res_lo=" << res_lo
+                                          << ", res_hi=" << res_hi << " — using nearest endpoint" << std::endl;
+                            }
+                            // Pick the S with smallest |residual| and skip bisection
+                            if (LvArray::math::abs(res_lo) < LvArray::math::abs(res_hi)) {
+                                S_hi_bracket = S_lo_bracket; // collapse bracket to lo
+                            } else {
+                                S_lo_bracket = S_hi_bracket; // collapse bracket to hi
+                            }
+                        }
+                        
+                        // Step 3: Bisection (guaranteed convergence within bracket)
+                        S = 0.5 * (S_lo_bracket + S_hi_bracket); // start at midpoint
+                        constexpr integer maxBisectIter = 50; // 50 bisections give ~15 digits of precision
+                        
+                        for (integer iter = 0; iter < maxBisectIter; ++iter) {
+                            real64 const pc_computed = EVAL_SCANNING_PC(S);
+                            real64 const residual = pc_computed - Pc_target;
+                            
+                            if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                                if (iter <= 3 || iter == maxBisectIter - 1 || LvArray::math::abs(residual) < tol) {
+                                    std::cout << "[2P_SCAN_INV] Bisect iter=" << iter
+                                              << ", S=" << S << ", Pc(S)=" << pc_computed
+                                              << ", residual=" << residual
+                                              << ", bracket=[" << S_lo_bracket << "," << S_hi_bracket << "]" << std::endl;
+                                }
+                            }
+                            
+                            if (LvArray::math::abs(residual) < tol) {
+                                if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                                    std::cout << "[2P_SCAN_INV] Converged at iter=" << iter << ", S=" << S << std::endl;
+                                }
+                                break;
+                            }
+                            
+                            // Update bracket — use <= to correctly handle res_lo ≈ 0
+                            // (when the root is very near S_lo, residual * res_lo ≈ 0
+                            //  and the < test would take the wrong branch)
+                            if (residual * res_lo <= 0) {
+                                S_hi_bracket = S;
+                                res_hi = residual;
+                            } else {
+                                S_lo_bracket = S;
+                                res_lo = residual;
+                            }
+                            
+                            // Bisection step
+                            S = 0.5 * (S_lo_bracket + S_hi_bracket);
+                            
+                            // Check if bracket is too small
+                            if (S_hi_bracket - S_lo_bracket < 1e-12) {
+                                break;
+                            }
+                        }
+                        } // end if (!skipBisection)
+                        
+                        #undef EVAL_SCANNING_PC
+                        
+                        if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                            real64 pc_final_check = this->computeCapillaryPressureForSaturation(
+                            S, mode, ipWater,
+                            phaseMinHistoricalVolFraction[ipWater],
+                            phaseMaxHistoricalVolFraction[ipWater],
+                                phaseMode2PeakVolFraction[ipWater],
+                                m_wettingNonWettingCapillaryPressureKernelWrappers,
+                                m_wettingCurve, m_nonWettingCurve,
+                                m_landParam[ipWater],
+                                m_phaseIntermediateMinVolFraction,
+                                m_killoughCurvatureParamCapPres,
+                                m_jerauldParam_a, m_jerauldParam_b,
+                                true, precomputedScrt_water, precomputedDenomF_water, precomputedShy_water);
+                            std::cout << "[2P_SCAN_INV] FINAL: S=" << S
+                                      << ", Pc(S)=" << pc_final_check
+                                      << ", Pc_target=" << phaseCapPressure[ipWater]
+                                      << ", error=" << (pc_final_check - phaseCapPressure[ipWater]) << std::endl;
+                        }
+                        
+                        phaseVolFraction[ipWater] = S;
+                        // Set non-wetting phase
+                        if (ipGas >= 0) {
+                            phaseVolFraction[ipGas] = 1.0 - S;
+                        } else if (ipOil >= 0) {
+                            phaseVolFraction[ipOil] = 1.0 - S;
+                        }
+                        
+                        // Compute derivative dPc/dS at final S using finite difference
+                        // (matching the three-phase scanning curve path)
+                        {
+                            real64 const dS_final_requested = 1e-6;
+                            real64 S_pert_final = S + dS_final_requested;
+                            if (S_pert_final > maxS) {
+                                S_pert_final = S - dS_final_requested; // backward difference if at upper bound
+                                S_pert_final = LvArray::math::max(S_pert_final, minS);
+                            }
+                            real64 const dS_final = S_pert_final - S;
+                            real64 const pc_final = this->computeCapillaryPressureForSaturation(
+                                S, mode, ipWater,
+                                phaseMinHistoricalVolFraction[ipWater],
+                                phaseMaxHistoricalVolFraction[ipWater],
+                                phaseMode2PeakVolFraction[ipWater],
+                            m_wettingNonWettingCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipWater],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            true, // isWettingPhase
+                            precomputedScrt_water,
+                            precomputedDenomF_water,
+                            precomputedShy_water);
+                            real64 const pc_pert_final = this->computeCapillaryPressureForSaturation(
+                                S_pert_final, mode, ipWater,
+                            phaseMinHistoricalVolFraction[ipWater],
+                            phaseMaxHistoricalVolFraction[ipWater],
+                                phaseMode2PeakVolFraction[ipWater],
+                            m_wettingNonWettingCapillaryPressureKernelWrappers,
+                            m_wettingCurve,
+                            m_nonWettingCurve,
+                            m_landParam[ipWater],
+                            m_phaseIntermediateMinVolFraction,
+                            m_killoughCurvatureParamCapPres,
+                            m_jerauldParam_a,
+                            m_jerauldParam_b,
+                            true, // isWettingPhase
+                            precomputedScrt_water,
+                            precomputedDenomF_water,
+                            precomputedShy_water);
+                            real64 dpc_dS_final = 0.0;
+                            if (LvArray::math::abs(dS_final) > 1e-14) {
+                                dpc_dS_final = (pc_pert_final - pc_final) / dS_final;
+                            }
+                            // computeInv must return dS/dPc (not dPc/dS), matching the inverse table convention.
+                            // The local solver uses this as: dV/dPc = dV/dS * dS/dPc.
+                            real64 const dS_dPc_final = (LvArray::math::abs(dpc_dS_final) > 1e-14) ? (1.0 / dpc_dS_final) : 0.0;
+                            dPhaseCapPressure_dPhaseVolFrac[ipWater][ipWater] = dS_dPc_final;
+                            if constexpr (ENABLE_TWOPHASE_SCANNINGINV_DEBUG) {
+                                std::cout << "[2P_SCAN_INV] dPc/dS=" << dpc_dS_final 
+                                          << ", dS/dPc=" << dS_dPc_final
+                                          << ", Pc(S)=" << pc_final << ", Pc(S+dS)=" << pc_pert_final << std::endl;
+                            }
+                            // --- Concise one-line debug for scanning curve computeInv ---
+                            constexpr bool ENABLE_SCANINV_SUMMARY = false;
+                            if constexpr (ENABLE_SCANINV_SUMMARY) {
+                                std::cout << "[SCAN_INV] mode=" << static_cast<int>(mode)
+                                          << " Pc_tgt=" << phaseCapPressure[ipWater]
+                                          << " Shy=" << precomputedShy_water
+                                          << " Swma=" << Swma_debug
+                                          << " S=" << S
+                                          << " dS/dPc=" << dS_dPc_final
+                                          << (skipBisection ? " SKIP_BISECT" : " BISECT")
+                                          << std::endl;
+                            }
+                        }
+                        } // end if (!degenerateBracket)
+                    } // End else block for scanning curves
+                }
+            }
+        }
+
+/// kernel creation
+
+        TableCapillaryPressureHysteresis::KernelWrapper TableCapillaryPressureHysteresis::createKernelWrapper() {
+
+            // we want to make sure that the wrappers are always up-to-date, so we recreate them everytime
+            createAllTableKernelWrappers();
+
+            // Validate that the arrays are properly populated
+            integer const numPhases = m_phaseNames.size();
+            if (numPhases == 2) {
+                GEOS_THROW_IF(m_wettingNonWettingCapillaryPressureKernelWrappers.size() != 2,
+                               GEOS_FMT("{}: Expected 2 kernel wrappers for two-phase flow, but got {}. "
+                                        "This usually means createAllTableKernelWrappers() failed to populate the arrays. "
+                                        "Check that table functions '{}' and '{}' exist and are properly defined.",
+                                         getFullName(),
+                                         m_wettingNonWettingCapillaryPressureKernelWrappers.size(),
+                                         m_drainageWettingNonWettingCapPresTableName,
+                                         m_imbibitionWettingNonWettingCapPresTableName.empty() ? m_drainageWettingNonWettingCapPresTableName : m_imbibitionWettingNonWettingCapPresTableName),
+                               InputError);
+            } else if (numPhases == 3) {
+                GEOS_THROW_IF(m_wettingIntermediateCapillaryPressureKernelWrappers.size() != 2,
+                               GEOS_FMT("{}: Expected 2 wetting-intermediate kernel wrappers for three-phase flow, but got {}",
+                                         getFullName(),
+                                         m_wettingIntermediateCapillaryPressureKernelWrappers.size()),
+                               InputError);
+                GEOS_THROW_IF(m_nonWettingIntermediateCapillaryPressureKernelWrappers.size() != 2,
+                               GEOS_FMT("{}: Expected 2 non-wetting-intermediate kernel wrappers for three-phase flow, but got {}",
+                                         getFullName(),
+                                         m_nonWettingIntermediateCapillaryPressureKernelWrappers.size()),
+                               InputError);
+            }
+
+            // Validate that m_phaseHasHysteresis is properly initialized
+            GEOS_THROW_IF(m_phaseHasHysteresis.size() != 2,
+                           GEOS_FMT("{}: m_phaseHasHysteresis must have size 2, but got {}",
+                                     getFullName(),
+                                     m_phaseHasHysteresis.size()),
+                           InputError);
+
+            // Validate that the historical volume fraction arrays have been resized
+            // These arrays should be resized by resizeFields() before the KernelWrapper is used
+            // If they're empty, it means resizeFields() hasn't been called yet
+            GEOS_THROW_IF(m_phaseMaxHistoricalVolFraction.size(0) == 0 || m_phaseMaxHistoricalVolFraction.size(1) == 0,
+                           GEOS_FMT("{}: phaseMaxHistoricalVolFraction array has not been resized (size=[{}, {}]). "
+                                    "This usually means resizeFields() has not been called yet. "
+                                    "The arrays must be resized before the KernelWrapper can be used.",
+                                     getFullName(),
+                                     m_phaseMaxHistoricalVolFraction.size(0),
+                                     m_phaseMaxHistoricalVolFraction.size(1)),
+                           InputError);
+            GEOS_THROW_IF(m_phaseMinHistoricalVolFraction.size(0) == 0 || m_phaseMinHistoricalVolFraction.size(1) == 0,
+                           GEOS_FMT("{}: phaseMinHistoricalVolFraction array has not been resized (size=[{}, {}]). "
+                                    "This usually means resizeFields() has not been called yet. "
+                                    "The arrays must be resized before the KernelWrapper can be used.",
+                                     getFullName(),
+                                     m_phaseMinHistoricalVolFraction.size(0),
+                                     m_phaseMinHistoricalVolFraction.size(1)),
+                           InputError);
+            GEOS_THROW_IF(m_phaseMode2PeakVolFraction.size(0) == 0 || m_phaseMode2PeakVolFraction.size(1) == 0,
+                           GEOS_FMT("{}: phaseMode2PeakVolFraction array has not been resized (size=[{}, {}]). "
+                                    "This usually means resizeFields() has not been called yet. "
+                                    "The arrays must be resized before the KernelWrapper can be used.",
+                                     getFullName(),
+                                     m_phaseMode2PeakVolFraction.size(0),
+                                     m_phaseMode2PeakVolFraction.size(1)),
+                           InputError);
+
+            // then we create the actual TableRelativePermeabilityHysteresis::KernelWrapper
+            return KernelWrapper(m_wettingNonWettingCapillaryPressureKernelWrappers,
+                                 m_inverseWettingNonWettingCapillaryPressureKernelWrappers,
+                                 m_wettingIntermediateCapillaryPressureKernelWrappers,
+                                 m_inverseWettingIntermediateCapillaryPressureKernelWrappers,
+                                 m_nonWettingIntermediateCapillaryPressureKernelWrappers,
+                                 m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers,
+                                 m_phaseHasHysteresis,
+                                 m_landParam,
+                                 m_jerauldParam_a,
+                                 m_jerauldParam_b,
+                                 m_killoughCurvatureParamCapPres,
+                                 m_phaseIntermediateMinVolFraction,
+                                 m_wettingCurve,
+                                 m_nonWettingCurve,
+                                 m_phaseMinHistoricalVolFraction,
+                                 m_phaseMaxHistoricalVolFraction,
+                                 m_phaseMode2PeakVolFraction,
+                                 m_phaseTypes,
+                                 m_phaseOrder,
+                                 m_mode,
+                                 m_phaseTrappedVolFrac,
+                                 m_phaseCapPressure,
+                                 m_dPhaseCapPressure_dPhaseVolFrac);
+        }
+
+        void TableCapillaryPressureHysteresis::createAllTableKernelWrappers() {
+            using TPP = ThreePhasePairPhaseType;
+
+            FunctionManager const &functionManager = FunctionManager::getInstance();
+
+            integer const numPhases = m_phaseNames.size();
+
+            // Ensure m_phaseHasHysteresis is initialized before accessing it
+            // This can happen if createKernelWrapper is called before postProcessInput
+            if (m_phaseHasHysteresis.size() == 0) {
+                m_phaseHasHysteresis.resize(2);
+                if (numPhases == 2) {
+                    m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING] = 
+                        (m_imbibitionWettingNonWettingCapPresTableName.empty() ||
+                         m_imbibitionWettingNonWettingCapPresTableName == m_drainageWettingNonWettingCapPresTableName)
+                        ? 0 : 1;
+                    m_phaseHasHysteresis[TPP::INTERMEDIATE_NONWETTING] = m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING];
+                } else if (numPhases == 3) {
+                    m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING] = 
+                        (m_imbibitionWettingIntermediateCapPresTableName.empty() ||
+                         m_imbibitionWettingIntermediateCapPresTableName == m_drainageWettingIntermediateCapPresTableName)
+                        ? 0 : 1;
+                    m_phaseHasHysteresis[TPP::INTERMEDIATE_NONWETTING] = 
+                        (m_imbibitionNonWettingIntermediateCapPresTableName.empty() ||
+                         m_imbibitionNonWettingIntermediateCapPresTableName == m_drainageNonWettingIntermediateCapPresTableName)
+                        ? 0 : 1;
+                }
+            }
+
+            // we want to make sure that the wrappers are always up-to-date, so we recreate them everytime
+
+            m_wettingNonWettingCapillaryPressureKernelWrappers.clear();
+            m_inverseWettingNonWettingCapillaryPressureKernelWrappers.clear();
+            m_wettingIntermediateCapillaryPressureKernelWrappers.clear();
+            m_inverseWettingIntermediateCapillaryPressureKernelWrappers.clear();
+            m_nonWettingIntermediateCapillaryPressureKernelWrappers.clear();
+            m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers.clear();
+            m_inverseTables.clear();
+
+            if (numPhases == 2) {
+                GEOS_THROW_IF(m_drainageWettingNonWettingCapPresTableName.empty(),
+                               GEOS_FMT("{}: drainageWettingNonWettingCapPressureTableName is empty for two-phase flow",
+                                         getFullName()),
+                               InputError);
+
+                GEOS_THROW_IF(!functionManager.hasGroup(m_drainageWettingNonWettingCapPresTableName),
+                               GEOS_FMT("{}: the table function named '{}' could not be found",
+                                         getFullName(),
+                                         m_drainageWettingNonWettingCapPresTableName),
+                               InputError);
+                TableFunction const &drainageCapPresTable = functionManager.getGroup<TableFunction>(
+                        m_drainageWettingNonWettingCapPresTableName);
+                m_wettingNonWettingCapillaryPressureKernelWrappers.emplace_back(
+                        drainageCapPresTable.createKernelWrapper());
+
+
+                string const &imbibitionTableName = m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING]
+                                                                     ? m_imbibitionWettingNonWettingCapPresTableName
+                                                                     : m_drainageWettingNonWettingCapPresTableName;
+                GEOS_THROW_IF(imbibitionTableName.empty(),
+                               GEOS_FMT("{}: imbibition table name is empty for two-phase flow",
+                                         getFullName()),
+                               InputError);
+                GEOS_THROW_IF(!functionManager.hasGroup(imbibitionTableName),
+                               GEOS_FMT("{}: the table function named '{}' could not be found",
+                                         getFullName(),
+                                         imbibitionTableName),
+                               InputError);
+                TableFunction const &imbibitionWettingCapPresTable = functionManager.getGroup<TableFunction>(
+                                imbibitionTableName);
+                m_wettingNonWettingCapillaryPressureKernelWrappers.emplace_back(
+                        imbibitionWettingCapPresTable.createKernelWrapper());
+                
+                GEOS_THROW_IF(m_wettingNonWettingCapillaryPressureKernelWrappers.size() != 2,
+                               GEOS_FMT("{}: Expected 2 kernel wrappers after creation, but got {}",
+                                         getFullName(),
+                                         m_wettingNonWettingCapillaryPressureKernelWrappers.size()),
+                               InputError);
+
+                // Create inverse tables for drainage and imbibition (for direct lookup in computeInv)
+                // Inverse for drainage (index 0)
+                auto const &drainageSatArrayView = drainageCapPresTable.getCoordinates()[0];
+                auto const &drainagePcArrayView = drainageCapPresTable.getValues();
+                std::vector<real64> drainageSatVec(drainageSatArrayView.size());
+                std::vector<real64> drainagePcVec(drainagePcArrayView.size());
+                std::copy(drainageSatArrayView.begin(), drainageSatArrayView.end(), drainageSatVec.begin());
+                std::copy(drainagePcArrayView.begin(), drainagePcArrayView.end(), drainagePcVec.begin());
+                // Reverse both arrays (if original Pc is decreasing in S)
+                std::reverse(drainagePcVec.begin(), drainagePcVec.end());
+                std::reverse(drainageSatVec.begin(), drainageSatVec.end());
+                
+                
+                auto inverseDrainageTable = std::make_shared<TableFunction>("inverseDrainageCapPres", this);
+                real64_array invDrainagePcVec(drainagePcVec.size());
+                real64_array invDrainageSatVec(drainageSatVec.size());
+                std::copy(drainagePcVec.begin(), drainagePcVec.end(), invDrainagePcVec.data());
+                std::copy(drainageSatVec.begin(), drainageSatVec.end(), invDrainageSatVec.data());
+                array1d<real64_array> drainageCoordinates;
+                drainageCoordinates.emplace_back(std::move(invDrainagePcVec));
+                std::vector<units::Unit> dimUnits = {units::Unknown};
+                inverseDrainageTable->setTableCoordinates(drainageCoordinates, dimUnits);
+                inverseDrainageTable->setTableValues(std::move(invDrainageSatVec), units::Unknown);
+                inverseDrainageTable->setInterpolationMethod(TableFunction::InterpolationType::Linear);
+                m_inverseWettingNonWettingCapillaryPressureKernelWrappers.emplace_back(
+                        inverseDrainageTable->createKernelWrapper());
+                m_inverseTables.emplace_back(std::move(inverseDrainageTable));
+                
+                // Inverse for imbibition (index 1)
+                auto const &imbibitionSatArrayView = imbibitionWettingCapPresTable.getCoordinates()[0];
+                auto const &imbibitionPcArrayView = imbibitionWettingCapPresTable.getValues();
+                std::vector<real64> imbibitionSatVec(imbibitionSatArrayView.size());
+                std::vector<real64> imbibitionPcVec(imbibitionPcArrayView.size());
+                std::copy(imbibitionSatArrayView.begin(), imbibitionSatArrayView.end(), imbibitionSatVec.begin());
+                std::copy(imbibitionPcArrayView.begin(), imbibitionPcArrayView.end(), imbibitionPcVec.begin());
+                // Reverse both arrays (if original Pc is decreasing in S)
+                std::reverse(imbibitionPcVec.begin(), imbibitionPcVec.end());
+                std::reverse(imbibitionSatVec.begin(), imbibitionSatVec.end());
+                
+                auto inverseImbibitionTable = std::make_shared<TableFunction>("inverseImbibitionCapPres", this);
+                real64_array invImbibitionPcVec(imbibitionPcVec.size());
+                real64_array invImbibitionSatVec(imbibitionSatVec.size());
+                std::copy(imbibitionPcVec.begin(), imbibitionPcVec.end(), invImbibitionPcVec.data());
+                std::copy(imbibitionSatVec.begin(), imbibitionSatVec.end(), invImbibitionSatVec.data());
+                array1d<real64_array> imbibitionCoordinates;
+                imbibitionCoordinates.emplace_back(std::move(invImbibitionPcVec));
+                inverseImbibitionTable->setTableCoordinates(imbibitionCoordinates, dimUnits);
+                inverseImbibitionTable->setTableValues(std::move(invImbibitionSatVec), units::Unknown);
+                inverseImbibitionTable->setInterpolationMethod(TableFunction::InterpolationType::Linear);
+                m_inverseWettingNonWettingCapillaryPressureKernelWrappers.emplace_back(
+                        inverseImbibitionTable->createKernelWrapper());
+                m_inverseTables.emplace_back(std::move(inverseImbibitionTable));
+
+            } else if (numPhases == 3) {
+                TableFunction const &drainageWICapPres = functionManager.getGroup<TableFunction>(
+                        m_drainageWettingIntermediateCapPresTableName);
+                m_wettingIntermediateCapillaryPressureKernelWrappers.emplace_back(
+                        drainageWICapPres.createKernelWrapper());
+
+                TableFunction const &drainageNWICapPres = functionManager.getGroup<TableFunction>(
+                        m_drainageNonWettingIntermediateCapPresTableName);
+                m_nonWettingIntermediateCapillaryPressureKernelWrappers.emplace_back(
+                        drainageNWICapPres.createKernelWrapper());
+
+                TableFunction const &imbibitionWICapPres = m_phaseHasHysteresis[TPP::INTERMEDIATE_WETTING]
+                                                           ? functionManager.getGroup<TableFunction>(
+                                m_imbibitionWettingIntermediateCapPresTableName)
+                                                           : functionManager.getGroup<TableFunction>(
+                                m_drainageWettingIntermediateCapPresTableName);
+                m_wettingIntermediateCapillaryPressureKernelWrappers.emplace_back(
+                        imbibitionWICapPres.createKernelWrapper());
+
+                TableFunction const &imbibitionNWICapPres = m_phaseHasHysteresis[TPP::INTERMEDIATE_NONWETTING]
+                                                            ? functionManager.getGroup<TableFunction>(
+                                m_imbibitionNonWettingIntermediateCapPresTableName)
+                                                            : functionManager.getGroup<TableFunction>(
+                                m_drainageNonWettingIntermediateCapPresTableName);
+                m_nonWettingIntermediateCapillaryPressureKernelWrappers.emplace_back(
+                        imbibitionNWICapPres.createKernelWrapper());
+                
+                // Create inverse tables for 3-phase (wetting-intermediate and non-wetting-intermediate)
+                // Inverse for wetting-intermediate drainage (index 0)
+                auto const &wiDrainageSatArrayView = drainageWICapPres.getCoordinates()[0];
+                auto const &wiDrainagePcArrayView = drainageWICapPres.getValues();
+                std::vector<real64> wiDrainageSatVec(wiDrainageSatArrayView.size());
+                std::vector<real64> wiDrainagePcVec(wiDrainagePcArrayView.size());
+                std::copy(wiDrainageSatArrayView.begin(), wiDrainageSatArrayView.end(), wiDrainageSatVec.begin());
+                std::copy(wiDrainagePcArrayView.begin(), wiDrainagePcArrayView.end(), wiDrainagePcVec.begin());
+                std::reverse(wiDrainagePcVec.begin(), wiDrainagePcVec.end());
+                std::reverse(wiDrainageSatVec.begin(), wiDrainageSatVec.end());
+                
+                auto inverseWIDrainageTable = std::make_shared<TableFunction>("inverseWIDrainageCapPres", this);
+                real64_array invWIDrainagePcVec(wiDrainagePcVec.size());
+                real64_array invWIDrainageSatVec(wiDrainageSatVec.size());
+                std::copy(wiDrainagePcVec.begin(), wiDrainagePcVec.end(), invWIDrainagePcVec.data());
+                std::copy(wiDrainageSatVec.begin(), wiDrainageSatVec.end(), invWIDrainageSatVec.data());
+                array1d<real64_array> wiDrainageCoordinates;
+                wiDrainageCoordinates.emplace_back(std::move(invWIDrainagePcVec));
+                std::vector<units::Unit> dimUnits = {units::Unknown};
+                inverseWIDrainageTable->setTableCoordinates(wiDrainageCoordinates, dimUnits);
+                inverseWIDrainageTable->setTableValues(std::move(invWIDrainageSatVec), units::Unknown);
+                inverseWIDrainageTable->setInterpolationMethod(TableFunction::InterpolationType::Linear);
+                m_inverseWettingIntermediateCapillaryPressureKernelWrappers.emplace_back(
+                        inverseWIDrainageTable->createKernelWrapper());
+                m_inverseTables.emplace_back(std::move(inverseWIDrainageTable));
+                
+                // Inverse for wetting-intermediate imbibition (index 1)
+                auto const &wiImbibitionSatArrayView = imbibitionWICapPres.getCoordinates()[0];
+                auto const &wiImbibitionPcArrayView = imbibitionWICapPres.getValues();
+                std::vector<real64> wiImbibitionSatVec(wiImbibitionSatArrayView.size());
+                std::vector<real64> wiImbibitionPcVec(wiImbibitionPcArrayView.size());
+                std::copy(wiImbibitionSatArrayView.begin(), wiImbibitionSatArrayView.end(), wiImbibitionSatVec.begin());
+                std::copy(wiImbibitionPcArrayView.begin(), wiImbibitionPcArrayView.end(), wiImbibitionPcVec.begin());
+                std::reverse(wiImbibitionPcVec.begin(), wiImbibitionPcVec.end());
+                std::reverse(wiImbibitionSatVec.begin(), wiImbibitionSatVec.end());
+                
+                auto inverseWIImbibitionTable = std::make_shared<TableFunction>("inverseWIImbibitionCapPres", this);
+                real64_array invWIImbibitionPcVec(wiImbibitionPcVec.size());
+                real64_array invWIImbibitionSatVec(wiImbibitionSatVec.size());
+                std::copy(wiImbibitionPcVec.begin(), wiImbibitionPcVec.end(), invWIImbibitionPcVec.data());
+                std::copy(wiImbibitionSatVec.begin(), wiImbibitionSatVec.end(), invWIImbibitionSatVec.data());
+                array1d<real64_array> wiImbibitionCoordinates;
+                wiImbibitionCoordinates.emplace_back(std::move(invWIImbibitionPcVec));
+                inverseWIImbibitionTable->setTableCoordinates(wiImbibitionCoordinates, dimUnits);
+                inverseWIImbibitionTable->setTableValues(std::move(invWIImbibitionSatVec), units::Unknown);
+                inverseWIImbibitionTable->setInterpolationMethod(TableFunction::InterpolationType::Linear);
+                m_inverseWettingIntermediateCapillaryPressureKernelWrappers.emplace_back(
+                        inverseWIImbibitionTable->createKernelWrapper());
+                m_inverseTables.emplace_back(std::move(inverseWIImbibitionTable));
+                
+                // Inverse for non-wetting-intermediate drainage (index 0)
+                auto const &nwiDrainageSatArrayView = drainageNWICapPres.getCoordinates()[0];
+                auto const &nwiDrainagePcArrayView = drainageNWICapPres.getValues();
+                std::vector<real64> nwiDrainageSatVec(nwiDrainageSatArrayView.size());
+                std::vector<real64> nwiDrainagePcVec(nwiDrainagePcArrayView.size());
+                std::copy(nwiDrainageSatArrayView.begin(), nwiDrainageSatArrayView.end(), nwiDrainageSatVec.begin());
+                std::copy(nwiDrainagePcArrayView.begin(), nwiDrainagePcArrayView.end(), nwiDrainagePcVec.begin());
+                std::reverse(nwiDrainagePcVec.begin(), nwiDrainagePcVec.end());
+                std::reverse(nwiDrainageSatVec.begin(), nwiDrainageSatVec.end());
+                
+                auto inverseNWIDrainageTable = std::make_shared<TableFunction>("inverseNWIDrainageCapPres", this);
+                real64_array invNWIDrainagePcVec(nwiDrainagePcVec.size());
+                real64_array invNWIDrainageSatVec(nwiDrainageSatVec.size());
+                std::copy(nwiDrainagePcVec.begin(), nwiDrainagePcVec.end(), invNWIDrainagePcVec.data());
+                std::copy(nwiDrainageSatVec.begin(), nwiDrainageSatVec.end(), invNWIDrainageSatVec.data());
+                array1d<real64_array> nwiDrainageCoordinates;
+                nwiDrainageCoordinates.emplace_back(std::move(invNWIDrainagePcVec));
+                inverseNWIDrainageTable->setTableCoordinates(nwiDrainageCoordinates, dimUnits);
+                inverseNWIDrainageTable->setTableValues(std::move(invNWIDrainageSatVec), units::Unknown);
+                inverseNWIDrainageTable->setInterpolationMethod(TableFunction::InterpolationType::Linear);
+                m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers.emplace_back(
+                        inverseNWIDrainageTable->createKernelWrapper());
+                m_inverseTables.emplace_back(std::move(inverseNWIDrainageTable));
+                
+                // Inverse for non-wetting-intermediate imbibition (index 1)
+                auto const &nwiImbibitionSatArrayView = imbibitionNWICapPres.getCoordinates()[0];
+                auto const &nwiImbibitionPcArrayView = imbibitionNWICapPres.getValues();
+                std::vector<real64> nwiImbibitionSatVec(nwiImbibitionSatArrayView.size());
+                std::vector<real64> nwiImbibitionPcVec(nwiImbibitionPcArrayView.size());
+                std::copy(nwiImbibitionSatArrayView.begin(), nwiImbibitionSatArrayView.end(), nwiImbibitionSatVec.begin());
+                std::copy(nwiImbibitionPcArrayView.begin(), nwiImbibitionPcArrayView.end(), nwiImbibitionPcVec.begin());
+                std::reverse(nwiImbibitionPcVec.begin(), nwiImbibitionPcVec.end());
+                std::reverse(nwiImbibitionSatVec.begin(), nwiImbibitionSatVec.end());
+                
+                auto inverseNWIImbibitionTable = std::make_shared<TableFunction>("inverseNWIImbibitionCapPres", this);
+                real64_array invNWIImbibitionPcVec(nwiImbibitionPcVec.size());
+                real64_array invNWIImbibitionSatVec(nwiImbibitionSatVec.size());
+                std::copy(nwiImbibitionPcVec.begin(), nwiImbibitionPcVec.end(), invNWIImbibitionPcVec.data());
+                std::copy(nwiImbibitionSatVec.begin(), nwiImbibitionSatVec.end(), invNWIImbibitionSatVec.data());
+                array1d<real64_array> nwiImbibitionCoordinates;
+                nwiImbibitionCoordinates.emplace_back(std::move(invNWIImbibitionPcVec));
+                inverseNWIImbibitionTable->setTableCoordinates(nwiImbibitionCoordinates, dimUnits);
+                inverseNWIImbibitionTable->setTableValues(std::move(invNWIImbibitionSatVec), units::Unknown);
+                inverseNWIImbibitionTable->setInterpolationMethod(TableFunction::InterpolationType::Linear);
+                m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers.emplace_back(
+                        inverseNWIImbibitionTable->createKernelWrapper());
+                m_inverseTables.emplace_back(std::move(inverseNWIImbibitionTable));
+            }
+
+        }
+
+///kernel ctor
+        TableCapillaryPressureHysteresis::KernelWrapper::KernelWrapper(
+                arrayView1d<const TableFunction::KernelWrapper> const &wettingNonWettingCapillaryPressureKernelWrappers,
+                arrayView1d<const TableFunction::KernelWrapper> const &inverseWettingNonWettingCapillaryPressureKernelWrappers,
+                arrayView1d<const TableFunction::KernelWrapper> const &wettingIntermediateCapillaryPressureKernelWrappers,
+                arrayView1d<const TableFunction::KernelWrapper> const &inverseWettingIntermediateCapillaryPressureKernelWrappers,
+                arrayView1d<const TableFunction::KernelWrapper> const &nonWettingIntermediateCapillaryPressureKernelWrappers,
+                arrayView1d<const TableFunction::KernelWrapper> const &inverseNonWettingIntermediateCapillaryPressureKernelWrappers,
+                const arrayView1d<const geos::integer> &phaseHasHysteresis,
+                const arrayView1d<const geos::real64> &landParam,
+                const real64 & jerauldParam_a,
+                const real64 & jerauldParam_b,
+                const real64 & killoughCurvaturePcParam,
+                const geos::real64 &phaseIntermediateMinVolFraction,
+                const KilloughHysteresis::HysteresisCurve &wettingCurve,
+                const KilloughHysteresis::HysteresisCurve &nonWettingCurve,
+                const arrayView2d<const geos::real64, compflow::USD_PHASE> &phaseMinHistoricalVolFraction,
+                const arrayView2d<const geos::real64, compflow::USD_PHASE> &phaseMaxHistoricalVolFraction,
+                arrayView2d<geos::real64, compflow::USD_PHASE> &phaseMode2PeakVolFraction,
+                arrayView1d<integer const> const &phaseTypes,
+                arrayView1d<integer const> const &phaseOrder,
+                arrayView1d<integer> const &mode,
+                arrayView3d<real64, cappres::USD_CAPPRES> const &phaseTrapped,
+                const arrayView3d<geos::real64, relperm::USD_RELPERM> &phaseCapPressure,
+                const arrayView4d<geos::real64, relperm::USD_RELPERM_DS> &dPhaseCapPressure_dPhaseVolFrac)
+                :
+                CapillaryPressureBaseUpdate(phaseTypes,
+                                            phaseOrder,
+                                            phaseTrapped,
+                                            phaseCapPressure,
+                                            dPhaseCapPressure_dPhaseVolFrac),
+                m_wettingNonWettingCapillaryPressureKernelWrappers(wettingNonWettingCapillaryPressureKernelWrappers),
+                m_inverseWettingNonWettingCapillaryPressureKernelWrappers(inverseWettingNonWettingCapillaryPressureKernelWrappers),
+                m_wettingIntermediateCapillaryPressureKernelWrappers(
+                        wettingIntermediateCapillaryPressureKernelWrappers),
+                m_inverseWettingIntermediateCapillaryPressureKernelWrappers(inverseWettingIntermediateCapillaryPressureKernelWrappers),
+                m_nonWettingIntermediateCapillaryPressureKernelWrappers(
+                        nonWettingIntermediateCapillaryPressureKernelWrappers),
+                m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers(inverseNonWettingIntermediateCapillaryPressureKernelWrappers),
+                m_phaseHasHysteresis(phaseHasHysteresis),
+                m_landParam(landParam),
+                m_jerauldParam_a(jerauldParam_a),
+                m_jerauldParam_b(jerauldParam_b),
+                m_killoughCurvatureParamCapPres(killoughCurvaturePcParam),
+                m_phaseIntermediateMinVolFraction(phaseIntermediateMinVolFraction),
+                m_wettingCurve(wettingCurve),
+                m_nonWettingCurve(nonWettingCurve),
+                m_phaseMinHistoricalVolFraction(phaseMinHistoricalVolFraction),
+                m_phaseMaxHistoricalVolFraction(phaseMaxHistoricalVolFraction),
+                m_phaseMode2PeakVolFraction(phaseMode2PeakVolFraction),
+                m_mode(mode) {}
+
+        REGISTER_CATALOG_ENTRY(ConstitutiveBase, TableCapillaryPressureHysteresis, std::string const &, Group * const)
+
+    } // namespace constitutive
+} // namespace geos
diff --git a/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHysteresis.hpp b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHysteresis.hpp
new file mode 100644
index 00000000000..c68c46c4194
--- /dev/null
+++ b/src/coreComponents/constitutive/capillaryPressure/TableCapillaryPressureHysteresis.hpp
@@ -0,0 +1,739 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2018-2020 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2020 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2018-2020 TotalEnergies
+ * Copyright (c) 2019-     GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+
+#ifndef GEOS_CONSTITUTIVE_TABLECAPILLARYPRESSUREHYSTERESIS_HPP
+#define GEOS_CONSTITUTIVE_TABLECAPILLARYPRESSUREHYSTERESIS_HPP
+
+#include "constitutive/capillaryPressure/CapillaryPressureBase.hpp"
+#include "functions/TableFunction.hpp"
+
+#include "constitutive/KilloughHysteresis.hpp"
+#include "CapillaryPressureFields.hpp"
+#include "common/DataLayouts.hpp"
+
+namespace geos {
+
+
+    namespace constitutive {
+
+        class TableCapillaryPressureHysteresis : public CapillaryPressureBase {
+//  /// useful constant
+//  static constexpr real64 CAP_INF = 1e9;
+////          std::numeric_limits< real64 >::max();
+//  static constexpr real64 CAP_INF_DERIV = 1e9;
+////          std::numeric_limits< real64 >::max();
+
+            typedef fields::cappres::ModeIndexType ModeIndexType;
+
+        public:
+
+            /// order of the phase properties for three-phase flow
+            struct ThreePhasePairPhaseType {
+                enum : integer {
+                    INTERMEDIATE_WETTING = 0,   ///< index for intermediate-wetting
+                    INTERMEDIATE_NONWETTING = 1 ///< index for intermediate-non-wetting
+                };
+            };
+
+
+            TableCapillaryPressureHysteresis(std::string const &name,
+                                             dataRepository::Group *const parent);
+
+            static std::string catalogName() { return "TableCapillaryPressureHysteresis"; }
+
+            virtual string getCatalogName() const override { return catalogName(); }
+
+            ///Kernel
+            class KernelWrapper final : public CapillaryPressureBaseUpdate {
+            public:
+
+                KernelWrapper(
+                        arrayView1d<TableFunction::KernelWrapper const> const &wettingNonWettingCapillaryPressureKernelWrappers,
+                        arrayView1d<TableFunction::KernelWrapper const> const &inverseWettingNonWettingCapillaryPressureKernelWrappers,
+                        arrayView1d<TableFunction::KernelWrapper const> const &wettingIntermediateCapillaryPressureKernelWrappers,
+                        arrayView1d<TableFunction::KernelWrapper const> const &inverseWettingIntermediateCapillaryPressureKernelWrappers,
+                        arrayView1d<TableFunction::KernelWrapper const> const &nonWettingIntermediateCapillaryPressureKernelWrappers,
+                        arrayView1d<TableFunction::KernelWrapper const> const &inverseNonWettingIntermediateCapillaryPressureKernelWrappers,
+                        arrayView1d<integer const> const &phaseHasHysteresis,
+                        arrayView1d<real64 const> const &landParam,
+                        real64 const &jerauldParam_a,
+                        real64 const &jerauldParam_b,
+                        real64 const &killoughCurvaturePcParameter,
+                        real64 const &phaseIntermediateMinVolFraction,
+                        KilloughHysteresis::HysteresisCurve const &wettingCurve,
+                        KilloughHysteresis::HysteresisCurve const &nonWettingCurve,
+                        arrayView2d<real64 const, compflow::USD_PHASE> const &phaseMinHistoricalVolFraction,
+                        arrayView2d<real64 const, compflow::USD_PHASE> const &phaseMaxHistoricalVolFraction,
+                        arrayView2d<real64, compflow::USD_PHASE> &phaseMode2PeakVolFraction,
+                        arrayView1d<integer const> const &phaseTypes,
+                        arrayView1d<integer const> const &phaseOrder,
+                        arrayView1d<integer> const &mode,
+                        arrayView3d<real64, relperm::USD_RELPERM> const &phaseTrappedVolFrac,
+                        arrayView3d<real64, relperm::USD_RELPERM> const &phaseCapPressure,
+                        arrayView4d<real64, relperm::USD_RELPERM_DS> const &dPhaseCapPressure_dPhaseVolFrac);
+
+                //actual workers
+                GEOS_HOST_DEVICE
+                void computeBoundCapillaryPressure(TableFunction::KernelWrapper const &drainageCapPressureWrapper,
+                                                   real64 const &phaseVolFraction,
+                                                   real64 &phaseCapPressure,
+                                                   real64 &dPhaseCapPressure_dPhaseVolFrac) const;
+
+                GEOS_HOST_DEVICE
+                void
+                computeImbibitionWettingCapillaryPressure(
+                        const arrayView1d<const TableFunction::KernelWrapper> &wettingKernelWapper,
+                        const KilloughHysteresis::HysteresisCurve &wettingCurve,
+                        const KilloughHysteresis::HysteresisCurve &nonWettingCurve,
+                        const geos::real64 &landParam,
+                        const geos::real64 &phaseVolFraction,
+                        const geos::real64 &phaseMinHistoricalVolFraction,
+                        const geos::real64 &phaseMaxHistoricalVolFraction,
+                        const geos::real64 &phaseMode2PeakVolFraction,
+                        geos::real64 &phaseTrappedVolFrac,
+                        geos::real64 &phaseCapPressure,
+                        geos::real64 &dPhaseCapPressure_dPhaseVolFrac,
+                        const ModeIndexType &mode) const;
+
+                //two phase flow overload
+                GEOS_HOST_DEVICE
+                void
+                computeImbibitionWettingCapillaryPressure(
+                        const arrayView1d<const TableFunction::KernelWrapper> &wettingKernelWapper,
+                        const KilloughHysteresis::HysteresisCurve &wettingCurve,
+                        const geos::real64 &landParam,
+                        const geos::real64 &phaseVolFraction,
+                        const geos::real64 &phaseMinHistoricalVolFraction,
+                        const geos::real64 &phaseMaxHistoricalVolFraction,
+                        const geos::real64 &phaseMode2PeakVolFraction,
+                        geos::real64 &phaseTrappedVolFrac,
+                        geos::real64 &phaseCapPressure,
+                        geos::real64 &dPhaseCapPressure_dPhaseVolFrac,
+                        const ModeIndexType &mode) const;
+
+                GEOS_HOST_DEVICE
+                void
+                computeImbibitionNonWettingCapillaryPressure(
+                        const arrayView1d<const TableFunction::KernelWrapper> &nonWettingKernelWrapper,
+                        const KilloughHysteresis::HysteresisCurve &nonWettingCurve,
+                        const KilloughHysteresis::HysteresisCurve &wettingCurve,
+                        const geos::real64 &landParam,
+                        const geos::real64 &phaseVolFraction,
+                        const geos::real64 &phaseMaxHistoricalVolFraction,
+                        geos::real64 &phaseTrappedVolFrac,
+                        geos::real64 &phaseCapPressure,
+                        geos::real64 &dPhaseCapPressure_dPhaseVolFrac,
+                        const ModeIndexType &mode) const;
+
+                //2phase flow overload
+                GEOS_HOST_DEVICE
+                void
+                computeImbibitionNonWettingCapillaryPressure(
+                        const arrayView1d<const TableFunction::KernelWrapper> &nonWettingKernelWrapper,
+                        const KilloughHysteresis::HysteresisCurve &nonWettingCurve,
+                        const geos::real64 &landParam,
+                        const geos::real64 &phaseVolFraction,
+                        const geos::real64 &phaseMaxHistoricalVolFraction,
+                        geos::real64 &phaseTrappedVolFrac,
+                        geos::real64 &phaseCapPressure,
+                        geos::real64 &dPhaseCapPressure_dPhaseVolFrac,
+                        const ModeIndexType &mode) const;
+
+
+
+                //wrapper call wrt number of phase
+                GEOS_HOST_DEVICE
+                void computeTwoPhaseWetting(integer const ipWetting,
+                                            integer const ipNonWetting,
+                                            arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseVolFraction,
+                                            arraySlice1d<real64 const,
+                                                    compflow::USD_PHASE - 1> const &phaseMaxHistoricalVolFraction,
+                                            arraySlice1d<real64 const,
+                                                    compflow::USD_PHASE - 1> const &phaseMinHistoricalVolFraction,
+                                            arraySlice1d<real64, relperm::USD_RELPERM - 2> const &phaseTrappedVolFrac,
+                                            arraySlice1d<real64, relperm::USD_RELPERM - 2> const &phaseCapPressure,
+                                            arraySlice2d<real64,
+                                                    relperm::USD_RELPERM_DS - 2> const &dPhaseCapPressure_dPhaseVolFrac,
+                                            ModeIndexType &mode,
+                                            arraySlice1d<real64, compflow::USD_PHASE - 1> &phaseMode2PeakVolFraction) const;
+
+
+                GEOS_HOST_DEVICE
+                void computeTwoPhaseNonWetting(integer const ipWetting,
+                                               integer const ipNonWetting,
+                                               arraySlice1d<real64 const,
+                                                       compflow::USD_PHASE - 1> const &phaseVolFraction,
+                                               arraySlice1d<real64 const,
+                                                       compflow::USD_PHASE - 1> const &phaseMaxHistoricalVolFraction,
+                                               arraySlice1d<real64 const,
+                                                       compflow::USD_PHASE - 1> const &phaseMinHistoricalVolFraction,
+                                               arraySlice1d<real64,
+                                                       relperm::USD_RELPERM - 2> const &phaseTrappedVolFrac,
+                                               arraySlice1d<real64, relperm::USD_RELPERM - 2> const &phaseCapPressure,
+                                               arraySlice2d<real64, relperm::USD_RELPERM_DS -
+                                                                    2> const &dPhaseCapPressure_dPhaseVolFrac,
+                                               ModeIndexType &mode) const;
+
+                GEOS_HOST_DEVICE
+                void computeThreePhase(integer const ipWetting,
+                                       integer const ipInter,
+                                       integer const ipNonWetting,
+                                       arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseVolFraction,
+                                       arraySlice1d<real64 const,
+                                               compflow::USD_PHASE - 1> const &phaseMaxHistoricalVolFraction,
+                                       arraySlice1d<real64 const,
+                                               compflow::USD_PHASE - 1> const &phaseMinHistoricalVolFraction,
+                                       arraySlice1d<real64, relperm::USD_RELPERM - 2> const &phaseTrappedVolFrac,
+                                       arraySlice1d<real64, relperm::USD_RELPERM - 2> const &phaseCapPressure,
+                                       arraySlice2d<real64,
+                                               relperm::USD_RELPERM_DS - 2> const &dPhaseCapPressure_dPhaseVolFrac,
+                                       ModeIndexType &mode,
+                                       arraySlice1d<real64, compflow::USD_PHASE - 1> &phaseMode2PeakVolFraction) const;
+
+                //uppermost call-wrappers
+                // Standard 3-argument compute method for compatibility with InverseCapillaryPressure
+                GEOS_HOST_DEVICE
+                void compute(arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseVolFraction,
+                             arraySlice1d<real64, cappres::USD_CAPPRES - 2> const &phaseCapPressure,
+                             arraySlice2d<real64, cappres::USD_CAPPRES_DS - 2> const &dPhaseCapPressure_dPhaseVolFrac) const;
+
+                GEOS_HOST_DEVICE
+                virtual void compute(arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseVolFraction,
+                                     arraySlice1d<real64 const,
+                                             compflow::USD_PHASE - 1> const &phaseMaxHistoricalVolFraction,
+                                     arraySlice1d<real64 const,
+                                             compflow::USD_PHASE - 1> const &phaseMinHistoricalVolFraction,
+                                     arraySlice1d<real64, cappres::USD_CAPPRES - 2> const &phaseTrappedVolFrac,
+                                     arraySlice1d<real64, cappres::USD_CAPPRES - 2> const &phaseCapPressure,
+                                     arraySlice2d<real64,
+                                             cappres::USD_CAPPRES_DS - 2> const &dPhaseCapPressure_dPhaseVolFrac,
+                                     ModeIndexType &mode,
+                                     arraySlice1d<real64, compflow::USD_PHASE - 1> &phaseMode2PeakVolFraction) const;
+
+                GEOS_HOST_DEVICE
+                virtual void update(localIndex const k,
+                                    localIndex const q,
+                                    arraySlice1d<real64 const,
+                                            compflow::USD_PHASE - 1> const &phaseVolFraction) const override;
+
+                /**
+                 * @brief Compute phase volume fraction from capillary pressure (inverse operation).
+                 * @param phaseVolFraction [out] Computed phase volume fractions
+                 * @param phaseMaxHistoricalVolFraction [in] Maximum historical phase volume fractions
+                 * @param phaseMinHistoricalVolFraction [in] Minimum historical phase volume fractions
+                 * @param phaseTrappedVolFrac [in] Trapped phase volume fractions
+                 * @param phaseCapPressure [in] Target capillary pressures (input)
+                 * @param dPhaseCapPressure_dPhaseVolFrac [out] Derivatives of capillary pressure w.r.t. phase volume fraction
+                 * @param mode [in] Hysteresis mode (DRAINAGE, IMBIBITION, DRAINAGE_TO_IMBIBITION, IMBIBITION_TO_DRAINAGE)
+                 * 
+                 * Uses Newton-Raphson iteration to invert the capillary pressure function.
+                 */
+                GEOS_HOST_DEVICE
+                void computeInv(arraySlice1d<real64, compflow::USD_PHASE - 1> const &phaseVolFraction,
+                                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseMaxHistoricalVolFraction,
+                                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseMinHistoricalVolFraction,
+                                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseMode2PeakVolFraction,
+                                arraySlice1d<real64 const, cappres::USD_CAPPRES - 2> const &phaseTrappedVolFrac,
+                                arraySlice1d<real64 const, cappres::USD_CAPPRES - 2> const &phaseCapPressure,
+                                arraySlice2d<real64, cappres::USD_CAPPRES_DS - 2> const &dPhaseCapPressure_dPhaseVolFrac,
+                                fields::cappres::ModeIndexType const &mode) const;
+
+                /**
+                 * @brief Evaluate the raw drainage or imbibition table at a given saturation,
+                 *        bypassing the hysteresis mode-transition logic in compute().
+                 * @param tableIdx Table index (0 = DRAINAGE, 1 = IMBIBITION)
+                 * @param phaseVolFraction Phase volume fraction to evaluate at
+                 * @param phaseCapPressure [out] Capillary pressure from the table
+                 * @param dPhaseCapPressure_dPhaseVolFrac [out] Derivative of Pc w.r.t. S
+                 */
+                GEOS_HOST_DEVICE
+                void computeRawTablePc( integer const tableIdx,
+                                        real64 const & phaseVolFraction,
+                                        real64 & phaseCapPressure,
+                                        real64 & dPhaseCapPressure_dPhaseVolFrac ) const
+                {
+                    computeBoundCapillaryPressure(
+                        m_wettingNonWettingCapillaryPressureKernelWrappers[tableIdx],
+                        phaseVolFraction, phaseCapPressure, dPhaseCapPressure_dPhaseVolFrac );
+                }
+
+                /**
+                 * @brief Compute the actual Pc range [Pc_lo, Pc_hi] for a scanning curve.
+                 *
+                 * For Mode 2 (DRAINAGE_TO_IMBIBITION):
+                 *   Pc_hi = Pc_drainage(Shy)          (departure point)
+                 *   Pc_lo = Pc_imbibition(Swma)       (endpoint, where F=1)
+                 * For Mode 3 (IMBIBITION_TO_DRAINAGE):
+                 *   Pc_lo = Pc_imbibition(Shy)         (departure point)
+                 *   Pc_hi = Pc_drainage(Scrt)          (endpoint, where F=1)
+                 *
+                 * @param phaseMinHistVolFrac  Minimum historical volume fraction (Shy for Mode 2)
+                 * @param phaseMaxHistVolFrac  Maximum historical volume fraction (Shy for Mode 3)
+                 * @param mode                 Hysteresis mode
+                 * @param Pc_lo  [out] Lower bound of scanning curve Pc range
+                 * @param Pc_hi  [out] Upper bound of scanning curve Pc range
+                 */
+                GEOS_HOST_DEVICE
+                void computeScanningCurvePcRange( real64 const phaseMinHistVolFrac,
+                                                  real64 const phaseMaxHistVolFrac,
+                                                  ModeIndexType const mode,
+                                                  real64 & Pc_lo,
+                                                  real64 & Pc_hi ) const
+                {
+                    integer const ipWater = 0;
+                    real64 dPc_dummy;
+
+                    if( mode == ModeIndexType::DRAINAGE_TO_IMBIBITION )
+                    {
+                        // Shy = min historical saturation (departure from drainage)
+                        real64 const Smin_curve = m_wettingCurve.oppositeBoundPhaseVolFraction;
+                        real64 const Shy = LvArray::math::max( phaseMinHistVolFrac, Smin_curve );
+
+                        // Compute Scrt (trapped saturation) from Land model
+                        real64 Scrt = 0.0;
+                        KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(
+                            m_wettingCurve, Shy, m_landParam[ipWater],
+                            m_jerauldParam_a, m_jerauldParam_b, Scrt );
+
+                        // For wetting phase, Swma = Scrt (= 1 - (1 - Scrt))
+                        real64 const Swma = Scrt;
+
+                        // Pc_hi = Pc_drainage(Shy) — departure point, highest Pc on scanning curve
+                        computeRawTablePc( 0 /* drainage */, Shy, Pc_hi, dPc_dummy );
+
+                        // Pc_lo = Pc_imbibition(Swma) — endpoint where F=1, lowest Pc on scanning curve
+                        computeRawTablePc( 1 /* imbibition */, Swma, Pc_lo, dPc_dummy );
+                    }
+                    else if( mode == ModeIndexType::IMBIBITION_TO_DRAINAGE ||
+                             mode == ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING )
+                    {
+                        // Shy = max historical saturation (departure from imbibition)
+                        real64 const Smax_curve = m_wettingCurve.drainageExtremaPhaseVolFraction;
+                        real64 const Shy = LvArray::math::min( phaseMaxHistVolFrac, Smax_curve );
+
+                        // Compute Scrt
+                        real64 Scrt = 0.0;
+                        KilloughHysteresis::computeTrappedCriticalPhaseVolFraction(
+                            m_wettingCurve, Shy, m_landParam[ipWater],
+                            m_jerauldParam_a, m_jerauldParam_b, Scrt );
+
+                        // Pc_lo = Pc_imbibition(Shy) — departure point, lowest Pc on scanning curve
+                        computeRawTablePc( 1 /* imbibition */, Shy, Pc_lo, dPc_dummy );
+
+                        // Pc_hi = Pc_drainage(Scrt) — endpoint where F=1, highest Pc on scanning curve
+                        computeRawTablePc( 0 /* drainage */, Scrt, Pc_hi, dPc_dummy );
+                    }
+                    else
+                    {
+                        // Fallback: use raw table full range
+                        computeRawTablePc( 0 /* drainage */, 0.0, Pc_hi, dPc_dummy );
+                        computeRawTablePc( 1 /* imbibition */, 1.0, Pc_lo, dPc_dummy );
+                    }
+
+                    // Ensure Pc_lo <= Pc_hi
+                    if( Pc_lo > Pc_hi )
+                    {
+                        real64 tmp = Pc_lo;
+                        Pc_lo = Pc_hi;
+                        Pc_hi = tmp;
+                    }
+                }
+
+            private:
+
+                /**
+                 * @brief Helper function to compute Pc(S) for given S, mode, and historical values.
+                 * @param S Phase volume fraction
+                 * @param mode Hysteresis mode
+                 * @param ipPhase Phase index
+                 * @param phaseMinHistoricalVolFraction Minimum historical volume fraction
+                 * @param phaseMaxHistoricalVolFraction Maximum historical volume fraction
+                 * @param capPresKernelWrappers Capillary pressure kernel wrappers
+                 * @param wettingCurve Wetting curve data
+                 * @param nonWettingCurve Non-wetting curve data
+                 * @param landParam Land parameter
+                 * @param phaseIntermediateMinVolFraction Intermediate phase minimum volume fraction
+                 * @param killoughCurvatureParam Killough curvature parameter
+                 * @param jerauldParam_a Jerauld parameter a
+                 * @param jerauldParam_b Jerauld parameter b
+                 * @param isWettingPhase Whether this is the wetting phase
+                 * @param precomputedScrt Precomputed trapped critical saturation (optional, use -1.0 to compute)
+                 * @param precomputedDenomF Precomputed denominator for F calculation (optional, use 0.0 to compute)
+                 * @param precomputedShy Precomputed historical saturation Shy (optional, use -1.0 to compute)
+                 * @return Computed capillary pressure
+                 * 
+                 * Used for Newton-Raphson inversion in computeInv.
+                 * If precomputed values are provided (precomputedScrt >= 0, precomputedDenomF != 0, precomputedShy >= 0),
+                 * they will be used instead of recomputing them.
+                 */
+                GEOS_HOST_DEVICE
+                real64 computeCapillaryPressureForSaturation(
+                        real64 const S,
+                        fields::cappres::ModeIndexType const &mode,
+                        integer const ipPhase,
+                        real64 const &phaseMinHistoricalVolFraction,
+                        real64 const &phaseMaxHistoricalVolFraction,
+                        real64 const &phaseMode2PeakVolFraction,
+                        arrayView1d<TableFunction::KernelWrapper const> const &capPresKernelWrappers,
+                        KilloughHysteresis::HysteresisCurve const &wettingCurve,
+                        KilloughHysteresis::HysteresisCurve const &nonWettingCurve,
+                        real64 const &landParam,
+                        real64 const &phaseIntermediateMinVolFraction,
+                        real64 const &killoughCurvatureParam,
+                        real64 const &jerauldParam_a,
+                        real64 const &jerauldParam_b,
+                        bool const isWettingPhase,
+                        real64 const precomputedScrt = -1.0,
+                        real64 const precomputedDenomF = 0.0,
+                        real64 const precomputedShy = -1.0) const;
+
+                static constexpr real64 flowReversalBuffer = KilloughHysteresis::flowReversalBuffer;
+//    ModeIndexType& m_mode;
+
+                //2p
+                arrayView1d<TableFunction::KernelWrapper const> const m_wettingNonWettingCapillaryPressureKernelWrappers;
+                arrayView1d<TableFunction::KernelWrapper const> const m_inverseWettingNonWettingCapillaryPressureKernelWrappers;
+                //3p
+                arrayView1d<TableFunction::KernelWrapper const> const m_wettingIntermediateCapillaryPressureKernelWrappers;
+                arrayView1d<TableFunction::KernelWrapper const> const m_inverseWettingIntermediateCapillaryPressureKernelWrappers;
+                arrayView1d<TableFunction::KernelWrapper const> const m_nonWettingIntermediateCapillaryPressureKernelWrappers;
+                arrayView1d<TableFunction::KernelWrapper const> const m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers;
+
+                ///Land Coeff
+                arrayView1d<integer const> m_phaseHasHysteresis;
+                arrayView1d<real64 const> m_landParam;
+
+                /// Parameter a introduced by Jerauld in the Land model
+                const real64 m_jerauldParam_a;
+
+                /// Parameter b introduced by Jerauld in the Land model
+                const real64 m_jerauldParam_b;
+
+                /// Curvature parameter in Killough wetting phase hysteresis (enpoints curvatures)
+                const real64 m_killoughCurvatureParamCapPres;
+
+                /// needed in 3p-wetting hysteresis as we need to get the max accessible pore space
+                real64 const m_phaseIntermediateMinVolFraction;
+
+                KilloughHysteresis::HysteresisCurve const m_wettingCurve;
+                KilloughHysteresis::HysteresisCurve const m_nonWettingCurve;
+
+                /// Minimum historical phase volume fraction for each phase
+                arrayView2d<real64 const, compflow::USD_PHASE> m_phaseMinHistoricalVolFraction;
+
+                /// Maximum historical phase volume fraction for each phase
+                arrayView2d<real64 const, compflow::USD_PHASE> m_phaseMaxHistoricalVolFraction;
+
+                /// Peak saturation reached during Mode 2 (DRAINAGE_TO_IMBIBITION) for each phase (mutable for updates)
+                arrayView2d<real64, compflow::USD_PHASE> m_phaseMode2PeakVolFraction;
+
+                // Drainage / Imbibition flags cellwise
+                arrayView1d<ModeIndexType> m_mode;
+
+            };
+
+            /**
+             * @brief Create an update kernel wrapper.
+             * @return the wrapper
+             */
+            KernelWrapper createKernelWrapper();
+
+            //might need it to be virtual one level higher --> from Killough/Hysteresis common class
+            virtual void saveConvergedPhaseVolFractionState(
+                    arrayView2d<real64 const, compflow::USD_PHASE> const &phaseVolFraction) const override;
+
+
+            struct viewKeyStruct : CapillaryPressureBase::viewKeyStruct {
+
+
+                ///Land Coeff
+                static constexpr char const *landParameterString() { return "landParameter"; }
+
+                ///flag
+                static constexpr char const *phaseHasHysteresisString() { return "phaseHasHysteresis"; }
+
+                ///and packed curves data struct
+                static constexpr char const *wettingCurveString() { return "wettingCurve"; };
+
+                static constexpr char const *nonWettingCurveString() { return "nonWettingCurve"; };
+
+
+                ///tables and assoc. wrappers
+                //2phase
+                static constexpr char const *
+                drainageWettingNonWettingCapPresTableNameString() { return "drainageWettingNonWettingCapPressureTableName"; }
+
+                static constexpr char const *
+                imbibitionWettingNonWettingCapPresTableNameString() { return "imbibitionWettingNonWettingCapPressureTableName"; }
+
+                //3phase
+                static constexpr char const *
+                drainageWettingIntermediateCapPresTableNameString() { return "drainageWettingIntermediateCapPressureTableName"; }
+
+                static constexpr char const *
+                drainageNonWettingIntermediateCapPresTableNameString() { return "drainageNonWettingIntermediateCapPressureTableName"; }
+
+                static constexpr char const *
+                imbibitionWettingIntermediateCapPresTableNameString() { return "imbibitionWettingIntermediateCapPressureTableName"; }
+
+                static constexpr char const *
+                imbibitionNonWettingIntermediateCapPresTableNameString() { return "imbibitionNonWettingIntermediateCapPressureTableName"; }
+
+                static constexpr char const *
+                wettingNonWettingCapillaryPressureKernelWrappersString() { return "wettingNonWettingCapillaryPressureKernelWrappers"; }
+
+                static constexpr char const *
+                wettingIntermediateCapillaryPressureKernelWrappersString() { return "wettingIntermediateCapillaryPressureKernelWrappers"; }
+
+                static constexpr char const *
+                nonWettingIntermediateCapillaryPressureKernelWrappersString() { return "nonWettingIntermediateCapillaryPressureKernelWrappers"; }
+
+                //misc
+                static constexpr char const *
+                phaseIntermediateMinVolFractionString() { return "phaseIntermediateMinVolFraction"; }
+                //to decide wheter drainage/drainage to imbibition or imbibition/imbibition to drainage
+            };
+
+
+        private:
+            virtual void postProcessInput();
+
+            virtual void initializePreSubGroups() override;
+
+            void resizeFields(localIndex const size,
+                              localIndex const numPts) override;
+
+
+            /**
+             * @brief Create all the table kernel wrappers needed for the simulation (for all the phases present)
+             */
+            void createAllTableKernelWrappers();
+
+            /**
+             * @brief Compute the Land coefficient for the wetting and non-wetting phases
+             */
+            void computeLandCoefficient();
+
+            ///data members
+
+
+            //TODO impl
+//  array1d< integer >  m_tCurveOption;
+
+            KilloughHysteresis::HysteresisCurve m_wettingCurve;
+            KilloughHysteresis::HysteresisCurve m_nonWettingCurve;
+
+            ///tables
+            //2p
+            string m_drainageWettingNonWettingCapPresTableName;
+            string m_imbibitionWettingNonWettingCapPresTableName;
+            //3p
+            string m_drainageWettingIntermediateCapPresTableName;
+            string m_drainageNonWettingIntermediateCapPresTableName;
+            string m_imbibitionWettingIntermediateCapPresTableName;
+            string m_imbibitionNonWettingIntermediateCapPresTableName;
+            // kernel wrappers
+            /// Imbibition kernel wrappers for relative permeabilities in the following order:
+            /// 0- drainage
+            /// 1- imbibition (cf. struct ModeIndexType)
+            //2p
+            array1d<TableFunction::KernelWrapper> m_wettingNonWettingCapillaryPressureKernelWrappers;
+            array1d<TableFunction::KernelWrapper> m_inverseWettingNonWettingCapillaryPressureKernelWrappers;
+            //3p
+            array1d<TableFunction::KernelWrapper> m_wettingIntermediateCapillaryPressureKernelWrappers;
+            array1d<TableFunction::KernelWrapper> m_inverseWettingIntermediateCapillaryPressureKernelWrappers;
+            array1d<TableFunction::KernelWrapper> m_nonWettingIntermediateCapillaryPressureKernelWrappers;
+            array1d<TableFunction::KernelWrapper> m_inverseNonWettingIntermediateCapillaryPressureKernelWrappers;
+            
+            // Store inverse tables to keep them alive
+            std::vector<std::shared_ptr<TableFunction>> m_inverseTables;
+
+
+            /// Flag to specify whether the phase has hysteresis or not (deduced from table input)
+            array1d<integer> m_phaseHasHysteresis;
+
+            /// Trapping parameter from the Land model (typically called C)
+            array1d<real64> m_landParam;
+
+            /// Parameter a introduced by Jerauld in the Land model
+            real64 m_jerauldParam_a;
+
+            /// Parameter b introduced by Jerauld in the Land model
+            real64 m_jerauldParam_b;
+
+            /// Curvature parameter in Killough wetting phase hysteresis (Scanning curves curvatures)
+            real64 m_killoughCurvatureParamCapPres;
+
+            /// Cell-wise status imbibition, imbibitioon_to_drainage, ... etc
+            array1d<integer> m_mode;
+
+            // Max historical saturations
+            /// Minimum historical phase volume fraction for each phase
+            array2d<real64, compflow::LAYOUT_PHASE> m_phaseMinHistoricalVolFraction;
+
+            /// Maximum historical phase volume fraction for each phase
+            array2d<real64, compflow::LAYOUT_PHASE> m_phaseMaxHistoricalVolFraction;
+
+            /// Peak saturation reached during Mode 2 (DRAINAGE_TO_IMBIBITION) for each phase
+            array2d<real64, compflow::LAYOUT_PHASE> m_phaseMode2PeakVolFraction;
+
+            //needed in hysteresis of wetting phase
+            real64 m_phaseIntermediateMinVolFraction;
+
+        };
+
+        // Standard 3-argument compute method for compatibility with InverseCapillaryPressure
+        // Uses zero/default values for historical fractions (no hysteresis in inverse computation)
+        GEOS_HOST_DEVICE
+        inline void TableCapillaryPressureHysteresis::KernelWrapper::compute(
+                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseVolFraction,
+                arraySlice1d<real64, cappres::USD_CAPPRES - 2> const &phaseCapPressure,
+                arraySlice2d<real64, cappres::USD_CAPPRES_DS - 2> const &dPhaseCapPressure_dPhaseVolFrac
+        ) const {
+            // Create temporary arrays for historical fractions and trapped fraction
+            // Initialize to zero/default values since inverse computation doesn't use hysteresis
+            constexpr integer MAX_NUM_PHASES = CapillaryPressureBase::MAX_NUM_PHASES;
+            real64 phaseMaxHistoricalVolFraction[MAX_NUM_PHASES]{};
+            real64 phaseMinHistoricalVolFraction[MAX_NUM_PHASES]{};
+            real64 phaseTrappedVolFrac[MAX_NUM_PHASES]{};
+            real64 phaseMode2PeakVolFraction[MAX_NUM_PHASES]{};
+            ModeIndexType mode = ModeIndexType::DRAINAGE; // Default to drainage mode
+            
+            // Create ArrayView from stack arrays, then get slices
+            integer const numPhases = LvArray::integerConversion< integer >( phaseVolFraction.size() );
+            localIndex dims[1] = { numPhases };
+            localIndex strides[1] = { 1 };
+            
+            arraySlice1d< real64 const, compflow::USD_PHASE - 1 > const phaseMaxHistSlice(
+                phaseMaxHistoricalVolFraction, dims, strides );
+            arraySlice1d< real64 const, compflow::USD_PHASE - 1 > const phaseMinHistSlice(
+                phaseMinHistoricalVolFraction, dims, strides );
+            arraySlice1d< real64, cappres::USD_CAPPRES - 2 > phaseTrappedSlice(
+                phaseTrappedVolFrac, dims, strides );
+            arraySlice1d< real64, compflow::USD_PHASE - 1 > phaseMode2PeakSlice(
+                phaseMode2PeakVolFraction, dims, strides );
+            
+            // Call the full compute method
+            compute( phaseVolFraction,
+                     phaseMaxHistSlice,
+                     phaseMinHistSlice,
+                     phaseTrappedSlice,
+                     phaseCapPressure,
+                     dPhaseCapPressure_dPhaseVolFrac,
+                     mode,
+                     phaseMode2PeakSlice );
+        }
+
+        GEOS_HOST_DEVICE
+        inline void TableCapillaryPressureHysteresis::KernelWrapper::compute(
+                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseVolFraction,
+                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseMaxHistoricalVolFraction,
+                arraySlice1d<real64 const, compflow::USD_PHASE - 1> const &phaseMinHistoricalVolFraction,
+                arraySlice1d<real64, cappres::USD_CAPPRES - 2> const &phaseTrappedVolFrac,
+                arraySlice1d<real64, cappres::USD_CAPPRES - 2> const &phaseCapPressure,
+                arraySlice2d<real64, cappres::USD_CAPPRES_DS - 2> const &dPhaseCapPressure_dPhaseVolFrac,
+                ModeIndexType &mode,
+                arraySlice1d<real64, compflow::USD_PHASE - 1> &phaseMode2PeakVolFraction
+        ) const {
+            // Early return if m_phaseOrder is empty or input arrays are empty
+            if( m_phaseOrder.size() == 0 || 
+                phaseVolFraction.size() == 0 ||
+                phaseCapPressure.size() == 0 )
+            {
+                return;
+            }
+
+            LvArray::forValuesInSlice(dPhaseCapPressure_dPhaseVolFrac, [](real64 &val) { val = 0.0; });
+
+            using PT = CapillaryPressureBase::PhaseType;
+            // Check bounds before accessing m_phaseOrder
+            integer const ipWater = ( PT::WATER < m_phaseOrder.size() ) ? m_phaseOrder[PT::WATER] : -1;
+            integer const ipOil = ( PT::OIL < m_phaseOrder.size() ) ? m_phaseOrder[PT::OIL] : -1;
+            integer const ipGas = ( PT::GAS < m_phaseOrder.size() ) ? m_phaseOrder[PT::GAS] : -1;
+
+            if (ipWater >= 0 && ipOil >= 0 && ipGas >= 0) {
+                computeThreePhase(ipWater, // wetting
+                                  ipOil,   // intermediate
+                                  ipGas,   // non-wetting
+                                  phaseVolFraction,
+                                  phaseMaxHistoricalVolFraction,
+                                  phaseMinHistoricalVolFraction,
+                                  phaseTrappedVolFrac,
+                                  phaseCapPressure,
+                                  dPhaseCapPressure_dPhaseVolFrac,
+                                  mode,
+                                  phaseMode2PeakVolFraction);
+
+            } else if (ipWater < 0) {
+                computeTwoPhaseNonWetting(ipOil, // leading
+                                          ipGas, // deduced
+                                          phaseVolFraction,
+                                          phaseMaxHistoricalVolFraction,
+                                          phaseMinHistoricalVolFraction,
+                                          phaseTrappedVolFrac,
+                                          phaseCapPressure,
+                                          dPhaseCapPressure_dPhaseVolFrac,
+                                          mode);
+            } else if (ipOil < 0) {
+                computeTwoPhaseWetting(ipWater, // leading
+                                       ipGas,   // deduced
+                                       phaseVolFraction,
+                                       phaseMaxHistoricalVolFraction,
+                                       phaseMinHistoricalVolFraction,
+                                       phaseTrappedVolFrac,
+                                       phaseCapPressure,
+                                       dPhaseCapPressure_dPhaseVolFrac,
+                                       mode,
+                                       phaseMode2PeakVolFraction);
+            } else if (ipGas < 0) {
+                computeTwoPhaseWetting(ipWater, //leading
+                                       ipOil,   //deduced
+                                       phaseVolFraction,
+                                       phaseMaxHistoricalVolFraction,
+                                       phaseMinHistoricalVolFraction,
+                                       phaseTrappedVolFrac,
+                                       phaseCapPressure,
+                                       dPhaseCapPressure_dPhaseVolFrac,
+                                       mode,
+                                       phaseMode2PeakVolFraction);
+            }
+
+
+        }
+
+        GEOS_HOST_DEVICE
+        inline void TableCapillaryPressureHysteresis::KernelWrapper::update(const geos::localIndex k,
+                                                                            const geos::localIndex q,
+                                                                            const arraySlice1d<const geos::real64,
+                                                                                    compflow::USD_PHASE
+                                                                                    - 1> &phaseVolFraction) const {
+            // Create a reference to the Mode 2 peak slice for this element
+            // m_phaseMode2PeakVolFraction uses compflow::LAYOUT_PHASE, so use compflow::USD_PHASE - 1
+            arraySlice1d<real64, compflow::USD_PHASE - 1> phaseMode2PeakSlice = m_phaseMode2PeakVolFraction[k];
+            compute(phaseVolFraction,
+                    m_phaseMaxHistoricalVolFraction[k],
+                    m_phaseMinHistoricalVolFraction[k],
+                    m_phaseTrappedVolFrac[k][q],
+                    m_phaseCapPressure[k][q],
+                    m_dPhaseCapPressure_dPhaseVolFrac[k][q],
+                    m_mode[k],
+                    phaseMode2PeakSlice);
+        }
+
+
+    } //constitutive
+} // geos
+
+#endif //GEOS_CONSTITUTIVE_TABLECAPILLARYPRESSUREHYSTERESIS_HPP
diff --git a/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.cpp b/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.cpp
index b324366f4f2..17a0a74e426 100644
--- a/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.cpp
+++ b/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.cpp
@@ -122,6 +122,7 @@ VanGenuchtenCapillaryPressure::createKernelWrapper()
                         m_volFracScale,
                         m_phaseTypes,
                         m_phaseOrder,
+                        m_phaseTrappedVolFrac,
                         m_phaseCapPressure,
                         m_dPhaseCapPressure_dPhaseVolFrac );
 }
diff --git a/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp b/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp
index f3af8198d60..2234b405037 100644
--- a/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp
+++ b/src/coreComponents/constitutive/capillaryPressure/VanGenuchtenCapillaryPressure.hpp
@@ -39,10 +39,12 @@ class VanGenuchtenCapillaryPressureUpdate final : public CapillaryPressureBaseUp
                                        real64 const volFracScale,
                                        arrayView1d< integer const > const & phaseTypes,
                                        arrayView1d< integer const > const & phaseOrder,
+                                       arrayView3d< geos::real64, cappres::USD_CAPPRES > const & phaseTrapped,
                                        arrayView3d< real64, cappres::USD_CAPPRES > const & phaseCapPressure,
                                        arrayView4d< real64, cappres::USD_CAPPRES_DS > const & dPhaseCapPressure_dPhaseVolFrac )
     : CapillaryPressureBaseUpdate( phaseTypes,
                                    phaseOrder,
+                                   phaseTrapped,
                                    phaseCapPressure,
                                    dPhaseCapPressure_dPhaseVolFrac ),
     m_phaseMinVolumeFraction( phaseMinVolumeFraction ),
@@ -57,6 +59,11 @@ class VanGenuchtenCapillaryPressureUpdate final : public CapillaryPressureBaseUp
                 arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
                 arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
 
+  GEOS_HOST_DEVICE
+  void computeInv( arraySlice1d< real64 const, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+                   arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+                   arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const;
+
   GEOS_HOST_DEVICE
   virtual void update( localIndex const k,
                        localIndex const q,
@@ -189,6 +196,69 @@ VanGenuchtenCapillaryPressureUpdate::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+VanGenuchtenCapillaryPressureUpdate::
+  computeInv( arraySlice1d< real64 const, compflow::USD_PHASE - 1 > const & phaseVolFraction,
+              arraySlice1d< real64, cappres::USD_CAPPRES - 2 > const & phaseCapPres,
+              arraySlice2d< real64, cappres::USD_CAPPRES_DS - 2 > const & dPhaseCapPres_dPhaseVolFrac ) const
+{
+  LvArray::forValuesInSlice( dPhaseCapPres_dPhaseVolFrac, []( real64 & val ){ val = 0.0; } );
+
+  // the VanGenuchten model does not support volFracScaled = 0 and = 1
+  // hence we need an epsilon value to avoid a division by zero
+  // TODO: for S < epsilon and S > 1 - epsilon, replace the original unbounded VG curve with a bounded power-law
+  // extension
+  real64 const eps = m_capPressureEpsilon;
+  real64 const volFracScaleInv = 1.0 / m_volFracScale;
+
+  // compute first water-oil capillary pressure as a function of water-phase vol fraction
+  integer const ip_water = m_phaseOrder[CapillaryPressureBase::PhaseType::WATER];
+  if( ip_water >= 0 )
+  {
+
+    real64 const volFracScaled = (phaseVolFraction[ip_water] - m_phaseMinVolumeFraction[ip_water]) * volFracScaleInv;
+    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_water]; // div by 0 taken care of by initialization
+                                                                          // check
+    real64 const multiplier    = m_phaseCapPressureMultiplier[ip_water];
+
+    real64 const scaledWettingVolFrac                = volFracScaled;
+    real64 const dScaledWettingPhaseVolFrac_dVolFrac = volFracScaleInv;
+
+    evaluateVanGenuchtenFunction( scaledWettingVolFrac,
+                                  dScaledWettingPhaseVolFrac_dVolFrac,
+                                  exponentInv,
+                                  multiplier,
+                                  eps,
+                                  phaseCapPres[ip_water],
+                                  dPhaseCapPres_dPhaseVolFrac[ip_water][ip_water] );
+
+  }
+
+
+  // then compute the oil-gas capillary pressure as a function of gas-phase vol fraction
+  integer const ip_gas = m_phaseOrder[CapillaryPressureBase::PhaseType::GAS];
+  if( ip_gas >= 0 )
+  {
+    real64 const volFracScaled = (phaseVolFraction[ip_gas] - m_phaseMinVolumeFraction[ip_gas]) * volFracScaleInv;
+    real64 const exponentInv   = m_phaseCapPressureExponentInv[ip_gas]; // div by 0 taken care of by initialization
+                                                                        // check
+    real64 const multiplier    = -m_phaseCapPressureMultiplier[ip_gas]; // for gas capillary pressure, take the opposite
+                                                                        // of the VG function
+
+    real64 const scaledWettingVolFrac                = 1-volFracScaled;
+    real64 const dScaledWettingPhaseVolFrac_dVolFrac =  -volFracScaleInv;
+
+    evaluateVanGenuchtenFunction( scaledWettingVolFrac,
+                                  dScaledWettingPhaseVolFrac_dVolFrac,
+                                  exponentInv,
+                                  multiplier,
+                                  eps,
+                                  phaseCapPres[ip_gas],
+                                  dPhaseCapPres_dPhaseVolFrac[ip_gas][ip_gas] );
+  }
+}
+
 GEOS_HOST_DEVICE
 GEOS_FORCE_INLINE
 void
diff --git a/src/coreComponents/constitutive/docs/TwoPhaseFluid.rst b/src/coreComponents/constitutive/docs/TwoPhaseFluid.rst
new file mode 100644
index 00000000000..39b35510c63
--- /dev/null
+++ b/src/coreComponents/constitutive/docs/TwoPhaseFluid.rst
@@ -0,0 +1,90 @@
+.. _TwoPhaseFluid:
+
+############################################
+Two-phase fluid model
+############################################
+
+Overview
+=========================
+
+This model represents a two-phase fluid with pressure-dependent density and viscosity.
+
+For each phase, both density and viscosity are described as tabulated data, either in the form of ``TableFunction`` or text files.
+
+In the case of text files, one file is expected per phase and should consist of three columns: pressure, density and viscosity.
+
+Note that currently, there is no temperature dependence in the model.
+
+
+Parameters
+=========================
+
+The model is represented by ``<TwoPhaseFluid>`` node in the input.
+
+The following attributes are supported:
+
+.. include:: /docs/sphinx/datastructure/TwoPhaseFluid.rst
+              
+
+Example using TableFunctions
+============================
+
+.. code-block:: xml
+
+  <Constitutive>
+    <TwoPhaseFluid
+      name="fluid"
+      phaseNames="{ oil, water }"
+      densityTableNames="{ densityTableOil, densityTableWater }"
+      viscosityTableNames="{ viscosityTableOil, viscosityTableWater }" />
+  </Constitutive>
+
+  <Functions>
+    <TableFunction
+      name="densityTableOil"
+      coordinateFiles="{ pres_pvdo.txt }"
+      voxelFile="dens_pvdo.txt"
+      interpolation="linear" />
+
+    <TableFunction
+      name="viscosityTableOil"
+      coordinateFiles="{ pres_pvdo.txt }"
+      voxelFile="visc_pvdo.txt"
+      interpolation="linear" />
+
+    <TableFunction
+      name="densityTableWater"
+      coordinates="{ 2068000, 5516000, 30600000, 55160000 }"
+      values="{ 980.683, 982.07, 992.233, 1002.265 }"
+      interpolation="linear" />
+
+    <TableFunction
+      name="viscosityTableWater"
+      coordinates="{ 0 }"
+      values="{ 0.0003 }"
+      interpolation="linear" />
+  </Functions>  
+
+
+Example using text files
+=========================
+
+.. code-block:: xml
+
+  <Constitutive>
+    <TwoPhaseFluid
+      name="fluid"
+      phaseNames="{ oil, water }"
+      tableNames="{ oil.txt, water.txt }" />
+  </Constitutive>
+
+
+with, for example, ``water.txt`` being set as:
+
+.. code-block:: text
+
+  #  P(Pa) Dens(kg/m3) Visc(Pa.s)
+   2068000     980.683     0.0003     
+   5516000      982.07     0.0003
+  30600000     992.233     0.0003
+  55160000    1002.265     0.0003
diff --git a/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.cpp b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.cpp
new file mode 100644
index 00000000000..ad6379ea129
--- /dev/null
+++ b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.cpp
@@ -0,0 +1,268 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 Total, S.A
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file TwoPhaseFluid.cpp
+ */
+
+#include "constitutive/fluid/multifluid/CO2Brine/functions/PVTFunctionHelpers.hpp" // for readTable
+#include "TwoPhaseFluid.hpp"
+#include "TwoPhaseFluidFields.hpp"
+
+#include "functions/FunctionManager.hpp"
+
+
+namespace geos
+{
+
+using namespace dataRepository;
+
+namespace constitutive
+{
+
+
+TwoPhaseFluid::TwoPhaseFluid( string const & name, Group * const parent )
+  : ConstitutiveBase( name, parent )
+{
+  registerWrapper( viewKeyStruct::phaseNamesString(), &m_phaseNames ).
+    setRTTypeName( rtTypes::CustomTypes::groupNameRefArray ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setDescription( "List of fluid phases" );
+
+  // 1) First option: specify PVT tables from one file per phase, read the files line by line, and populate the internal TableFunctions
+  registerWrapper( viewKeyStruct::tableFilesString(), &m_tableFiles ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setRestartFlags( RestartFlags::NO_WRITE ).
+    setDescription( "List of filenames with input PVT tables (one per phase)" );
+
+  // 2) Second option: specify TableFunction names for each phase,
+  registerWrapper( viewKeyStruct::densityTableNamesString(), &m_densityTableNames ).
+    setRTTypeName( rtTypes::CustomTypes::groupNameRefArray ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setDescription( "List of density TableFuncion names from the Function block. \n"
+                    "The user must provide one TableFunction per phase, respecting the order provided in \"phaseNames\"." );
+
+  registerWrapper( viewKeyStruct::viscosityTableNamesString(), &m_viscosityTableNames ).
+    setRTTypeName( rtTypes::CustomTypes::groupNameRefArray ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setDescription( "List of viscosity TableFuncion names from the Function block. \n"
+                    "The user must provide one TableFunction per phase, respecting the order provided in \"phaseNames\"." );
+
+  registerField( fields::twophasefluid::phaseDensity{}, &m_phaseDensity.value );
+  registerField( fields::twophasefluid::dPhaseDensity{}, &m_phaseDensity.derivs );
+  registerField( fields::twophasefluid::phaseDensity_n{}, &m_phaseDensity_n );
+
+  registerField( fields::twophasefluid::phaseViscosity{}, &m_phaseViscosity.value );
+  registerField( fields::twophasefluid::dPhaseViscosity{}, &m_phaseViscosity.derivs );
+}
+
+
+std::unique_ptr< ConstitutiveBase >
+TwoPhaseFluid::deliverClone( string const & name, Group * const parent ) const
+{
+  return ConstitutiveBase::deliverClone( name, parent );
+}
+
+
+void TwoPhaseFluid::resizeFields( localIndex const size, localIndex const numPts )
+{
+  // Assume sole dependency on pressure, i.e. one derivative
+  m_phaseDensity.value.resize( size, numPts, 2 );
+  m_phaseDensity.derivs.resize( size, numPts, 2, 1 );
+
+  m_phaseDensity_n.resize( size, numPts, 2 );
+
+  m_phaseViscosity.value.resize( size, numPts, 2 );
+  m_phaseViscosity.derivs.resize( size, numPts, 2, 1 );
+}
+
+
+void TwoPhaseFluid::allocateConstitutiveData( dataRepository::Group & parent,
+                                              localIndex const numConstitutivePointsPerParentIndex )
+{
+  ConstitutiveBase::allocateConstitutiveData( parent, numConstitutivePointsPerParentIndex );
+  resizeFields( parent.size(), numConstitutivePointsPerParentIndex );
+}
+
+
+void TwoPhaseFluid::postInputInitialization()
+{
+  ConstitutiveBase::postInputInitialization();
+
+  // Input relationships can be provided either as text files or TableFunctions.
+  m_tableFiles.empty() ? readInputDataFromTableFunctions() : readInputDataFromFileTableFunctions();
+
+  checkTableConsistency();
+}
+
+
+void TwoPhaseFluid::fillData( integer const ip,
+                              array1d< array1d< real64 > > const & tableValues )
+{
+  array1d< array1d< real64 > > pressureCoords( 1 );
+  pressureCoords[0].resize( tableValues.size() );
+  array1d< real64 > density( tableValues.size() );
+  array1d< real64 > viscosity( tableValues.size() );
+
+  for( localIndex i = 0; i < tableValues.size(); ++i )
+  {
+    GEOS_THROW_IF_NE_MSG( tableValues[i].size(), 3,
+                          GEOS_FMT( "{}: three columns (pressure, density, and viscosity) are expected", getFullName() ),
+                          InputError );
+
+    pressureCoords[0][i] = tableValues[i][0];
+    density[i] = tableValues[i][1];
+    viscosity[i] = tableValues[i][2];
+  }
+
+  string const densityTableName = getName() + "DensityPhase" + GEOS_FMT( "{}", ip );
+  string const viscosityTableName = getName() +  "ViscosityPhase" + GEOS_FMT( "{}", ip );
+  m_densityTableNames.emplace_back( densityTableName );
+  m_viscosityTableNames.emplace_back( viscosityTableName );
+
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  TableFunction & tableDensity =
+    dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", densityTableName ) );
+  tableDensity.setTableCoordinates( pressureCoords, { units::Pressure } );
+  tableDensity.setTableValues( density, units::Density );
+  tableDensity.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  TableFunction & tableViscosity =
+    dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", viscosityTableName ) );
+  tableViscosity.setTableCoordinates( pressureCoords, { units::Pressure } );
+  tableViscosity.setTableValues( viscosity, units::Viscosity );
+  tableViscosity.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+}
+
+
+void TwoPhaseFluid::readInputDataFromFileTableFunctions()
+{
+  // Check for ambiguous definition
+  GEOS_THROW_IF( !(m_densityTableNames.empty() && m_viscosityTableNames.empty()),
+                 GEOS_FMT( "{}: input is redundant (both TableFunction names and text files)", getFullName() ),
+                 InputError );
+
+
+  // Check that we have exactly two table files (one per phase)
+  GEOS_THROW_IF_NE_MSG( m_tableFiles.size(), 2,
+                        GEOS_FMT( "{}: expecting two table files (one per phase)", getFullName() ),
+                        InputError );
+
+  array1d< array1d< real64 > > tableValues;
+  for( integer ip = 0; ip < 2; ++ip )
+  {
+    tableValues.clear();
+    geos::constitutive::PVTProps::BlackOilTables::readTable( m_tableFiles[ip], 3, tableValues );
+    fillData( ip, tableValues );
+  }
+}
+
+
+void TwoPhaseFluid::readInputDataFromTableFunctions()
+{
+  // Check for ambiguous definition
+  GEOS_THROW_IF( !m_tableFiles.empty(),
+                 GEOS_FMT( "{}: input is redundant (both TableFunction names and text files)", getFullName() ),
+                 InputError );
+
+  // Since we are considering a two phase fluid, we should have exactly 2 tables per property
+  GEOS_THROW_IF_NE_MSG( m_densityTableNames.size(), 2,
+                        GEOS_FMT( "{}: one density table must be provided for each phase", getFullName() ),
+                        InputError );
+
+  GEOS_THROW_IF_NE_MSG( m_viscosityTableNames.size(), 2,
+                        GEOS_FMT( "{}: one viscosity table must be provided for each phase", getFullName() ),
+                        InputError );
+
+
+  FunctionManager const & functionManager = FunctionManager::getInstance();
+
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    GEOS_THROW_IF( !functionManager.hasGroup( m_densityTableNames[iph] ),
+                   GEOS_FMT( "{}: density table '{}' not found", getFullName(), m_densityTableNames[iph] ),
+                   InputError );
+
+    GEOS_THROW_IF( !functionManager.hasGroup( m_viscosityTableNames[iph] ),
+                   GEOS_FMT( "{}: viscosity table '{}' not found", getFullName(), m_viscosityTableNames[iph] ),
+                   InputError );
+  }
+}
+
+
+void TwoPhaseFluid::initializePostSubGroups()
+{
+  ConstitutiveBase::initializePostSubGroups();
+
+  FunctionManager const & functionManager = FunctionManager::getInstance();
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    // Grab the tables by name from the function manager,
+    // then add them in a list to create their table wrappers when needed
+    TableFunction const & densityTable = functionManager.getGroup< TableFunction const >( m_densityTableNames[iph] );
+    m_densityTables.emplace_back( &densityTable );
+    m_densityTableKernels.emplace_back( m_densityTables[iph]->createKernelWrapper() );
+
+    TableFunction const & viscosityTable = functionManager.getGroup< TableFunction const >( m_viscosityTableNames[iph] );
+    m_viscosityTables.emplace_back( &viscosityTable );
+    m_viscosityTableKernels.emplace_back( m_viscosityTables[iph]->createKernelWrapper() );
+  }
+}
+
+
+void TwoPhaseFluid::checkTableConsistency() const
+{
+  FunctionManager const & functionManager = FunctionManager::getInstance();
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    TableFunction const & densityTable = functionManager.getGroup< TableFunction const >( m_densityTableNames[iph] );
+    arrayView1d< real64 const > const density = densityTable.getValues();
+
+    for( localIndex i = 1; i < density.size(); ++i )
+    {
+      GEOS_THROW_IF( density[i] - density[i-1] < 0,
+                     GEOS_FMT( "{}: in table '{}' density values must be increasing", getFullName(), densityTable.getName() ),
+                     InputError );
+    }
+  }
+}
+
+
+TwoPhaseFluid::KernelWrapper
+TwoPhaseFluid::createKernelWrapper()
+{
+  return KernelWrapper( m_densityTableKernels,
+                        m_viscosityTableKernels,
+                        m_phaseDensity.toView(),
+                        m_phaseViscosity.toView());
+}
+
+
+TwoPhaseFluid::KernelWrapper::KernelWrapper(
+  arrayView1d< TableFunction::KernelWrapper const > densityTables,
+  arrayView1d< TableFunction::KernelWrapper const > viscosityTables,
+  PhaseProp::ViewType phaseDensity,
+  PhaseProp::ViewType phaseViscosity )
+  : m_densityTables( std::move( densityTables )),
+  m_viscosityTables( std::move( viscosityTables )),
+  m_phaseDensity( std::move( phaseDensity )),
+  m_phaseViscosity( std::move( phaseViscosity )) {}
+
+
+REGISTER_CATALOG_ENTRY( ConstitutiveBase, TwoPhaseFluid, string const &, Group * const )
+
+}  // namespace constitutive
+}  // namespace geos
diff --git a/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.hpp b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.hpp
new file mode 100644
index 00000000000..18cdc357bb0
--- /dev/null
+++ b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluid.hpp
@@ -0,0 +1,344 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 Total, S.A
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file TwoPhaseFluid.hpp
+ */
+
+#ifndef GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUID_TWOPHASEFLUID_HPP_
+#define GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUID_TWOPHASEFLUID_HPP_
+
+#include "common/DataLayouts.hpp"
+#include "functions/TableFunction.hpp"
+#include "constitutive/ConstitutiveBase.hpp"
+
+#include "constitutive/fluid/multifluid/Layouts.hpp"
+#include "constitutive/fluid/multifluid/MultiFluidUtils.hpp"
+
+#include "constitutive/ConstitutivePassThruHandler.hpp"
+
+
+namespace geos
+{
+namespace constitutive
+{
+
+class TwoPhaseFluid : public ConstitutiveBase
+{
+public:
+
+  TwoPhaseFluid( string const & name,
+                 Group * const parent );
+
+  virtual std::unique_ptr< ConstitutiveBase >
+  deliverClone( string const & name,
+                Group * const parent ) const override;
+
+  virtual void allocateConstitutiveData( dataRepository::Group & parent,
+                                         localIndex const numConstitutivePointsPerParentIndex ) override;
+
+  /**
+   * @name Static Factory Catalog members and functions
+   */
+  ///@{
+
+  /**
+   * @brief Static catalog string
+   * @return A string that is used to register/lookup this class in the registry
+   */
+  static std::string catalogName() { return "TwoPhaseFluid"; }
+
+  /**
+   * @brief Get catalog name
+   * @return Name string
+   */
+  virtual string getCatalogName() const override { return catalogName(); }
+
+  ///@}
+
+
+
+  /**
+   * @brief Getter for the fluid phase names
+   * @return an array storing the phase names
+   */
+  string_array const & phaseNames() const { return m_phaseNames; }
+
+  struct viewKeyStruct : ConstitutiveBase::viewKeyStruct
+  {
+    static constexpr char const * tableFilesString() { return "tableFiles"; }
+    static constexpr char const * phaseNamesString() { return "phaseNames"; }
+    static constexpr char const * densityTableNamesString() { return "densityTableNames"; }
+    static constexpr char const * viscosityTableNamesString() { return "viscosityTableNames"; }
+  };
+
+  arrayView3d< real64 const, multifluid::USD_PHASE > phaseDensity_n() const
+  { return m_phaseDensity_n; }
+
+  arrayView3d< real64 const, multifluid::USD_PHASE > phaseDensity() const
+  { return m_phaseDensity.value; }
+
+  arrayView4d< real64 const, multifluid::USD_PHASE_DC > dPhaseDensity() const
+  { return m_phaseDensity.derivs; }
+
+  arrayView3d< real64 const, multifluid::USD_PHASE > phaseViscosity() const
+  { return m_phaseViscosity.value; }
+
+  arrayView4d< real64 const, multifluid::USD_PHASE_DC > dPhaseViscosity() const
+  { return m_phaseViscosity.derivs; }
+
+  using PhaseProp = MultiFluidVar< real64, 3, constitutive::multifluid::LAYOUT_PHASE, constitutive::multifluid::LAYOUT_PHASE_DC >;
+
+
+  class KernelWrapper
+  {
+public:
+
+    /// @cond DO_NOT_DOCUMENT
+    /// We need these SMFs to avoid host-device errors with CUDA.
+    KernelWrapper() = default;
+    KernelWrapper( KernelWrapper const & ) = default;
+    KernelWrapper & operator=( KernelWrapper const & ) = default;
+    KernelWrapper & operator=( KernelWrapper && ) = default;
+    /// @endcond
+
+    /**
+     * @brief Get number of elements in this wrapper.
+     * @return number of elements
+     */
+    GEOS_HOST_DEVICE
+    GEOS_FORCE_INLINE
+    localIndex numElems() const { return m_phaseDensity.value.size( 0 ); }
+
+    /**
+     * @brief Get number of gauss points per element.
+     * @return number of gauss points per element
+     */
+    GEOS_HOST_DEVICE
+    GEOS_FORCE_INLINE
+    localIndex numGauss() const { return m_phaseDensity.value.size( 1 ); }
+
+
+    GEOS_HOST_DEVICE
+    void compute( real64 const pressure,
+                  PhaseProp::SliceType const phaseDensity,
+                  PhaseProp::SliceType const phaseViscosity ) const;
+
+    GEOS_HOST_DEVICE
+    void update( localIndex const k,
+                 localIndex const q,
+                 real64 const pressure ) const;
+
+private:
+
+    friend class TwoPhaseFluid;
+
+    /**
+     * @brief Constructor for the class doing in-kernel two-phase fluid updates
+     * @param[in] densityTables density tables
+     * @param[in] viscosityTables viscosity tables
+     * @param[in] phaseDensity phase densities (+ derivatives) in the cell
+     * @param[in] phaseViscosity phase viscosities (+ derivatives) in the cell
+     */
+    KernelWrapper(
+      arrayView1d< TableFunction::KernelWrapper const > densityTables,
+      arrayView1d< TableFunction::KernelWrapper const > viscosityTables,
+      PhaseProp::ViewType phaseDensity,
+      PhaseProp::ViewType phaseViscosity );
+
+
+protected:
+
+    KernelWrapper(
+      arrayView1d< TableFunction::KernelWrapper const > densityTables,
+      arrayView1d< TableFunction::KernelWrapper const > viscosityTables
+      );
+
+    /// Table kernel wrappers to interpolate in the two phase (\rho vs p) tables
+    arrayView1d< TableFunction::KernelWrapper const > m_densityTables;
+
+    /// Table kernel wrappers to interpolate in the two phase (\mu vs p) tables
+    arrayView1d< TableFunction::KernelWrapper const > m_viscosityTables;
+
+    /**
+     * @brief Utility function to compute densities as a function of pressure (keeping derivatives)
+     * @param[in] pressure pressure in the cell
+     * @param[out] phaseDensity the phase density in the cell (+ derivatives)
+     */
+    GEOS_HOST_DEVICE
+    void computeDensities( real64 const pressure,
+                           PhaseProp::SliceType const & phaseDensity ) const;
+
+    /**
+     * @brief Utility function to compute viscosities as a function of pressure (keeping derivatives)
+     * @param[in] pressure pressure in the cell
+     * @param[out] phaseViscosity the phase viscosities in the cell (+ derivatives)
+     */
+    GEOS_HOST_DEVICE
+    void computeViscosities( real64 const pressure,
+                             PhaseProp::SliceType const & phaseViscosity ) const;
+
+    /// Views on the phase properties
+    PhaseProp::ViewType m_phaseDensity;
+    PhaseProp::ViewType m_phaseViscosity;
+
+  };  //class KernelWrapper
+
+
+  string_array m_phaseNames;
+
+
+  path_array m_tableFiles;
+
+  /// Names of the density tables (one per phase)
+  string_array m_densityTableNames;
+
+  /// Names of the viscosity tables (one per phase)
+  string_array m_viscosityTableNames;
+
+  PhaseProp m_phaseDensity;
+  PhaseProp m_phaseViscosity;
+
+  /// Backup data
+  array3d< real64, multifluid::LAYOUT_PHASE > m_phaseDensity_n;
+
+
+  virtual void resizeFields( localIndex const size, localIndex const numPts );
+
+  virtual void postInputInitialization() override;
+
+  virtual void initializePostSubGroups() override;
+
+  /// Table kernel wrappers to interpolate (\rho vs p) tables
+  array1d< TableFunction const * > m_densityTables;
+  /// Table kernel wrappers of m_densityTables
+  array1d< TableFunction::KernelWrapper > m_densityTableKernels;
+
+  /// Table kernel wrappers to interpolate (\mu vs p) tables
+  array1d< TableFunction const * > m_viscosityTables;
+  /// Table kernel wrappers of m_viscosityTables
+  array1d< TableFunction::KernelWrapper > m_viscosityTableKernels;
+
+  KernelWrapper createKernelWrapper();
+
+
+private:
+  void readInputDataFromTableFunctions();
+  void readInputDataFromFileTableFunctions();
+
+  /**
+   * @brief Fill the fluid data (pressure, density, viscosity)
+   * @param[in] ip the index of the phase
+   * @param[in] tableValues the values in the fluid table
+   */
+  void fillData( integer const ip,
+                 array1d< array1d< real64 > > const & tableValues );
+
+  /**
+   * @brief Check the monotonicity of the PVT relationship
+   */
+  void checkTableConsistency() const;
+};
+
+
+GEOS_HOST_DEVICE
+GEOS_FORCE_INLINE
+void TwoPhaseFluid::KernelWrapper::
+  computeDensities( real64 const pressure,
+                    PhaseProp::SliceType const & phaseDensity ) const
+{
+  using Deriv = constitutive::multifluid::DerivativeOffset;
+
+  LvArray::forValuesInSlice( phaseDensity.derivs, []( real64 & val ) { val = 0.0; } );
+
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    // interpolate in the table to get the phase density and derivatives
+    real64 dPhaseDens_dPres = 0.0;
+
+    phaseDensity.value[iph] = m_densityTables[iph].compute( &pressure, &dPhaseDens_dPres );
+    phaseDensity.derivs[iph][Deriv::dP] = dPhaseDens_dPres;
+  }
+}
+
+
+GEOS_HOST_DEVICE
+GEOS_FORCE_INLINE
+void TwoPhaseFluid::KernelWrapper::
+  computeViscosities( real64 const pressure,
+                      PhaseProp::SliceType const & phaseViscosity ) const
+{
+  using Deriv = constitutive::multifluid::DerivativeOffset;
+
+  LvArray::forValuesInSlice( phaseViscosity.derivs, []( real64 & val ) { val = 0.0; } );
+
+  for( integer iph = 0; iph < 2; ++iph )
+  {
+    // interpolate in the table to get the phase viscosity and derivatives
+    real64 dPhaseVisc_dPres = 0.0;
+    phaseViscosity.value[iph] = m_viscosityTables[iph].compute( &pressure, &dPhaseVisc_dPres );
+    phaseViscosity.derivs[iph][Deriv::dP] = dPhaseVisc_dPres;
+  }
+}
+
+
+GEOS_HOST_DEVICE
+GEOS_FORCE_INLINE
+void TwoPhaseFluid::KernelWrapper::
+  compute( real64 const pressure,
+           PhaseProp::SliceType const phaseDensity,
+           PhaseProp::SliceType const phaseViscosity ) const
+{
+  computeDensities( pressure,
+                    phaseDensity );
+
+  computeViscosities( pressure,
+                      phaseViscosity );
+}
+
+
+GEOS_HOST_DEVICE
+GEOS_FORCE_INLINE
+void TwoPhaseFluid::KernelWrapper::
+  update( localIndex const k,
+          localIndex const q,
+          real64 const pressure
+          ) const
+{
+  compute( pressure,
+           m_phaseDensity( k, q ),
+           m_phaseViscosity( k, q ) );
+}
+
+
+template< typename LAMBDA >
+void constitutiveUpdatePassThru( TwoPhaseFluid const & fluid,
+                                 LAMBDA && lambda )
+{
+  ConstitutivePassThruHandler< TwoPhaseFluid >::execute( fluid, std::forward< LAMBDA >( lambda ) );
+}
+
+
+template< typename LAMBDA >
+void constitutiveUpdatePassThru( TwoPhaseFluid & fluid,
+                                 LAMBDA && lambda )
+{
+  ConstitutivePassThruHandler< TwoPhaseFluid >::execute( fluid, std::forward< LAMBDA >( lambda ) );
+}
+
+}  // namespace constitutive
+}  // namespace geos
+
+#endif // GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUID_TWOPHASEFLUID_HPP_
diff --git a/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluidFields.hpp b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluidFields.hpp
new file mode 100644
index 00000000000..9ce0dc5c33d
--- /dev/null
+++ b/src/coreComponents/constitutive/fluid/twophasefluid/TwoPhaseFluidFields.hpp
@@ -0,0 +1,84 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 Total, S.A
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file TwoPhaseFluidFields.hpp
+ */
+
+#ifndef GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUIDFIELDS_HPP_
+#define GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUIDFIELDS_HPP_
+
+#include "constitutive/fluid/multifluid/Layouts.hpp"
+#include "mesh/MeshFields.hpp"
+
+
+namespace geos
+{
+
+namespace fields
+{
+
+namespace twophasefluid
+{
+
+using array3dLayoutPhase = array3d< real64, constitutive::multifluid::LAYOUT_PHASE >;
+using array4dLayoutPhase_d = array4d< real64, constitutive::multifluid::LAYOUT_PHASE_DC >;
+
+DECLARE_FIELD( phaseDensity,
+               "phaseDensity",
+               array3dLayoutPhase,
+               0,
+               LEVEL_0,
+               WRITE_AND_READ,
+               "Phase density" );
+
+DECLARE_FIELD( phaseDensity_n,
+               "phaseDensity_n",
+               array3dLayoutPhase,
+               0,
+               NOPLOT,
+               WRITE_AND_READ,
+               "Phase density at the previous converged time step" );
+
+DECLARE_FIELD( dPhaseDensity,
+               "dPhaseDensity",
+               array4dLayoutPhase_d,
+               0,
+               NOPLOT,
+               NO_WRITE,
+               "Derivative of phase density with respect to pressure" );
+
+DECLARE_FIELD( phaseViscosity,
+               "phaseViscosity",
+               array3dLayoutPhase,
+               0,
+               LEVEL_0,
+               WRITE_AND_READ,
+               "Phase viscosity" );
+
+DECLARE_FIELD( dPhaseViscosity,
+               "dPhaseViscosity",
+               array4dLayoutPhase_d,
+               0,
+               NOPLOT,
+               NO_WRITE,
+               "Derivative of phase viscosity with respect to pressure" );
+
+} // namespace twophasefluid
+
+} // namespace constitutive
+} // namespace geos
+
+#endif // GEOS_CONSTITUTIVE_FLUID_TWOPHASEFLUIDFIELDS_HPP_
diff --git a/src/coreComponents/constitutive/relativePermeability/BrooksCoreyBakerRelativePermeability.hpp b/src/coreComponents/constitutive/relativePermeability/BrooksCoreyBakerRelativePermeability.hpp
index 476def9f455..21fdbe4a8a6 100644
--- a/src/coreComponents/constitutive/relativePermeability/BrooksCoreyBakerRelativePermeability.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/BrooksCoreyBakerRelativePermeability.hpp
@@ -139,19 +139,17 @@ class BrooksCoreyBakerRelativePermeability : public RelativePermeabilityBase
     static constexpr char const * volFracScaleString() { return "volFracScale"; }
   };
 
-  arrayView1d< real64 const > getPhaseMinVolumeFraction() const override { return m_phaseMinVolumeFraction; };
-
   real64 getWettingPhaseMinVolumeFraction() const override
   {
     integer ipWetting;
-    std::tie( ipWetting, std::ignore ) = wettingAndNonWettingPhaseIndices();
+    std::tie( ipWetting, std::ignore ) = phaseIndex( getPhaseOrder());
     return m_phaseMinVolumeFraction[ipWetting];
   }
 
   real64 getNonWettingMinVolumeFraction() const override
   {
     integer ipNonWetting;
-    std::tie( std::ignore, ipNonWetting ) = wettingAndNonWettingPhaseIndices();
+    std::tie( std::ignore, ipNonWetting ) = phaseIndex( getPhaseOrder());
     return m_phaseMinVolumeFraction[ipNonWetting];
   };
 
diff --git a/src/coreComponents/constitutive/relativePermeability/BrooksCoreyRelativePermeability.hpp b/src/coreComponents/constitutive/relativePermeability/BrooksCoreyRelativePermeability.hpp
index 30ee2ff3692..2de3998a78e 100644
--- a/src/coreComponents/constitutive/relativePermeability/BrooksCoreyRelativePermeability.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/BrooksCoreyRelativePermeability.hpp
@@ -105,19 +105,18 @@ class BrooksCoreyRelativePermeability : public RelativePermeabilityBase
     static constexpr char const * volFracScaleString() { return "volFracScale"; }
   };
 //END_SPHINX_INCLUDE_01
-  arrayView1d< real64 const > getPhaseMinVolumeFraction() const override { return m_phaseMinVolumeFraction; };
 
   real64 getWettingPhaseMinVolumeFraction() const override
   {
     integer ipWetting;
-    std::tie( ipWetting, std::ignore ) = wettingAndNonWettingPhaseIndices();
+    std::tie( ipWetting, std::ignore ) = phaseIndex( getPhaseOrder());
     return m_phaseMinVolumeFraction[ipWetting];
   }
 
   real64 getNonWettingMinVolumeFraction() const override
   {
     integer ipNonWetting;
-    std::tie( std::ignore, ipNonWetting ) = wettingAndNonWettingPhaseIndices();
+    std::tie( std::ignore, ipNonWetting ) = phaseIndex( getPhaseOrder());
     return m_phaseMinVolumeFraction[ipNonWetting];
   };
 
diff --git a/src/coreComponents/constitutive/relativePermeability/BrooksCoreyStone2RelativePermeability.hpp b/src/coreComponents/constitutive/relativePermeability/BrooksCoreyStone2RelativePermeability.hpp
index 47eefdd512a..2d83dcda597 100644
--- a/src/coreComponents/constitutive/relativePermeability/BrooksCoreyStone2RelativePermeability.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/BrooksCoreyStone2RelativePermeability.hpp
@@ -138,7 +138,7 @@ class BrooksCoreyStone2RelativePermeability : public RelativePermeabilityBase
     static constexpr char const * volFracScaleString() { return "volFracScale"; }
   };
 
-  arrayView1d< real64 const > getPhaseMinVolumeFraction() const override { return m_phaseMinVolumeFraction; };
+  arrayView1d< real64 const > getPhaseMinVolumeFraction() const { return m_phaseMinVolumeFraction; };
 
   real64 getWettingPhaseMinVolumeFraction() const override
   {
diff --git a/src/coreComponents/constitutive/relativePermeability/KilloughHysteresis.hpp b/src/coreComponents/constitutive/relativePermeability/KilloughHysteresis.hpp
index 58499b94b64..48d2d3deaa2 100644
--- a/src/coreComponents/constitutive/relativePermeability/KilloughHysteresis.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/KilloughHysteresis.hpp
@@ -137,18 +137,8 @@ class KilloughHysteresis
                                m_extremumPhaseVolFraction ),
                      InputError );
 
-      GEOS_THROW_IF( m_criticalImbibitionValue < 0 || m_criticalImbibitionValue > 1,
-                     GEOS_FMT( "KilloughHysteresis: the critical imbibition relative permeability is equal to {} but must be between 0 an 1",
-                               m_criticalImbibitionValue ),
-                     InputError );
-      GEOS_THROW_IF( m_criticalDrainageValue < 0 || m_criticalDrainageValue > 1,
-                     GEOS_FMT( "KilloughHysteresis: the critical drainage relative permeability is equal to {} but must be between 0 an 1",
-                               m_criticalDrainageValue ),
-                     InputError );
-      GEOS_THROW_IF( m_extremumValue < 0 || m_extremumValue > 1,
-                     GEOS_FMT( "KilloughHysteresis: the extremum relative permeability is equal to {} but must be between 0 an 1",
-                               m_extremumValue ),
-                     InputError );
+      // Note: value validation removed because this struct is used for both relative permeability (0-1 range)
+      // and capillary pressure (can be in Pa or other units, typically >> 1). The value range depends on the application.
 
       m_isWetting = m_criticalDrainagePhaseVolFraction > m_extremumPhaseVolFraction;
 
diff --git a/src/coreComponents/constitutive/relativePermeability/RelativePermeabilityBase.cpp b/src/coreComponents/constitutive/relativePermeability/RelativePermeabilityBase.cpp
index d93d335873e..57890850fab 100644
--- a/src/coreComponents/constitutive/relativePermeability/RelativePermeabilityBase.cpp
+++ b/src/coreComponents/constitutive/relativePermeability/RelativePermeabilityBase.cpp
@@ -153,6 +153,7 @@ std::tuple< integer, integer > RelativePermeabilityBase::wettingAndNonWettingPha
   return std::make_tuple( ipWetting, ipNonWetting );
 }
 
+
 } // namespace constitutive
 
 } // namespace geos
diff --git a/src/coreComponents/constitutive/relativePermeability/RelativePermeabilityBase.hpp b/src/coreComponents/constitutive/relativePermeability/RelativePermeabilityBase.hpp
index 0bc67b26a39..0600a41643a 100644
--- a/src/coreComponents/constitutive/relativePermeability/RelativePermeabilityBase.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/RelativePermeabilityBase.hpp
@@ -165,8 +165,8 @@ class RelativePermeabilityBase : public ConstitutiveBase
   static std::tuple< integer, integer > phaseIndex( arrayView1d< integer const > const & phaseOrder );
   arrayView1d< integer const > getPhaseOrder() const { return m_phaseOrder; }
 
-  virtual arrayView1d< real64 const > getPhaseMinVolumeFraction() const = 0;
   virtual real64 getWettingPhaseMinVolumeFraction() const = 0;
+
   virtual real64 getNonWettingMinVolumeFraction() const = 0;
 
   std::tuple< integer, integer > wettingAndNonWettingPhaseIndices() const;
@@ -217,6 +217,45 @@ class RelativePermeabilityBase : public ConstitutiveBase
 
 };
 
+
+/// for use in RelpermDriver to browse the drainage curves
+/// by setting the MaxHistoricalNonWettingSat to Snwmin and MinWettingSat to Sw
+inline std::tuple< integer, integer > RelativePermeabilityBase::phaseIndex( arrayView1d< integer const > const & phaseOrder )
+{
+  using PT = PhaseType;
+  integer const ipWater = phaseOrder[PT::WATER];
+  integer const ipOil = phaseOrder[PT::OIL];
+  integer const ipGas = phaseOrder[PT::GAS];
+
+  integer ipWetting = -1, ipNonWetting = -1;
+
+  if( ipWater >= 0 && ipOil >= 0 && ipGas >= 0 )
+  {
+    ipWetting = ipWater;
+    ipNonWetting = ipGas;
+  }
+  else if( ipWater < 0 )
+  {
+    ipWetting = ipOil;
+    ipNonWetting = ipGas;
+  }
+  else if( ipOil < 0 )
+  {
+    ipWetting = ipWater;
+    ipNonWetting = ipGas;
+  }
+  else if( ipGas < 0 )
+  {
+    ipWetting = ipWater;
+    ipNonWetting = ipOil;
+  }
+
+  //maybe a bit too pythonic
+  return std::make_tuple( ipWetting, ipNonWetting );
+}
+
+
+
 } // namespace constitutive
 
 } // namespace geos
diff --git a/src/coreComponents/constitutive/relativePermeability/TableRelativePermeability.hpp b/src/coreComponents/constitutive/relativePermeability/TableRelativePermeability.hpp
index 7b2fb4d7bcd..255fa33aca3 100644
--- a/src/coreComponents/constitutive/relativePermeability/TableRelativePermeability.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/TableRelativePermeability.hpp
@@ -142,19 +142,17 @@ class TableRelativePermeability : public RelativePermeabilityBase
     static constexpr char const * threePhaseInterpolatorString() { return "threePhaseInterpolator"; }
   };
 
-  arrayView1d< real64 const > getPhaseMinVolumeFraction() const override { return m_phaseMinVolumeFraction; };
-
   real64 getWettingPhaseMinVolumeFraction() const override
   {
     integer ipWetting;
-    std::tie( ipWetting, std::ignore ) = wettingAndNonWettingPhaseIndices();
+    std::tie( ipWetting, std::ignore ) = phaseIndex( getPhaseOrder());
     return m_phaseMinVolumeFraction[ipWetting];
   }
 
   real64 getNonWettingMinVolumeFraction() const override
   {
     integer ipNonWetting;
-    std::tie( std::ignore, ipNonWetting ) = wettingAndNonWettingPhaseIndices();
+    std::tie( std::ignore, ipNonWetting ) = phaseIndex( getPhaseOrder());
     return m_phaseMinVolumeFraction[ipNonWetting];
   };
 
diff --git a/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHelpers.cpp b/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHelpers.cpp
index 965c9278fc1..3d360fc6362 100644
--- a/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHelpers.cpp
+++ b/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHelpers.cpp
@@ -81,7 +81,7 @@ TableRelativePermeabilityHelpers::validateRelativePermeabilityTable( TableFuncti
     if( isZero( relPerm[i-1] ) && !isZero( relPerm[i] ) )
     {
       phaseMinVolFrac = phaseVolFrac[i-1];
-      phaseRelPermMinEndPoint = 0.;
+      phaseRelPermMinEndPoint = relPerm[i-1];
 
     }
   }
diff --git a/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHysteresis.cpp b/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHysteresis.cpp
index 910c42cce41..08fc87ea6a0 100644
--- a/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHysteresis.cpp
+++ b/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHysteresis.cpp
@@ -22,7 +22,8 @@
 #include "constitutive/relativePermeability/RelativePermeabilityFields.hpp"
 #include "constitutive/relativePermeability/TableRelativePermeabilityHelpers.hpp"
 #include "functions/FunctionManager.hpp"
-#include "LogLevelsInfo.hpp"
+#include "constitutiveDrivers/relativePermeability/RelpermDriver.hpp"
+#include "constitutive/ConstitutiveManager.hpp"
 
 namespace geos
 {
@@ -89,48 +90,68 @@ TableRelativePermeabilityHysteresis::TableRelativePermeabilityHysteresis( std::s
                     "To neglect hysteresis on this phase, just use the same table name for the drainage and imbibition curves" );
 
   // hysteresis input parameters
-
-  registerWrapper( viewKeyStruct::landParameterString(), &m_landParam ).
-    setInputFlag( InputFlags::FALSE ). // will be deduced from tables
+  registerWrapper( viewKeyStruct::phaseHasHysteresisString(), &m_phaseHasHysteresis ).
+    setInputFlag( InputFlags::FALSE )
+    .                                                                                  // will be deduced from tables
     setSizedFromParent( 0 );
 
-  // forwarded to KilloughHysteresis
-  registerWrapper( KilloughHysteresis::viewKeyStruct::jerauldParameterAString(), &m_jerauldParam_a ).
-    setInputFlag( InputFlags::OPTIONAL ).
-    setApplyDefaultValue( 0.1 ).
-    setDescription( "First parameter (modification parameter) introduced by Jerauld in the Land trapping model (see RTD documentation)." );
-
-  registerWrapper( KilloughHysteresis::viewKeyStruct::jerauldParameterBString(), &m_jerauldParam_b ).
-    setInputFlag( InputFlags::OPTIONAL ).
-    setApplyDefaultValue( 0.0 ).
-    setDescription( "Second parameter (modification parameter) introduced by Jerauld in the Land trapping model (see RTD documentation)." );
+  registerField< fields::relperm::phaseMaxHistoricalVolFraction >(
+                 &m_phaseMaxHistoricalVolFraction );
+  registerField< fields::relperm::phaseMinHistoricalVolFraction >(
+                 &m_phaseMinHistoricalVolFraction );
 
-  registerWrapper( KilloughHysteresis::viewKeyStruct::killoughCurvatureParameterString(), &m_killoughCurvatureParamRelPerm ).
-    setInputFlag( InputFlags::OPTIONAL ).
-    setApplyDefaultValue( 1.0 ).
-    setDescription( "Curvature parameter introduced by Killough for wetting-phase hysteresis (see RTD documentation)." );
-
-  // structs
+  /// Killough data
   registerWrapper( viewKeyStruct::drainageRelPermKernelWrappersString(),
                    &m_drainageRelPermKernelWrappers ).
     setSizedFromParent( 0 ).
-    setRestartFlags( RestartFlags::NO_WRITE );
+    setRestartFlags(
+    RestartFlags::NO_WRITE );
 
   registerWrapper( viewKeyStruct::imbibitionRelPermKernelWrappersString(),
                    &m_imbibitionRelPermKernelWrappers ).
     setSizedFromParent( 0 ).
-    setRestartFlags( RestartFlags::NO_WRITE );
+    setRestartFlags(
+    RestartFlags::NO_WRITE );
 
-  // Killough data
-  registerWrapper( viewKeyStruct::wettingCurveString(), &m_wettingCurve ).
+  registerWrapper( viewKeyStruct::landParameterString(), &m_landParam ).
     setInputFlag( InputFlags::FALSE ). // will be deduced from tables
-    setSizedFromParent( 0 ).
-    setRestartFlags( RestartFlags::NO_WRITE );
+    setSizedFromParent( 0 );
+
+
+  registerWrapper( viewKeyStruct::wettingCurveString(), &m_wettingCurve ).
+    setInputFlag(
+    InputFlags::FALSE ).         // will be deduced from tables
+    setSizedFromParent(
+    0 )
+    .setRestartFlags( RestartFlags::NO_WRITE );
 
   registerWrapper( viewKeyStruct::nonWettingCurveString(), &m_nonWettingCurve ).
-    setInputFlag( InputFlags::FALSE ). // will be deduced from tables
-    setSizedFromParent( 0 ).
-    setRestartFlags( RestartFlags::NO_WRITE );
+    setInputFlag(
+    InputFlags::FALSE ).         // will be deduced from tables
+    setSizedFromParent(
+    0 )
+    .setRestartFlags( RestartFlags::NO_WRITE );
+
+  //Forwarded to KilloughHysteresis
+  registerWrapper( KilloughHysteresis::viewKeyStruct::jerauldParameterAString(), &m_jerauldParam_a ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setApplyDefaultValue( 0.1 ).
+    setDescription(
+    "First parameter (modification parameter) introduced by Jerauld in the Land trapping model (see RTD documentation)." );
+
+  registerWrapper( KilloughHysteresis::viewKeyStruct::jerauldParameterBString(), &m_jerauldParam_b ).
+    setInputFlag( InputFlags::OPTIONAL ).
+    setApplyDefaultValue( 0.0 ).
+    setDescription(
+    "Second parameter (modification parameter) introduced by Jerauld in the Land trapping model (see RTD documentation)." );
+
+  registerWrapper(KilloughHysteresis::viewKeyStruct::killoughCurvatureParameterRelPermString(), &m_killoughCurvatureParamRelPerm ).
+    setInputFlag(
+    InputFlags::OPTIONAL ).
+    setApplyDefaultValue(
+    1.0 ).
+    setDescription(
+    "Curvature parameter introduced by Killough for wetting-phase hysteresis (see RTD documentation)." );
 
   registerWrapper( viewKeyStruct::waterOilMaxRelPermString(), &m_waterOilMaxRelPerm ).
     setInputFlag( InputFlags::FALSE ). // will be deduced from tables
@@ -165,7 +186,6 @@ void TableRelativePermeabilityHysteresis::postInputInitialization()
                            getFullName() ),
                  InputError, getDataContext() );
 
-  m_phaseMinVolumeFraction.resize( numPhases );
   m_phaseHasHysteresis.resize( numPhases );
 
   //initialize STONE-II only used var to avoid discrepancies in baselines
@@ -228,14 +248,14 @@ void TableRelativePermeabilityHysteresis::postInputInitialization()
   }
 
   GEOS_THROW_IF( m_phaseHasHysteresis[IPT::WETTING] == 0 && m_phaseHasHysteresis[IPT::NONWETTING] == 0,
-                 GEOS_FMT( "{}: we must use {} or {} to specify at least one imbibition relative permeability table",
-                           getFullName(),
-                           viewKeyStruct::imbibitionWettingRelPermTableNameString(),
-                           viewKeyStruct::imbibitionNonWettingRelPermTableNameString() ),
+                  GEOS_FMT( "{}: we must use {} or {} to specify at least one imbibition relative permeability table",
+                             getFullName(),
+                             viewKeyStruct::imbibitionWettingRelPermTableNameString(),
+                             viewKeyStruct::imbibitionNonWettingRelPermTableNameString() ),
                  InputError, getDataContext() );
 
   //Killough section
-  KilloughHysteresis::postProcessInput( m_jerauldParam_a, m_jerauldParam_b, m_killoughCurvatureParamRelPerm );
+    KilloughHysteresis::postProcessInput(m_jerauldParam_a, m_jerauldParam_b, m_killoughCurvatureParamRelPerm, 0.0);
 }
 
 void TableRelativePermeabilityHysteresis::initializePreSubGroups()
@@ -262,73 +282,65 @@ void TableRelativePermeabilityHysteresis::checkExistenceAndValidateWettingRelPer
   using IPT = TableRelativePermeabilityHysteresis::ImbibitionPhasePairPhaseType;
   integer const numPhases = m_phaseNames.size();
   integer ipWetting = -1, ipNonWetting = -1;
-  std::tie( ipWetting, ipNonWetting ) = RelativePermeabilityBase::wettingAndNonWettingPhaseIndices();
+  std::tie( ipWetting, ipNonWetting ) = RelativePermeabilityBase::phaseIndex( m_phaseOrder );
 
   // Step 1.a: take care of the two-phase case
-  real64 drainagePhaseMinVolFraction = -1; // output
-  real64 drainagePhaseMaxVolFraction = -1;
-  real64 drainagePhaseRelPermMinEndPoint = -1;
-  real64 drainagePhaseRelPermMaxEndPoint = -1;
-
-  string const tableName = ( numPhases == 2 ) ?
-                           m_drainageWettingNonWettingRelPermTableNames[0] : m_drainageWettingIntermediateRelPermTableNames[0];
-
-  checkExistenceAndValidateRelPermTable( tableName, // input
-                                         drainagePhaseMinVolFraction, // output
+  real64 drainagePhaseMinVolFraction,     // output
+         drainagePhaseMaxVolFraction,
+         drainagePhaseRelPermMinEndPoint,
+         drainagePhaseRelPermMaxEndPoint;
+  GEOS_ASSERT( m_drainageWettingNonWettingRelPermTableNames.size() == 2 );
+  auto tableName = ( numPhases == 2 ) ?   m_drainageWettingNonWettingRelPermTableNames[0] : m_drainageWettingIntermediateRelPermTableNames[0];
+//        integer const ipWetting = ( m_phaseOrder[PhaseType::WATER] >= 0 ) ? m_phaseOrder[PhaseType::WATER] : m_phaseOrder[PhaseType::OIL];
+  checkExistenceAndValidateRelPermTable( tableName,    // input
+                                         drainagePhaseMinVolFraction,    // output
                                          drainagePhaseMaxVolFraction,
                                          drainagePhaseRelPermMinEndPoint,
                                          drainagePhaseRelPermMaxEndPoint );
 
-  // imbibition if provided
-  real64 imbibitionPhaseMinVolFraction = drainagePhaseMinVolFraction; // output
-  real64 imbibitionPhaseMaxVolFraction = drainagePhaseMaxVolFraction;
-  real64 imbibitionPhaseRelPermMinEndPoint = drainagePhaseRelPermMinEndPoint;
-  real64 imbibitionPhaseRelPermMaxEndPoint = drainagePhaseRelPermMaxEndPoint;
+
+  //imbibition if provided
+  real64 imbibitionPhaseMinVolFraction,    // output
+         imbibitionPhaseMaxVolFraction,
+         imbibitionPhaseRelPermMinEndPoint,
+         imbibitionPhaseRelPermMaxEndPoint;
 
   if( m_phaseHasHysteresis[IPT::WETTING] )
   {
-    checkExistenceAndValidateRelPermTable( m_imbibitionWettingRelPermTableName, // input
-                                           imbibitionPhaseMinVolFraction, // output
+    checkExistenceAndValidateRelPermTable( m_imbibitionWettingRelPermTableName,    // input
+                                           imbibitionPhaseMinVolFraction,    // output
                                            imbibitionPhaseMaxVolFraction,
                                            imbibitionPhaseRelPermMinEndPoint,
                                            imbibitionPhaseRelPermMaxEndPoint );
 
     GEOS_THROW_IF( !isZero( imbibitionPhaseMinVolFraction - drainagePhaseMinVolFraction ),
-                   GEOS_FMT( "{}: the critical wetting-phase volume fraction (saturation) must be the same in drainage and imbibition.\n"
-                             "However, we found that the drainage critical wetting-phase volume fraction is {}, "
-                             "whereas the imbibition critical wetting-phase volume fraction is {}",
-                             getFullName(),
-                             drainagePhaseMinVolFraction, imbibitionPhaseMinVolFraction ),
+                    GEOS_FMT( "{}: the critical wetting-phase volume fraction (saturation) must be the same in drainage and imbibition.\n"
+                               "However, we found that the drainage critical wetting-phase volume fraction is {}, "
+                               "whereas the imbibition critical wetting-phase volume fraction is {}",
+                               getFullName(),
+                               drainagePhaseMinVolFraction, imbibitionPhaseMinVolFraction ),
                    InputError, getDataContext() );
 
     GEOS_THROW_IF( imbibitionPhaseMaxVolFraction > drainagePhaseMaxVolFraction,
-                   GEOS_FMT( "{}: the maximum wetting-phase volume fraction (saturation) must be smaller in imbibition (compared to the drainage value).\n"
-                             "However, we found that the drainage maximum wetting-phase volume fraction is {}, "
-                             "whereas the imbibition maximum wetting-phase volume fraction is {}",
-                             getFullName(),
-                             drainagePhaseMaxVolFraction, imbibitionPhaseMaxVolFraction ),
+                    GEOS_FMT( "{}: the maximum wetting-phase volume fraction (saturation) must be smaller in imbibition (compared to the drainage value).\n"
+                               "However, we found that the drainage maximum wetting-phase volume fraction is {}, "
+                               "whereas the imbibition maximum wetting-phase volume fraction is {}",
+                               getFullName(),
+                               drainagePhaseMaxVolFraction, imbibitionPhaseMaxVolFraction ),
                    InputError, getDataContext() );
 
     GEOS_THROW_IF( imbibitionPhaseRelPermMaxEndPoint > drainagePhaseRelPermMaxEndPoint,
-                   GEOS_FMT( "{}: the maximum wetting-phase relperm must be smaller in imbibition (compared to the drainage value).\n"
-                             "However, we found that the drainage maximum wetting-phase relperm is {}, "
-                             "whereas the imbibition maximum wetting-phase relperm is {}",
-                             getFullName(),
-                             drainagePhaseRelPermMaxEndPoint, imbibitionPhaseRelPermMaxEndPoint ),
+                    GEOS_FMT( "{}: the maximum wetting-phase relperm must be smaller in imbibition (compared to the drainage value).\n"
+                               "However, we found that the drainage maximum wetting-phase relperm is {}, "
+                               "whereas the imbibition maximum wetting-phase relperm is {}",
+                               getFullName(),
+                               drainagePhaseRelPermMaxEndPoint, imbibitionPhaseRelPermMaxEndPoint ),
                    InputError, getDataContext() );
   }
 
-  m_wettingCurve.setPoints( drainagePhaseMinVolFraction, drainagePhaseRelPermMinEndPoint,   // same as imbibition min
-                            imbibitionPhaseMaxVolFraction, imbibitionPhaseRelPermMaxEndPoint,
-                            drainagePhaseMaxVolFraction, drainagePhaseRelPermMaxEndPoint );
-
-  m_phaseMinVolumeFraction[ipWetting] = drainagePhaseMinVolFraction;
-
-  GEOS_LOG_LEVEL_RANK_0( logInfo::Init, GEOS_FMT( "Initializing wetting relperm curve with {(smin,krmin), (simax,krimax), (sdmax,krdmax)} : {({},{}),({},{}),({},{})}",
-                                                  m_wettingCurve.m_extremumPhaseVolFraction, m_wettingCurve.m_extremumValue,
-                                                  m_wettingCurve.m_criticalImbibitionPhaseVolFraction, m_wettingCurve.m_criticalImbibitionValue,
-                                                  m_wettingCurve.m_criticalDrainagePhaseVolFraction, m_wettingCurve.m_criticalDrainageValue
-                                                  ));
+  m_wettingCurve.setPoints( {drainagePhaseMinVolFraction, drainagePhaseRelPermMinEndPoint},   // extremum
+                            {imbibitionPhaseMaxVolFraction, imbibitionPhaseRelPermMaxEndPoint},   // imbibition critical
+                            {drainagePhaseMaxVolFraction, drainagePhaseRelPermMaxEndPoint} );   // drainage critical
 }
 
 void TableRelativePermeabilityHysteresis::checkExistenceAndValidateNonWettingRelPermTables()
@@ -337,17 +349,17 @@ void TableRelativePermeabilityHysteresis::checkExistenceAndValidateNonWettingRel
 
   integer const numPhases = m_phaseNames.size();
   integer ipWetting = -1, ipNonWetting = -1;
-  std::tie( ipWetting, ipNonWetting ) = RelativePermeabilityBase::wettingAndNonWettingPhaseIndices();
-
-  // treat drainage
-  real64 drainagePhaseMinVolFraction = -1; // output
-  real64 drainagePhaseMaxVolFraction = -1;
-  real64 drainagePhaseRelPermMinEndPoint = -1;
-  real64 drainagePhaseRelPermMaxEndPoint = -1;
+  std::tie( ipWetting, ipNonWetting ) = RelativePermeabilityBase::phaseIndex( m_phaseOrder );
 
+  //treat drainage
+  real64 drainagePhaseMinVolFraction,   // output
+         drainagePhaseMaxVolFraction,
+         drainagePhaseRelPermMinEndPoint,
+         drainagePhaseRelPermMaxEndPoint;
   // Step 1: Read the drainage for the non wetting phase
-  string const tableName = ( numPhases == 2 ) ? m_drainageWettingNonWettingRelPermTableNames[1] :
-                           m_drainageNonWettingIntermediateRelPermTableNames[0];
+  GEOS_ASSERT( m_drainageWettingNonWettingRelPermTableNames.size() == 2 );
+  auto tableName = ( numPhases == 2 ) ? m_drainageWettingNonWettingRelPermTableNames[1] :
+                   m_drainageNonWettingIntermediateRelPermTableNames[0];
   checkExistenceAndValidateRelPermTable( tableName,       // input
                                          drainagePhaseMinVolFraction,      // output
                                          drainagePhaseMaxVolFraction,
@@ -355,10 +367,10 @@ void TableRelativePermeabilityHysteresis::checkExistenceAndValidateNonWettingRel
                                          drainagePhaseRelPermMaxEndPoint );
 
   // Step 2: validate non-wetting-phase imbibition relative permeability table
-  real64 imbibitionPhaseMinVolFraction = drainagePhaseMinVolFraction; // output
-  real64 imbibitionPhaseMaxVolFraction = drainagePhaseMaxVolFraction;
-  real64 imbibitionPhaseRelPermMinEndPoint = drainagePhaseRelPermMinEndPoint;
-  real64 imbibitionPhaseRelPermMaxEndPoint = drainagePhaseRelPermMaxEndPoint;
+  real64 imbibitionPhaseMinVolFraction, // output
+         imbibitionPhaseMaxVolFraction,
+         imbibitionPhaseRelPermMinEndPoint,
+         imbibitionPhaseRelPermMaxEndPoint;
 
   if( m_phaseHasHysteresis[IPT::NONWETTING] )
   {
@@ -370,42 +382,35 @@ void TableRelativePermeabilityHysteresis::checkExistenceAndValidateNonWettingRel
                                            imbibitionPhaseRelPermMaxEndPoint );
 
     GEOS_THROW_IF( !isZero ( imbibitionPhaseMaxVolFraction - drainagePhaseMaxVolFraction ),
-                   GEOS_FMT( string( "{}: the maximum non-wetting-phase volume fraction (saturation) must be the same in drainage and imbibition.\n" )
-                             + string( "However, we found that the drainage maximum wetting-phase volume fraction is {}, " )
-                             + string( "whereas the imbibition maximum wetting-phase volume fraction is {}" ),
-                             getFullName(),
-                             drainagePhaseMaxVolFraction, imbibitionPhaseMaxVolFraction ),
+                    GEOS_FMT( string( "{}: the maximum non-wetting-phase volume fraction (saturation) must be the same in drainage and imbibition.\n" )
+                               + string( "However, we found that the drainage maximum wetting-phase volume fraction is {}, " )
+                               + string( "whereas the imbibition maximum wetting-phase volume fraction is {}" ),
+                               getFullName(),
+                               drainagePhaseMaxVolFraction, imbibitionPhaseMaxVolFraction ),
                    InputError, getDataContext() );
 
     GEOS_THROW_IF( !isZero ( imbibitionPhaseRelPermMaxEndPoint - drainagePhaseRelPermMaxEndPoint ),
-                   GEOS_FMT( string( "{}: the non-wetting-phase relperm endpoint must be the same in drainage and imbibition.\n" )
-                             + string( "However, we found that the drainage endpoint wetting-phase relperm is {}, " )
-                             + string( "whereas the imbibition endpoint wetting-phase relperm is {}" ),
-                             getFullName(),
-                             drainagePhaseRelPermMaxEndPoint, imbibitionPhaseRelPermMaxEndPoint ),
+                    GEOS_FMT( string( "{}: the non-wetting-phase relperm endpoint must be the same in drainage and imbibition.\n" )
+                               + string( "However, we found that the drainage endpoint wetting-phase relperm is {}, " )
+                               + string( "whereas the imbibition endpoint wetting-phase relperm is {}" ),
+                               getFullName(),
+                               drainagePhaseRelPermMaxEndPoint, imbibitionPhaseRelPermMaxEndPoint ),
                    InputError, getDataContext() );
 
     GEOS_THROW_IF( imbibitionPhaseMinVolFraction < drainagePhaseMinVolFraction,
-                   GEOS_FMT( string( "{}: the critical wetting-phase volume fraction (saturation) must be larger in imbibition (compared to the drainage value).\n" )
-                             + string( "However, we found that the drainage critical wetting-phase volume fraction is {}, " )
-                             + string( "whereas the imbibition critical wetting-phase volume fraction is {}" ),
-                             getFullName(),
-                             drainagePhaseMinVolFraction, imbibitionPhaseMinVolFraction ),
+                    GEOS_FMT( string( "{}: the critical wetting-phase volume fraction (saturation) must be larger in imbibition (compared to the drainage value).\n" )
+                               + string( "However, we found that the drainage critical wetting-phase volume fraction is {}, " )
+                               + string( "whereas the imbibition critical wetting-phase volume fraction is {}" ),
+                               getFullName(),
+                               drainagePhaseMinVolFraction, imbibitionPhaseMinVolFraction ),
                    InputError, getDataContext() );
 
   }
 
-  m_nonWettingCurve.setPoints( drainagePhaseMaxVolFraction, drainagePhaseRelPermMaxEndPoint,   // same as imbibition max
-                               imbibitionPhaseMinVolFraction, imbibitionPhaseRelPermMinEndPoint,
-                               drainagePhaseMinVolFraction, drainagePhaseRelPermMinEndPoint );
-
-  m_phaseMinVolumeFraction[ipNonWetting] = drainagePhaseMinVolFraction;
 
-  GEOS_LOG_LEVEL_RANK_0( logInfo::Init, GEOS_FMT( "Initializing non-wetting relperm curve with {(sdmin,krdmin), (simin,krimin), (smax,krmax)} : {({},{}),({},{}),({},{})}",
-                                                  m_nonWettingCurve.m_criticalDrainagePhaseVolFraction, m_nonWettingCurve.m_criticalDrainageValue,
-                                                  m_nonWettingCurve.m_criticalImbibitionPhaseVolFraction, m_nonWettingCurve.m_criticalImbibitionValue,
-                                                  m_nonWettingCurve.m_extremumPhaseVolFraction, m_nonWettingCurve.m_extremumValue
-                                                  ));
+  m_nonWettingCurve.setPoints( {drainagePhaseMaxVolFraction, drainagePhaseRelPermMaxEndPoint},   // extremum
+                               {imbibitionPhaseMinVolFraction, imbibitionPhaseRelPermMinEndPoint},   // imbibition critical
+                               {drainagePhaseMinVolFraction, drainagePhaseRelPermMinEndPoint} );   // drainage critical
 
 }
 
@@ -414,19 +419,21 @@ void TableRelativePermeabilityHysteresis::checkExistenceAndValidateIntermediateR
 
   if( m_phaseNames.size() == 3 )
   {
-    real64 drainagePhaseMinVolFraction,
+
+    real64 drainagePhaseMinVolFraction,     //
            drainagePhaseMaxVolFraction,
            drainagePhaseRelPermMinEndPoint,
            drainagePhaseRelPermMaxEndPoint;
 
 
-    // intermediate drainage from wetting
+    //intermediate drainage from wetting
     checkExistenceAndValidateRelPermTable( m_drainageWettingIntermediateRelPermTableNames[1],    // input
                                            drainagePhaseMinVolFraction,    // output
                                            drainagePhaseMaxVolFraction,
                                            drainagePhaseRelPermMinEndPoint,
                                            drainagePhaseRelPermMaxEndPoint );
 
+    //??
     checkExistenceAndValidateRelPermTable( m_drainageNonWettingIntermediateRelPermTableNames[1],    // input
                                            drainagePhaseMinVolFraction,
                                            drainagePhaseMaxVolFraction,
@@ -468,9 +475,8 @@ void TableRelativePermeabilityHysteresis::computeLandCoefficient()
   // For two-phase flow, we make sure that they are equal
   m_landParam.resize( 2 );
 
-  // Note: for simplicity, the notations are taken classical reservoir notations (although this breaks our phaseVolFrac naming convention)
+  // Note: for simplicity, the notations are taken reservoir simulation literature (although this breaks our phaseVolFrac naming convention)
   using IPT = TableRelativePermeabilityHysteresis::ImbibitionPhasePairPhaseType;
-
   KilloughHysteresis::computeLandCoefficient( m_wettingCurve, m_landParam[IPT::WETTING] );
   KilloughHysteresis::computeLandCoefficient( m_nonWettingCurve, m_landParam[IPT::NONWETTING] );
 }
@@ -566,12 +572,14 @@ void TableRelativePermeabilityHysteresis::allocateConstitutiveData( Group & pare
 {
   integer const numPhases = numFluidPhases();
 
-  m_phaseMinVolumeFraction.resize( numPhases );
-  m_phaseMaxHistoricalVolFraction.resize( 0, numPhases );
-  m_phaseMinHistoricalVolFraction.resize( 0, numPhases );
-
   RelativePermeabilityBase::allocateConstitutiveData( parent, numPts );
 
+  m_phaseMaxHistoricalVolFraction.resize( parent.size(), numPhases );
+  m_phaseMinHistoricalVolFraction.resize( parent.size(), numPhases );
+
+  m_phaseMaxHistoricalVolFraction.setValues< parallelDevicePolicy<> >( 0.0 );
+  m_phaseMinHistoricalVolFraction.setValues< parallelDevicePolicy<> >( 1.0 );
+
   m_phaseMaxHistoricalVolFraction.setValues< parallelDevicePolicy<> >( 0.0 );
   m_phaseMinHistoricalVolFraction.setValues< parallelDevicePolicy<> >( 1.0 );
 }
@@ -597,24 +605,25 @@ void TableRelativePermeabilityHysteresis::saveConvergedPhaseVolFractionState( ar
 
 }
 
-TableRelativePermeabilityHysteresis::KernelWrapper::KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & drainageRelPermKernelWrappers,
-                                                                   arrayView1d< TableFunction::KernelWrapper const > const & imbibitionRelPermKernelWrappers,
-                                                                   arrayView1d< integer const > const & phaseHasHysteresis,
-                                                                   arrayView1d< real64 const > const & landParam,
+TableRelativePermeabilityHysteresis::KernelWrapper::
+  KernelWrapper( arrayView1d< TableFunction::KernelWrapper const > const & drainageRelPermKernelWrappers,
+                 arrayView1d< TableFunction::KernelWrapper const > const & imbibitionRelPermKernelWrappers,
+                 arrayView1d< integer const > const & phaseHasHysteresis,
+                 arrayView1d< real64 const > const & landParam,
                                                                    real64 const & jerauldParam_a,
                                                                    real64 const & jerauldParam_b,
                                                                    real64 const & killoughCurvatureParamRelPerm,
                                                                    KilloughHysteresis::HysteresisCurve const & wettingCurve,
                                                                    KilloughHysteresis::HysteresisCurve const & nonWettingCurve,
-                                                                   arrayView1d< integer const > const & phaseTypes,
-                                                                   arrayView1d< integer const > const & phaseOrder,
-                                                                   ThreePhaseInterpolator const & threePhaseInterpolator,
-                                                                   real64 const & waterOilRelPermMaxValue,
-                                                                   arrayView2d< real64 const, compflow::USD_PHASE > const & phaseMinHistoricalVolFraction,
-                                                                   arrayView2d< real64 const, compflow::USD_PHASE > const & phaseMaxHistoricalVolFraction,
-                                                                   arrayView3d< real64, relperm::USD_RELPERM > const & phaseTrappedVolFrac,
-                                                                   arrayView3d< real64, relperm::USD_RELPERM > const & phaseRelPerm,
-                                                                   arrayView4d< real64, relperm::USD_RELPERM_DS > const & dPhaseRelPerm_dPhaseVolFrac )
+                 arrayView1d< integer const > const & phaseTypes,
+                 arrayView1d< integer const > const & phaseOrder,
+                 ThreePhaseInterpolator const & threePhaseInterpolator,
+                 real64 const & waterOilRelPermMaxValue,
+                 arrayView2d< real64 const, compflow::USD_PHASE > const & phaseMinHistoricalVolFraction,
+                 arrayView2d< real64 const, compflow::USD_PHASE > const & phaseMaxHistoricalVolFraction,
+                 arrayView3d< real64, relperm::USD_RELPERM > const & phaseTrappedVolFrac,
+                 arrayView3d< real64, relperm::USD_RELPERM > const & phaseRelPerm,
+                 arrayView4d< real64, relperm::USD_RELPERM_DS > const & dPhaseRelPerm_dPhaseVolFrac )
   :
   RelativePermeabilityBaseUpdate( phaseTypes,
                                   phaseOrder,
diff --git a/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHysteresis.hpp b/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHysteresis.hpp
index 3f0d5611f4c..df63094083c 100644
--- a/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHysteresis.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/TableRelativePermeabilityHysteresis.hpp
@@ -21,12 +21,11 @@
 #define GEOS_CONSTITUTIVE_TABLERELATIVEPERMEABILITYHYSTERESIS_HPP
 
 
-#include "constitutive/relativePermeability/KilloughHysteresis.hpp"
+#include "constitutive/KilloughHysteresis.hpp"
 #include "constitutive/relativePermeability/RelativePermeabilityBase.hpp"
 #include "constitutive/relativePermeability/RelativePermeabilityInterpolators.hpp"
 #include "functions/TableFunction.hpp"
-
-
+///helper model class with data struct for curves and computing recipe for trapped and Land Coeff
 
 namespace geos
 {
@@ -79,8 +78,6 @@ class TableRelativePermeabilityHysteresis : public RelativePermeabilityBase
 
   virtual string getCatalogName() const override { return catalogName(); }
 
-  virtual void allocateConstitutiveData( dataRepository::Group & parent, localIndex const numPts ) override;
-
   /// Type of kernel wrapper for in-kernel update
   class KernelWrapper final : public RelativePermeabilityBaseUpdate
   {
@@ -140,7 +137,24 @@ class TableRelativePermeabilityHysteresis : public RelativePermeabilityBase
                                  real64 & phaseRelPerm,
                                  real64 & dPhaseRelPerm_dPhaseVolFrac ) const;
 
-
+    /**
+     * @brief Function computing the trapped critical phase volume fraction (Sgcrt)
+     * @param[in] Scrd the drainage critical phase volume fraction
+     * @param[in] Shy the max historical phase volume fraction
+     * @param[in] Smx the max phase volume fraction (= end-point phase volume fraction)
+     * @param[in] jerauldParam_a first (modification) parameter proposed by Jerauld
+     * @param[in] jerauldParam_b second (exponent) parameter proposed by Jerauld
+     * @param[in] landParam Land trapping parameter
+     * @param[out] Scrt the trapped critical phase volume fraction
+     */
+    GEOS_HOST_DEVICE
+    void computeTrappedCriticalPhaseVolFraction( real64 const & Scrd,
+                                                 real64 const & Shy,
+                                                 real64 const & Smx,
+                                                 real64 const & jerauldParam_a,
+                                                 real64 const & jerauldParam_b,
+                                                 real64 const & landParam,
+                                                 real64 & Scrt ) const;
     /**
      * @brief Function updating the relperm (and derivative) for the wetting phase in imbibition using Killough's method
      * @param[in] drainageRelPermKernelWrapper kernel wrapper storing the drainage relperm table for the wetting phase
@@ -270,19 +284,13 @@ class TableRelativePermeabilityHysteresis : public RelativePermeabilityBase
     /// Trapping parameter from the Land model (typically called C)
     arrayView1d< real64 const > m_landParam;
 
-    /// Parameter a introduced by Jerauld in the Land model
     real64 const & m_jerauldParam_a;
 
-    /// Parameter b introduced by Jerauld in the Land model
     real64 const & m_jerauldParam_b;
 
-    /// Curvature parameter introduced for wetting phase hysteresis in Killough
     real64 const & m_killoughCurvatureParamRelPerm;
 
-    /// The wetting phase hysteretic curve
     KilloughHysteresis::HysteresisCurve const & m_wettingCurve;
-
-    /// The non-wetting phase hysteretic curve
     KilloughHysteresis::HysteresisCurve const & m_nonWettingCurve;
 
     /// Minimum historical phase volume fraction for each phase
@@ -307,17 +315,17 @@ class TableRelativePermeabilityHysteresis : public RelativePermeabilityBase
 
   struct viewKeyStruct : RelativePermeabilityBase::viewKeyStruct
   {
-    /// Land coefficient
+    ///Land Coeff
     static constexpr char const * landParameterString() { return "landParameter"; }
 
-    /// Hysteretic curves
+    ///and packed curves data struct
     static constexpr char const * wettingCurveString() { return "wettingCurve"; };
     static constexpr char const * nonWettingCurveString() { return "nonWettingCurve"; };
 
-    /// Flag to determine whether a phase has hysteresis or not
+    ///flag
     static constexpr char const * phaseHasHysteresisString() { return "phaseHasHysteresis"; }
 
-    /// Tables and associated wrappers
+    ///tables and assoc. wrappers
     static constexpr char const * drainageRelPermKernelWrappersString() { return "drainageRelPermWrappers"; }
     static constexpr char const * imbibitionRelPermKernelWrappersString() { return "imbibitionRelPermWrappers"; }
 
@@ -334,18 +342,18 @@ class TableRelativePermeabilityHysteresis : public RelativePermeabilityBase
 
   };
 
-  arrayView1d< real64 const > getPhaseMinVolumeFraction() const override { return m_phaseMinVolumeFraction; };
-
   real64  getWettingPhaseMinVolumeFraction() const override
   {
-    return m_wettingCurve.m_extremumPhaseVolFraction;
+    return m_wettingCurve.oppositeBoundPhaseVolFraction;
   }
 
   real64 getNonWettingMinVolumeFraction() const override
   {
-    return m_nonWettingCurve.m_criticalDrainagePhaseVolFraction;
+    return m_nonWettingCurve.oppositeBoundPhaseVolFraction;
   }
 
+  virtual void allocateConstitutiveData( Group & parent, localIndex const numPts ) override;
+
 private:
 
   virtual void postInputInitialization() override;
@@ -453,17 +461,10 @@ class TableRelativePermeabilityHysteresis : public RelativePermeabilityBase
   /// Maximum historical phase volume fraction for each phase
   array2d< real64, compflow::LAYOUT_PHASE > m_phaseMaxHistoricalVolFraction;
 
-  /// The wetting phase hysteretic curve
   KilloughHysteresis::HysteresisCurve m_wettingCurve;
-
-  /// The non-wetting phase hysteretic curve
   KilloughHysteresis::HysteresisCurve m_nonWettingCurve;
 
-  /// Min phase volume fractions (deduced from the tables). With Baker, only the water phase entry is used
-  array1d< real64 > m_phaseMinVolumeFraction;
-
   real64 m_waterOilMaxRelPerm;
-
   ThreePhaseInterpolator m_threePhaseInterpolator;
 
 };
@@ -498,13 +499,13 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   // if consistent, S should be equal to 1 - imbibitionPhaseMinVolNonWettingFraction for two-phase flow
   // (but wetting and nonwetting phase hysteresis are implemented in a decoupled fashion)
   real64 const S = phaseVolFraction;
-  real64 const Smxi = m_wettingCurve.m_criticalImbibitionPhaseVolFraction;
-  real64 const Smxd = m_wettingCurve.m_criticalDrainagePhaseVolFraction;
+  real64 const Smxi = m_wettingCurve.imbibitionExtremaPhaseVolFraction;
+  real64 const Smxd = m_wettingCurve.drainageExtremaPhaseVolFraction;
 
   // Swc is the common end min endpoint saturation for wetting curves
-  real64 const Swc = m_wettingCurve.m_extremumPhaseVolFraction;
+  real64 const Swc = m_wettingCurve.oppositeBoundPhaseVolFraction;
 
-  using IPT = ImbibitionPhasePairPhaseType;
+  using IPT = TableRelativePermeabilityHysteresis::ImbibitionPhasePairPhaseType;
   if( S <= Swc )
   {
     phaseRelPerm = 0.0;
@@ -512,12 +513,12 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   }
   else if( S >= Smxd )
   {
-    phaseRelPerm = m_wettingCurve.m_criticalDrainageValue;
+    phaseRelPerm = m_wettingCurve.drainageExtremaSCALValue;
     dPhaseRelPerm_dPhaseVolFrac = 0.0;
   }
   else
   {
-    real64 const krwei = m_wettingCurve.m_criticalImbibitionValue;
+    real64 const krwei = m_wettingCurve.imbibitionExtremaSCALValue;
     real64 const krwedAtSmxi = drainageRelPermKernelWrapper.compute( &Smxi );
 
     // Step 1: Compute the new end point
@@ -578,12 +579,12 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   // Step 1: for a given value of the max historical saturation, Shy, compute the trapped critical saturation, Scrt,
   //         using Land's method. The calculation includes the modifications from Jerauld.
   real64 const S = phaseVolFraction;
-  real64 const Scri = m_nonWettingCurve.m_criticalImbibitionPhaseVolFraction;
-  real64 const Smx = m_nonWettingCurve.m_extremumPhaseVolFraction;
+  real64 const Scri = m_nonWettingCurve.imbibitionExtremaPhaseVolFraction;
+  real64 const Smx = m_nonWettingCurve.oppositeBoundPhaseVolFraction;
   real64 const Shy = (phaseMaxHistoricalVolFraction < Smx) ? phaseMaxHistoricalVolFraction : Smx; // to make sure that Shy < Smax
   real64 Scrt = 0;
 
-  using IPT = ImbibitionPhasePairPhaseType;
+  using IPT = TableRelativePermeabilityHysteresis::ImbibitionPhasePairPhaseType;
   KilloughHysteresis::computeTrappedCriticalPhaseVolFraction( m_nonWettingCurve,
                                                               Shy,
                                                               m_landParam[IPT::NONWETTING],
@@ -598,13 +599,13 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   }
   else if( S >= Smx ) // S is above the max saturation, so we just skip the rest and set the relperm to the endpoint
   {
-    phaseRelPerm = m_nonWettingCurve.m_extremumValue;
+    phaseRelPerm = m_nonWettingCurve.oppositeBoundSCALValue;
     dPhaseRelPerm_dPhaseVolFrac = 0.0;
   }
   else
   {
     // Step 2: compute the normalized saturation, S_norm, at which the imbibition relperm curve will be evaluated.
-    real64 const ratio = ( Smx - Scri ) / ( Shy - Scrt );
+    real64 const ratio = ( Smx - Scri ) / ( Shy - Scrt ); // non S-deps part (isolated for derivatives calculations)
     real64 const Snorm = Scri + ( S - Scrt ) * ratio; // normalized saturation
     real64 const dSnorm_dS = ratio;
 
@@ -618,7 +619,7 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
     real64 const krdAtShy = drainageRelPermKernelWrapper.compute( &Shy );
 
     // Step 5: evaluate the drainage relperm, krd(Smx), at the max drainage saturation, Smx.
-    real64 const krdAtSmx = m_nonWettingCurve.m_extremumValue;
+    real64 const krdAtSmx = m_nonWettingCurve.oppositeBoundSCALValue;
 
     // Step 6: apply the formula blending drainage and imbibition relperms from the Killough model.
     real64 const drainageRelPermRatio = krdAtShy / krdAtSmx;
@@ -646,11 +647,29 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   using TPT = constitutive::TableRelativePermeabilityHysteresis::TwoPhasePairPhaseType;
   using IPT = constitutive::TableRelativePermeabilityHysteresis::ImbibitionPhasePairPhaseType;
 
+  constexpr bool FORCE_IMBIBITION_MODE = false;
+  constexpr bool FORCE_DRAINAGE_MODE = false;
+
   // ---------- wetting rel perm
-  if( !m_phaseHasHysteresis[IPT::WETTING] ||
+  if( FORCE_DRAINAGE_MODE )
+  {
+    phaseTrappedVolFrac[ipWetting] = LvArray::math::min( phaseVolFraction[ipWetting], m_wettingCurve.oppositeBoundPhaseVolFraction );
+    computeDrainageRelPerm( m_drainageRelPermKernelWrappers[TPT::WETTING],
+                            phaseVolFraction[ipWetting],
+                            phaseRelPerm[ipWetting],
+                            dPhaseRelPerm_dPhaseVolFrac[ipWetting][ipWetting] );
+  }
+  else if( FORCE_IMBIBITION_MODE )
+  {
+    phaseTrappedVolFrac[ipWetting] = LvArray::math::min( phaseVolFraction[ipWetting], m_wettingCurve.oppositeBoundPhaseVolFraction );
+    auto const & imbibitionRelPermKernelWrapper = m_imbibitionRelPermKernelWrappers[IPT::WETTING];
+    phaseRelPerm[ipWetting] = imbibitionRelPermKernelWrapper.compute( &phaseVolFraction[ipWetting],
+                                                                       &dPhaseRelPerm_dPhaseVolFrac[ipWetting][ipWetting] );
+  }
+  else if( !m_phaseHasHysteresis[IPT::WETTING] ||
       phaseVolFraction[ipWetting] <= phaseMinHistoricalVolFraction[ipWetting] + flowReversalBuffer )
   {
-    phaseTrappedVolFrac[ipWetting] = LvArray::math::min( phaseVolFraction[ipWetting], m_wettingCurve.m_extremumPhaseVolFraction );
+    phaseTrappedVolFrac[ipWetting] = LvArray::math::min( phaseVolFraction[ipWetting], m_wettingCurve.oppositeBoundPhaseVolFraction );
     computeDrainageRelPerm( m_drainageRelPermKernelWrappers[TPT::WETTING],
                             phaseVolFraction[ipWetting],
                             phaseRelPerm[ipWetting],
@@ -667,12 +686,37 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   }
 
   // --------- non-wetting rel perm
-  if( !m_phaseHasHysteresis[IPT::NONWETTING] ||
+  if( FORCE_DRAINAGE_MODE )
+  {
+    phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min( phaseVolFraction[ipNonWetting], m_nonWettingCurve.drainageExtremaPhaseVolFraction );
+    computeDrainageRelPerm( m_drainageRelPermKernelWrappers[TPT::NONWETTING],
+                            phaseVolFraction[ipNonWetting],
+                            phaseRelPerm[ipNonWetting],
+                            dPhaseRelPerm_dPhaseVolFrac[ipNonWetting][ipNonWetting] );
+  }
+  else if( FORCE_IMBIBITION_MODE )
+  {
+    real64 const Shy = ( phaseVolFraction[ipNonWetting] < m_nonWettingCurve.oppositeBoundPhaseVolFraction )
+      ? phaseVolFraction[ipNonWetting] : m_nonWettingCurve.oppositeBoundPhaseVolFraction;
+    real64 Scrt = 0;
+    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction( m_nonWettingCurve,
+                                                                Shy,
+                                                                m_landParam[IPT::NONWETTING],
+                                                                m_jerauldParam_a,
+                                                                m_jerauldParam_b,
+                                                                Scrt );
+    phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min( Scrt, phaseVolFraction[ipNonWetting] );
+    
+    auto const & imbibitionRelPermKernelWrapper = m_imbibitionRelPermKernelWrappers[IPT::NONWETTING];
+    phaseRelPerm[ipNonWetting] = imbibitionRelPermKernelWrapper.compute( &phaseVolFraction[ipNonWetting],
+                                                                         &dPhaseRelPerm_dPhaseVolFrac[ipNonWetting][ipNonWetting] );
+  }
+  else if( !m_phaseHasHysteresis[IPT::NONWETTING] ||
       phaseVolFraction[ipNonWetting] >= phaseMaxHistoricalVolFraction[ipNonWetting] - flowReversalBuffer )
   {
     // for reporting purposes, compute Sgcrt first
-    real64 const Shy = ( phaseVolFraction[ipNonWetting] < m_nonWettingCurve.m_extremumPhaseVolFraction )
-      ? phaseVolFraction[ipNonWetting] : m_nonWettingCurve.m_extremumPhaseVolFraction; // to make sure that Shy < Smax
+    real64 const Shy = ( phaseVolFraction[ipNonWetting] < m_nonWettingCurve.oppositeBoundPhaseVolFraction )
+      ? phaseVolFraction[ipNonWetting] : m_nonWettingCurve.oppositeBoundPhaseVolFraction; // to make sure that Shy < Smax
     real64 Scrt = 0;
     KilloughHysteresis::computeTrappedCriticalPhaseVolFraction( m_nonWettingCurve,
                                                                 Shy,
@@ -721,13 +765,31 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   using TPT = constitutive::TableRelativePermeabilityHysteresis::ThreePhasePairPhaseType;
   using IPT = constitutive::TableRelativePermeabilityHysteresis::ImbibitionPhasePairPhaseType;
 
+  constexpr bool FORCE_IMBIBITION_MODE = false;
+  constexpr bool FORCE_DRAINAGE_MODE = false;
+
   // 1) Wetting and intermediate phase relative permeabilities using two-phase wetting-intermediate data
 
   // ---------- wetting rel perm
-  if( !m_phaseHasHysteresis[IPT::WETTING] ||
+  if( FORCE_DRAINAGE_MODE )
+  {
+    phaseTrappedVolFrac[ipWetting] = LvArray::math::min( m_wettingCurve.oppositeBoundPhaseVolFraction, phaseVolFraction[ipWetting] );
+    computeDrainageRelPerm( m_drainageRelPermKernelWrappers[TPT::WETTING],
+                            phaseVolFraction[ipWetting],
+                            phaseRelPerm[ipWetting],
+                            dPhaseRelPerm_dPhaseVolFrac[ipWetting][ipWetting] );
+  }
+  else if( FORCE_IMBIBITION_MODE )
+  {
+    phaseTrappedVolFrac[ipWetting] = LvArray::math::min( m_wettingCurve.oppositeBoundPhaseVolFraction, phaseVolFraction[ipWetting] );
+    auto const & imbibitionRelPermKernelWrapper = m_imbibitionRelPermKernelWrappers[IPT::WETTING];
+    phaseRelPerm[ipWetting] = imbibitionRelPermKernelWrapper.compute( &phaseVolFraction[ipWetting],
+                                                                       &dPhaseRelPerm_dPhaseVolFrac[ipWetting][ipWetting] );
+  }
+  else if( !m_phaseHasHysteresis[IPT::WETTING] ||
       phaseVolFraction[ipWetting] <= phaseMinHistoricalVolFraction[ipWetting] + flowReversalBuffer )
   {
-    phaseTrappedVolFrac[ipWetting] = LvArray::math::min( m_wettingCurve.m_extremumPhaseVolFraction, phaseVolFraction[ipWetting] );
+    phaseTrappedVolFrac[ipWetting] = LvArray::math::min( m_wettingCurve.oppositeBoundPhaseVolFraction, phaseVolFraction[ipWetting] );
     computeDrainageRelPerm( m_drainageRelPermKernelWrappers[TPT::WETTING],
                             phaseVolFraction[ipWetting],
                             phaseRelPerm[ipWetting],
@@ -752,12 +814,37 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   // 2) Non-wetting and intermediate phase relative permeabilities using two-phase non-wetting-intermediate data
 
   // ---------- non-wetting rel perm
-  if( !m_phaseHasHysteresis[IPT::NONWETTING] ||
+  if( FORCE_DRAINAGE_MODE )
+  {
+    phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min( m_nonWettingCurve.drainageExtremaPhaseVolFraction, phaseVolFraction[ipNonWetting] );
+    computeDrainageRelPerm( m_drainageRelPermKernelWrappers[TPT::NONWETTING],
+                            phaseVolFraction[ipNonWetting],
+                            phaseRelPerm[ipNonWetting],
+                            dPhaseRelPerm_dPhaseVolFrac[ipNonWetting][ipNonWetting] );
+  }
+  else if( FORCE_IMBIBITION_MODE )
+  {
+    real64 const Shy = ( phaseVolFraction[ipNonWetting] < m_nonWettingCurve.oppositeBoundPhaseVolFraction)
+      ? phaseVolFraction[ipNonWetting] : m_nonWettingCurve.oppositeBoundPhaseVolFraction;
+    real64 Scrt = 0;
+    KilloughHysteresis::computeTrappedCriticalPhaseVolFraction( m_nonWettingCurve,
+                                                                Shy,
+                                                                m_landParam[IPT::NONWETTING],
+                                                                m_jerauldParam_a,
+                                                                m_jerauldParam_b,
+                                                                Scrt );
+    phaseTrappedVolFrac[ipNonWetting] = LvArray::math::min( Scrt, phaseVolFraction[ipNonWetting] );
+    
+    auto const & imbibitionRelPermKernelWrapper = m_imbibitionRelPermKernelWrappers[IPT::NONWETTING];
+    phaseRelPerm[ipNonWetting] = imbibitionRelPermKernelWrapper.compute( &phaseVolFraction[ipNonWetting],
+                                                                         &dPhaseRelPerm_dPhaseVolFrac[ipNonWetting][ipNonWetting] );
+  }
+  else if( !m_phaseHasHysteresis[IPT::NONWETTING] ||
       phaseVolFraction[ipNonWetting] >= phaseMaxHistoricalVolFraction[ipNonWetting] - flowReversalBuffer )
   {
     // 2.a) compute Sgcrt for reporting purposes
-    real64 const Shy = ( phaseVolFraction[ipNonWetting] < m_nonWettingCurve.m_extremumPhaseVolFraction)
-      ? phaseVolFraction[ipNonWetting] : m_nonWettingCurve.m_extremumPhaseVolFraction; // to make sure that Shy < Smax
+    real64 const Shy = ( phaseVolFraction[ipNonWetting] < m_nonWettingCurve.oppositeBoundPhaseVolFraction)
+      ? phaseVolFraction[ipNonWetting] : m_nonWettingCurve.oppositeBoundPhaseVolFraction; // to make sure that Shy < Smax
     real64 Scrt = 0;
     KilloughHysteresis::computeTrappedCriticalPhaseVolFraction( m_nonWettingCurve,
                                                                 Shy,
@@ -792,7 +879,7 @@ TableRelativePermeabilityHysteresis::KernelWrapper::
   // 3) Compute the "three-phase" oil relperm
 
   // use saturation-weighted interpolation
-  real64 const shiftedWettingVolFrac = (phaseVolFraction[ipWetting] - m_wettingCurve.m_extremumPhaseVolFraction);
+  real64 const shiftedWettingVolFrac = (phaseVolFraction[ipWetting] - m_wettingCurve.oppositeBoundPhaseVolFraction);
 
   if( m_threePhaseInterpolator == ThreePhaseInterpolator::BAKER )
   {
diff --git a/src/coreComponents/constitutive/relativePermeability/VanGenuchtenBakerRelativePermeability.hpp b/src/coreComponents/constitutive/relativePermeability/VanGenuchtenBakerRelativePermeability.hpp
index 931f7d35b63..11bd206d906 100644
--- a/src/coreComponents/constitutive/relativePermeability/VanGenuchtenBakerRelativePermeability.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/VanGenuchtenBakerRelativePermeability.hpp
@@ -140,19 +140,17 @@ class VanGenuchtenBakerRelativePermeability : public RelativePermeabilityBase
   };
 
 
-  arrayView1d< real64 const > getPhaseMinVolumeFraction() const override { return m_phaseMinVolumeFraction; };
-
   real64 getWettingPhaseMinVolumeFraction() const override
   {
     integer ipWetting;
-    std::tie( ipWetting, std::ignore ) = wettingAndNonWettingPhaseIndices();
+    std::tie( ipWetting, std::ignore ) = phaseIndex( getPhaseOrder());
     return m_phaseMinVolumeFraction[ipWetting];
   }
 
   real64 getNonWettingMinVolumeFraction() const override
   {
     integer ipNonWetting;
-    std::tie( std::ignore, ipNonWetting ) = wettingAndNonWettingPhaseIndices();
+    std::tie( std::ignore, ipNonWetting ) = phaseIndex( getPhaseOrder());
     return m_phaseMinVolumeFraction[ipNonWetting];
   };
 
diff --git a/src/coreComponents/constitutive/relativePermeability/VanGenuchtenStone2RelativePermeability.hpp b/src/coreComponents/constitutive/relativePermeability/VanGenuchtenStone2RelativePermeability.hpp
index 3927764f236..e91e4fb39bd 100644
--- a/src/coreComponents/constitutive/relativePermeability/VanGenuchtenStone2RelativePermeability.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/VanGenuchtenStone2RelativePermeability.hpp
@@ -139,7 +139,7 @@ class VanGenuchtenStone2RelativePermeability : public RelativePermeabilityBase
     static constexpr char const * volFracScaleString() { return "volFracScale"; }
   };
 
-  arrayView1d< real64 const > getPhaseMinVolumeFraction() const override { return m_phaseMinVolumeFraction; };
+  arrayView1d< real64 const > getPhaseMinVolumeFraction() const { return m_phaseMinVolumeFraction; };
 
   real64  getWettingPhaseMinVolumeFraction() const override
   {
diff --git a/src/coreComponents/constitutive/relativePermeability/unitTests/constitutiveTestHelpers.hpp b/src/coreComponents/constitutive/relativePermeability/unitTests/constitutiveTestHelpers.hpp
index e2ddfa05933..c5463cca49f 100644
--- a/src/coreComponents/constitutive/relativePermeability/unitTests/constitutiveTestHelpers.hpp
+++ b/src/coreComponents/constitutive/relativePermeability/unitTests/constitutiveTestHelpers.hpp
@@ -32,7 +32,7 @@ namespace geos
 {
 namespace testing
 {
-void fillArray( array1d< real64_array > & arr, std::initializer_list< real64 > const & input_list )
+void fill_array( array1d< real64_array > & arr, std::initializer_list< real64 > const & input_list )
 {
   arr.resize( 1 );
   arr[0].resize( input_list.size());
@@ -42,7 +42,7 @@ void fillArray( array1d< real64_array > & arr, std::initializer_list< real64 > c
 
 }
 
-void fillArray( real64_array & arr, std::initializer_list< real64 > const & input_list )
+void fill_array( real64_array & arr, std::initializer_list< real64 > const & input_list )
 {
   arr.resize( input_list.size());
   int j = 0;
diff --git a/src/coreComponents/constitutive/unitTests/FluidModelTest_impl.hpp b/src/coreComponents/constitutive/unitTests/FluidModelTest_impl.hpp
index 72cfec6501c..ce731e6b775 100644
--- a/src/coreComponents/constitutive/unitTests/FluidModelTest_impl.hpp
+++ b/src/coreComponents/constitutive/unitTests/FluidModelTest_impl.hpp
@@ -35,7 +35,7 @@ template< typename FLUID_TYPE, integer NUM_COMP, integer NUM_PHASE >
 FluidModelTest< FLUID_TYPE, NUM_COMP, NUM_PHASE >::FluidModelTest():
   m_parent( "parent", m_node )
 {
-  createFunctionManager();
+  // createFunctionManager();
 }
 
 template< typename FLUID_TYPE, integer NUM_COMP, integer NUM_PHASE >
diff --git a/src/coreComponents/constitutive/unitTests/testCO2SpycherPruessModels.cpp.uncrustify b/src/coreComponents/constitutive/unitTests/testCO2SpycherPruessModels.cpp.uncrustify
new file mode 100644
index 00000000000..e69de29bb2d
diff --git a/src/coreComponents/constitutive/unitTests/testTwoPhaseFluid.cpp b/src/coreComponents/constitutive/unitTests/testTwoPhaseFluid.cpp
new file mode 100644
index 00000000000..207668e29cb
--- /dev/null
+++ b/src/coreComponents/constitutive/unitTests/testTwoPhaseFluid.cpp
@@ -0,0 +1,283 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 TotalEnergies
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+#include "constitutive/fluid/twophasefluid/TwoPhaseFluid.hpp"
+#include "constitutive/fluid/twophasefluid/TwoPhaseFluidFields.hpp"
+
+// Only for fill
+#include "unitTests/constitutiveTests/MultiFluidTest.hpp"
+
+// Only for initializeTable
+#include "unitTests/constitutiveTests/constitutiveTestHelpers.hpp"
+
+
+using namespace geos;
+using namespace geos::testing;
+using namespace geos::constitutive;
+using namespace geos::dataRepository;   /// Only for group definition
+
+
+static constexpr char const * tableContentPhase0 = "# Pg(Pa) Dens(kg/m3) Visc(Pa.s)\n"
+                                                   "0.22     0.00603  40203\n"
+                                                   "0.3      0.04224  31311\n"
+                                                   "0.5      0.15011  22423\n"
+                                                   "0.6      0.22423  15011\n"
+                                                   "0.8      0.31311  4224\n"
+                                                   "1.0      0.40203  603";
+
+static constexpr char const * tableContentPhase1 = "# Pg(Pa) Dens(kg/m3) Visc(Pa.s)\n"
+                                                   "1.22     0.00603  0.22\n"
+                                                   "1.3      0.04224  0.22\n"
+                                                   "1.5      0.15011  0.22\n"
+                                                   "1.6      0.22423  0.22\n"
+                                                   "1.8      0.31311  0.22\n"
+                                                   "2.0      0.40203  0.22";
+
+template< bool FROM_TABLE >
+class TwoPhaseFluidTest : public ConstitutiveTestBase< TwoPhaseFluid >
+{
+public:
+
+  TwoPhaseFluidTest()
+  {
+    if constexpr (!FROM_TABLE)
+    {
+      writeTableToFile( "phase0.txt", tableContentPhase0 );
+      writeTableToFile( "phase1.txt", tableContentPhase1 );
+    }
+
+    m_parent.resize( 1 );
+    string const fluidName = GEOS_FMT( "fluid{}", (FROM_TABLE ? "Tables" : "Files"));
+    m_model = makeTwoPhaseFluid( fluidName, m_parent );
+
+    m_parent.initialize();
+    m_parent.initializePostInitialConditions();
+  }
+
+  ~TwoPhaseFluidTest()
+  {
+    if constexpr (!FROM_TABLE)
+    {
+      removeFile( "phase0.txt" );
+      removeFile( "phase1.txt" );
+    }
+  }
+
+  constitutive::TwoPhaseFluid & getFluid() const { return *m_model; }
+
+  dataRepository::Group & getParent() { return m_parent; }
+
+
+  void testDerivatives( constitutive::TwoPhaseFluid & fluid,
+                        dataRepository::Group * parent,
+                        real64 const pressure,
+                        real64 const perturbParameter,
+                        real64 const relTol,
+                        real64 const absTol = std::numeric_limits< real64 >::max() )
+  {
+    auto const & phaseNames = fluid.getReference< string_array >( TwoPhaseFluid::viewKeyStruct::phaseNamesString() );
+
+    // create a clone of the fluid to run updates on
+    string const fluidCopyName = fluid.getName() + "Copy";
+    std::unique_ptr< constitutive::ConstitutiveBase > fluidCopyPtr = fluid.deliverClone( fluidCopyName, parent );
+    constitutive::TwoPhaseFluid & fluidCopy = dynamicCast< constitutive::TwoPhaseFluid & >( *fluidCopyPtr );
+    fluidCopy.initializePostSubGroups();
+
+    fluid.allocateConstitutiveData( fluid.getParent(), 1 );
+    fluidCopy.allocateConstitutiveData( fluid.getParent(), 1 );
+
+    // extract data views from both fluids
+    #define GET_FLUID_DATA( FLUID, TRAIT ) \
+      FLUID.getReference< TRAIT::type >( TRAIT::key() )[0][0]
+
+    constitutive::MultiFluidVarSlice< real64, 1, constitutive::multifluid::USD_PHASE - 2, constitutive::multifluid::USD_PHASE_DC - 2 > phaseVisc {
+      GET_FLUID_DATA( fluid, fields::twophasefluid::phaseViscosity ),
+      GET_FLUID_DATA( fluid, fields::twophasefluid::dPhaseViscosity )
+    };
+
+    constitutive::MultiFluidVarSlice< real64, 1, constitutive::multifluid::USD_PHASE - 2, constitutive::multifluid::USD_PHASE_DC - 2 > phaseDens {
+      GET_FLUID_DATA( fluid, fields::twophasefluid::phaseDensity ),
+      GET_FLUID_DATA( fluid, fields::twophasefluid::dPhaseDensity )
+    };
+
+    auto const & phaseDensCopy = GET_FLUID_DATA( fluidCopy, fields::twophasefluid::phaseDensity );
+    auto const & phaseViscCopy = GET_FLUID_DATA( fluidCopy, fields::twophasefluid::phaseViscosity );
+#undef GET_FLUID_DATA
+
+
+    // set the original fluid state to current
+    constitutive::constitutiveUpdatePassThru( fluid, [&] ( auto & castedFluid )
+    {
+      typename TYPEOFREF( castedFluid ) ::KernelWrapper fluidWrapper = castedFluid.createKernelWrapper();
+      fluidWrapper.update( 0, 0, pressure );
+    } );
+
+    // now perturb variables and update the copied fluid's state
+    constitutive::constitutiveUpdatePassThru( fluidCopy, [&] ( auto & castedFluid )
+    {
+      using Deriv = constitutive::multifluid::DerivativeOffset;
+
+      typename TYPEOFREF( castedFluid ) ::KernelWrapper fluidWrapper = castedFluid.createKernelWrapper();
+
+      // to be able to use the checkDerivative utility function, we have to invert the layout
+      auto dPhaseDens     = invertLayout( phaseDens.derivs.toSliceConst(), 2, 1 );
+      auto dPhaseVisc     = invertLayout( phaseVisc.derivs.toSliceConst(), 2, 1 );
+
+      // update pressure and check derivatives
+      real64 const dP = perturbParameter * (pressure + perturbParameter);
+      fluidWrapper.update( 0, 0, pressure + dP );
+
+      checkDerivative( phaseDensCopy.toSliceConst(), phaseDens.value.toSliceConst(), dPhaseDens[Deriv::dP].toSliceConst(),
+                       dP, relTol, absTol, "phaseDens", "Pressure", phaseNames );
+      checkDerivative( phaseViscCopy.toSliceConst(), phaseVisc.value.toSliceConst(), dPhaseVisc[Deriv::dP].toSliceConst(),
+                       dP, relTol, absTol, "phaseVisc", "Pressure", phaseNames );
+    } );
+  }   // void testDerivatives
+
+
+protected:
+  static void writeTableToFile( string const & fileName, char const * content )
+  {
+    std::ofstream os( fileName );
+    ASSERT_TRUE( os.is_open() );
+    os << content;
+    os.close();
+  }
+
+  static void removeFile( string const & fileName )
+  {
+    int const ret = std::remove( fileName.c_str() );
+    ASSERT_TRUE( ret == 0 );
+  }
+
+
+private:
+  static TwoPhaseFluid * makeTwoPhaseFluid( string const & name, Group & parent );
+
+};  // class TwoPhaseFluidTest
+
+
+template<>
+TwoPhaseFluid * TwoPhaseFluidTest< true >::makeTwoPhaseFluid( string const & name, Group & parent )
+{
+  // 1D table with linear interpolation
+  localIndex constexpr Naxis = 6;
+  localIndex constexpr NaxisSingle = 1;
+
+  array1d< real64_array > densityCoordPhase0( 1 );
+  fill< Naxis >( densityCoordPhase0[0], { 0.22, 0.3, 0.5, 0.6, 0.8, 1.0 } );
+  real64_array densityValuesPhase0;
+  fill< Naxis >( densityValuesPhase0, { 0.00603, 0.04224, 0.04224, 0.22423, 0.31311, 0.40203 } );
+
+  array1d< real64_array > densityCoordPhase1( 1 );
+  fill< Naxis >( densityCoordPhase1[0], { 1.22, 1.3, 1.5, 1.6, 1.8, 2.0 } );
+  real64_array densityValuesPhase1;
+  fill< Naxis >( densityValuesPhase1, { 0.00603, 0.04224, 0.04224, 0.22423, 0.31311, 0.40203 } );
+
+
+  array1d< real64_array > viscosityCoordPhase0( 1 );
+  fill< Naxis >( viscosityCoordPhase0[0], { 0.22, 0.3, 0.5, 0.6, 0.8, 1.0 } );
+  real64_array viscosityValuesPhase0;
+  fill< Naxis >( viscosityValuesPhase0, { 40203, 31311, 22423, 15011, 4224, 603 } );
+
+  array1d< real64_array > viscosityCoordPhase1( 1 );
+  fill< NaxisSingle >( viscosityCoordPhase1[0], { 0.22 } );
+  real64_array viscosityValuesPhase1;
+  fill< NaxisSingle >( viscosityValuesPhase1, { 45 } );
+
+  initializeTable( "densityTablePhase0", densityCoordPhase0, densityValuesPhase0 );
+  initializeTable( "densityTablePhase1", densityCoordPhase1, densityValuesPhase1 );
+  initializeTable( "viscosityTablePhase0", viscosityCoordPhase0, viscosityValuesPhase0 );
+  initializeTable( "viscosityTablePhase1", viscosityCoordPhase1, viscosityValuesPhase1 );
+
+
+  // 2) Set up the constitutive model
+  TwoPhaseFluid & fluid = parent.registerGroup< TwoPhaseFluid >( name );
+
+  string_array & phaseNames = fluid.getReference< string_array >( TwoPhaseFluid::viewKeyStruct::phaseNamesString() );
+  phaseNames.emplace_back( "oil" );
+  phaseNames.emplace_back( "water" );
+
+  string_array & densityTableNames = fluid.getReference< string_array >( TwoPhaseFluid::viewKeyStruct::densityTableNamesString() );
+  densityTableNames.emplace_back( "densityTablePhase0" );
+  densityTableNames.emplace_back( "densityTablePhase1" );
+
+  string_array & viscosityTableNames = fluid.getReference< string_array >( TwoPhaseFluid::viewKeyStruct::viscosityTableNamesString() );
+  viscosityTableNames.emplace_back( "viscosityTablePhase0" );
+  viscosityTableNames.emplace_back( "viscosityTablePhase1" );
+
+  fluid.postInputInitializationRecursive();
+  return &fluid;
+}
+
+
+template<>
+TwoPhaseFluid * TwoPhaseFluidTest< false >::makeTwoPhaseFluid( string const & name, Group & parent )
+{
+  TwoPhaseFluid & fluid = parent.registerGroup< TwoPhaseFluid >( name );
+
+  path_array & tableNames = fluid.getReference< path_array >( TwoPhaseFluid::viewKeyStruct::tableFilesString() );
+  fill< 2 >( tableNames, {"phase0.txt", "phase1.txt"} );
+
+  fluid.postInputInitializationRecursive();
+  return &fluid;
+}
+
+
+
+using TwoPhaseFluidTestFromFiles = TwoPhaseFluidTest< false >;
+using TwoPhaseFluidTestFromTables = TwoPhaseFluidTest< true >;
+
+
+TEST_F( TwoPhaseFluidTestFromTables, testNumericalDerivative_initFromTables )
+{
+  auto & fluid = getFluid();
+  real64 const eps = std::sqrt( std::numeric_limits< real64 >::epsilon());
+  real64 constexpr relTol = 1.0e-8;
+  real64 constexpr absTol = 1.0e-8;
+
+  for( real64 const pressure : { 0.55, 1.0, 10.0 } )
+  {
+    testDerivatives( fluid, &getParent(), pressure, eps, relTol, absTol );
+  }
+}
+
+
+TEST_F( TwoPhaseFluidTestFromFiles, testNumericalDerivative_initFromFiles )
+{
+  auto & fluid = getFluid();
+  real64 const eps = std::sqrt( std::numeric_limits< real64 >::epsilon());
+  real64 constexpr relTol = 1.0e-8;
+  real64 constexpr absTol = 1.0e-8;
+
+  for( real64 const pressure : { 0.55, 1.0, 10.0 } )
+  {
+    testDerivatives( fluid, &getParent(), pressure, eps, relTol, absTol );
+  }
+}
+
+
+int main( int argc, char * * argv )
+{
+  ::testing::InitGoogleTest( &argc, argv );
+
+  conduit::Node conduitNode;
+  dataRepository::Group rootNode( "root", conduitNode );
+  FunctionManager functionManager( "FunctionManager", &rootNode );
+
+  int const result = RUN_ALL_TESTS();
+
+  return result;
+}
diff --git a/src/coreComponents/constitutiveDrivers/relativePermeability/RelpermDriver.cpp b/src/coreComponents/constitutiveDrivers/relativePermeability/RelpermDriver.cpp
index 49dca10b482..6bd500b6dfa 100644
--- a/src/coreComponents/constitutiveDrivers/relativePermeability/RelpermDriver.cpp
+++ b/src/coreComponents/constitutiveDrivers/relativePermeability/RelpermDriver.cpp
@@ -13,7 +13,9 @@
  * ------------------------------------------------------------------------------------------------------------
  */
 
-#include "common/MpiWrapper.hpp"
+#include "RelpermDriver.hpp"
+
+//#include "common/MpiWrapper.hpp"
 #include "functions/FunctionManager.hpp"
 #include "functions/TableFunction.hpp"
 #include "constitutive/ConstitutiveManager.hpp"
@@ -110,7 +112,7 @@ bool RelpermDriver::execute( const geos::real64 GEOS_UNUSED_PARAM( time_n ),
 {
   // this code only makes sense in serial
 
-  GEOS_THROW_IF( MpiWrapper::commRank() > 0, "RelpermDriver should only be run in serial", std::runtime_error );
+  //GEOS_THROW_IF( MpiWrapper::commRank() > 0, "RelpermDriver should only be run in serial", std::runtime_error );
 
 
   ConstitutiveManager
diff --git a/src/coreComponents/constitutiveDrivers/relativePermeability/RelpermDriverRunTest.hpp b/src/coreComponents/constitutiveDrivers/relativePermeability/RelpermDriverRunTest.hpp
index eabe5616eee..750587bab88 100644
--- a/src/coreComponents/constitutiveDrivers/relativePermeability/RelpermDriverRunTest.hpp
+++ b/src/coreComponents/constitutiveDrivers/relativePermeability/RelpermDriverRunTest.hpp
@@ -19,7 +19,7 @@
 #include "constitutiveDrivers/relativePermeability/RelpermDriver.hpp"
 #include "constitutive/relativePermeability/RelativePermeabilityFields.hpp"
 #include "constitutive/relativePermeability/Layouts.hpp"
-#include "constitutive/relativePermeability/KilloughHysteresis.hpp"
+#include "constitutive/KilloughHysteresis.hpp"
 
 
 namespace geos
@@ -96,10 +96,6 @@ RelpermDriver::runTest( RELPERM_TYPE & relperm,
   arrayView2d< real64, compflow::USD_PHASE > phaseMaxHistoricalVolFraction = relperm.template getField< fields::relperm::phaseMaxHistoricalVolFraction >().reference();
   arrayView2d< real64, compflow::USD_PHASE >  phaseMinHistoricalVolFraction = relperm.template getField< fields::relperm::phaseMinHistoricalVolFraction >().reference();
 
-//  arrayView1d< real64 > const drainagePhaseMinVolFraction = relperm.template getReference< array1d< real64 > >(
-//    constitutive::TableRelativePermeabilityHysteresis::viewKeyStruct::drainagePhaseMinVolumeFractionString());
-//  arrayView1d< real64 > const drainagePhaseMaxVolFraction = relperm.template getReference< array1d< real64 > >(
-//    constitutive::TableRelativePermeabilityHysteresis::viewKeyStruct::drainagePhaseMaxVolumeFractionString());
   constitutive::KilloughHysteresis::HysteresisCurve const wettingCurve = relperm.template getReference< constitutive::KilloughHysteresis::HysteresisCurve >(
     constitutive::TableRelativePermeabilityHysteresis::viewKeyStruct::wettingCurveString());
 
@@ -109,14 +105,15 @@ RelpermDriver::runTest( RELPERM_TYPE & relperm,
   {
     if( phaseHasHysteresis[ipNonWetting] )
     {
-      phaseMaxHistoricalVolFraction[0][ipNonWetting] = nonWettingCurve.m_extremumPhaseVolFraction;
+      phaseMaxHistoricalVolFraction[0][ipNonWetting] = nonWettingCurve.oppositeBoundPhaseVolFraction;
       GEOS_LOG( GEOS_FMT( "New max non-wetting phase historical phase volume fraction: {}", phaseMaxHistoricalVolFraction[0][ipNonWetting] ) );
     }
     if( phaseHasHysteresis[ipWetting] )
     {
-      phaseMinHistoricalVolFraction[0][ipWetting] = wettingCurve.m_extremumPhaseVolFraction;
+      phaseMinHistoricalVolFraction[0][ipWetting] = wettingCurve.oppositeBoundPhaseVolFraction;
       GEOS_LOG( GEOS_FMT( "New min wetting phase historical phase volume fraction: {}", phaseMinHistoricalVolFraction[0][ipWetting] ) );
     }
+
   }
 
 
@@ -140,13 +137,12 @@ RelpermDriver::runTest( RELPERM_TYPE & relperm,
   {
     if( phaseHasHysteresis[ipNonWetting] )
     {
-
-      phaseMaxHistoricalVolFraction[0][ipNonWetting] = nonWettingCurve.m_criticalDrainagePhaseVolFraction;
+      phaseMaxHistoricalVolFraction[0][ipNonWetting] = nonWettingCurve.drainageExtremaPhaseVolFraction;
       GEOS_LOG( GEOS_FMT( "New max non-wetting phase historical phase volume fraction: {}", phaseMaxHistoricalVolFraction[0][ipNonWetting] ) );
     }
     if( phaseHasHysteresis[ipWetting] )
     {
-      phaseMinHistoricalVolFraction[0][ipWetting] = wettingCurve.m_criticalDrainagePhaseVolFraction;
+      phaseMinHistoricalVolFraction[0][ipWetting] = wettingCurve.drainageExtremaPhaseVolFraction;
       GEOS_LOG( GEOS_FMT( "New min wetting phase historical phase volume fraction: {}", phaseMinHistoricalVolFraction[0][ipWetting] ) );
     }
   }
diff --git a/src/coreComponents/finiteVolume/CellElementStencilTPFA.hpp b/src/coreComponents/finiteVolume/CellElementStencilTPFA.hpp
index 88fa3bb2b27..5c468d293cf 100644
--- a/src/coreComponents/finiteVolume/CellElementStencilTPFA.hpp
+++ b/src/coreComponents/finiteVolume/CellElementStencilTPFA.hpp
@@ -70,6 +70,20 @@ class CellElementStencilTPFAWrapper : public StencilWrapperBase< TwoPointStencil
                        CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
                        real64 ( &weight )[1][2],
                        real64 ( &dWeight_dVar )[1][2] ) const;
+/**
+ * @brief Compute half weights and derivatives w.r.t to one variable.
+ * @param[in] iconn connection index
+ * @param[in] coefficient view accessor to the coefficient used to compute the weights
+ * @param[in] dCoeff_dVar view accessor to the derivative of the coefficient w.r.t to the variable
+ * @param[out] weight view weights
+ * @param[out] dWeight_dVar derivative of the weights w.r.t to the variable
+ */
+  GEOS_HOST_DEVICE
+  void computeHalfWeights( localIndex const iconn,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                           real64 ( &weight )[1][2],
+                           real64 ( &dWeight_dVar )[1][2] ) const;
 
   /**
    * @brief Compute weights and derivatives w.r.t to one variable without coefficient
@@ -293,6 +307,92 @@ CellElementStencilTPFAWrapper::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+CellElementStencilTPFAWrapper::
+  computeHalfWeights( localIndex const iconn,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                      real64 (& weight)[1][2],
+                      real64 (& dWeight_dVar )[1][2] ) const
+{
+  real64 halfWeight[2];
+  real64 dHalfWeight_dVar[2];
+
+  // real64 const tolerance = 1e-30 * lengthTolerance; // TODO: choice of constant based on physics?
+
+  for( localIndex i = 0; i < 2; ++i )
+  {
+    localIndex const er  = m_elementRegionIndices[iconn][i];
+    localIndex const esr = m_elementSubRegionIndices[iconn][i];
+    localIndex const ei  = m_elementIndices[iconn][i];
+
+    halfWeight[i] = m_weights[iconn][i];
+    dHalfWeight_dVar[i] = m_weights[iconn][i];
+
+    // Proper computation
+    real64 faceNormal[3];
+    LvArray::tensorOps::copy< 3 >( faceNormal, m_faceNormal[iconn] );
+    if( LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], faceNormal ) < 0.0 )
+    {
+      LvArray::tensorOps::scale< 3 >( faceNormal, -1 );
+    }
+
+    real64 faceConormal[3];
+    real64 dFaceConormal_dVar[3];
+    LvArray::tensorOps::hadamardProduct< 3 >( faceConormal, coefficient[er][esr][ei][0], faceNormal );
+    LvArray::tensorOps::hadamardProduct< 3 >( dFaceConormal_dVar, dCoeff_dVar[er][esr][ei][0], faceNormal );
+    halfWeight[i] *= LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], faceConormal );
+    dHalfWeight_dVar[i] *= LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], dFaceConormal_dVar );
+
+    // correct negative weight issue arising from non-K-orthogonal grids
+    // if( halfWeight[i] < 0.0 )
+    // {
+    //   LvArray::tensorOps::hadamardProduct< 3 >( faceConormal,
+    //                                             coefficient[er][esr][ei][0],
+    //                                             m_cellToFaceVec[iconn][i] );
+    //   LvArray::tensorOps::hadamardProduct< 3 >( dFaceConormal_dVar,
+    //                                             dCoeff_dVar[er][esr][ei][0],
+    //                                             m_cellToFaceVec[iconn][i] );
+    //   halfWeight[i] = m_weights[iconn][i];
+    //   dHalfWeight_dVar[i] = m_weights[iconn][i];
+    //   halfWeight[i] *= LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], faceConormal );
+    //   dHalfWeight_dVar[i] *= LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn][i], dFaceConormal_dVar );
+    // }
+  }
+
+  // // Do harmonic and arithmetic averaging
+  // real64 const product = halfWeight[0]*halfWeight[1];
+  // real64 const sum = halfWeight[0]+halfWeight[1];
+
+  // real64 const harmonicWeight   = sum > 0 ? product / sum : 0.0;
+  // real64 const arithmeticWeight = sum / 2;
+
+  // real64 dHarmonicWeight_dVar[2];
+  // real64 dArithmeticWeight_dVar[2];
+
+  // dHarmonicWeight_dVar[0] = sum > 0 ? (dHalfWeight_dVar[0]*sum*halfWeight[1] - dHalfWeight_dVar[0]*halfWeight[0]*halfWeight[1]) / (
+  // sum*sum ) : 0.0;
+  // dHarmonicWeight_dVar[1] = sum > 0 ? (dHalfWeight_dVar[1]*sum*halfWeight[0] - dHalfWeight_dVar[1]*halfWeight[1]*halfWeight[0]) / (
+  // sum*sum ) : 0.0;
+
+  // dArithmeticWeight_dVar[0] = dHalfWeight_dVar[0] / 2;
+  // dArithmeticWeight_dVar[1] = dHalfWeight_dVar[1] / 2;
+
+  // real64 const meanPermCoeff = 1.0; //TODO make it a member if it is really necessary
+
+  // real64 const value = meanPermCoeff * harmonicWeight + (1 - meanPermCoeff) * arithmeticWeight;
+  for( localIndex ke = 0; ke < 2; ++ke )
+  {
+    // weight[0][ke] = m_transMultiplier[iconn] * value * (ke == 0 ? 1 : -1);
+    weight[0][ke] = m_transMultiplier[iconn] * halfWeight[ke] * (ke == 0 ? 1 : -1);
+
+    // real64 const dValue_dVar = meanPermCoeff * dHarmonicWeight_dVar[ke] + (1 - meanPermCoeff) * dArithmeticWeight_dVar[ke];
+    // dWeight_dVar[0][ke] = m_transMultiplier[iconn] * dValue_dVar;
+    dWeight_dVar[0][ke] = m_transMultiplier[iconn] * dHalfWeight_dVar[ke];
+  }
+}
+
 GEOS_HOST_DEVICE
 inline void
 CellElementStencilTPFAWrapper::
diff --git a/src/coreComponents/finiteVolume/EmbeddedSurfaceToCellStencil.hpp b/src/coreComponents/finiteVolume/EmbeddedSurfaceToCellStencil.hpp
index 7f9c1562366..4a191ca7614 100644
--- a/src/coreComponents/finiteVolume/EmbeddedSurfaceToCellStencil.hpp
+++ b/src/coreComponents/finiteVolume/EmbeddedSurfaceToCellStencil.hpp
@@ -98,6 +98,22 @@ class EmbeddedSurfaceToCellStencilWrapper : public StencilWrapperBase< TwoPointS
                        real64 ( &weight )[1][2],
                        real64 ( &dWeight_dVar )[1][2] ) const;
 
+  /**
+   * @brief Compute half weigths and derivatives w.r.t to one variable.
+   * @param[in] iconn connection index
+   * @param[in] coefficient view accessor to the coefficient used to compute the weights
+   * @param[in] dCoeff_dVar view accessor to the derivative of the coefficient w.r.t to the variable
+   * @param[out] weight view weights
+   * @param[out] dWeight_dVar derivative of the weigths w.r.t to the variable
+   */
+
+  GEOS_HOST_DEVICE
+  void computeHalfWeights( localIndex const iconn,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                           real64 ( &weight )[1][2],
+                           real64 ( &dWeight_dVar )[1][2] ) const;
+
   /**
    * @brief Compute weigths and derivatives w.r.t to one variable without coefficient
    * Used in ReactiveCompositionalMultiphaseOBL solver for thermal transmissibility computation:
@@ -243,6 +259,42 @@ EmbeddedSurfaceToCellStencilWrapper::
   dWeight_dVar[0][1] = ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
 }
 
+GEOS_HOST_DEVICE
+inline void
+EmbeddedSurfaceToCellStencilWrapper::
+  computeHalfWeights( localIndex iconn,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                      real64 ( & weight )[1][2],
+                      real64 ( & dWeight_dVar )[1][2] ) const
+{
+  localIndex const er0  =  m_elementRegionIndices[iconn][0];
+  localIndex const esr0 =  m_elementSubRegionIndices[iconn][0];
+  localIndex const ei0  =  m_elementIndices[iconn][0];
+
+  localIndex const er1  =  m_elementRegionIndices[iconn][1];
+  localIndex const esr1 =  m_elementSubRegionIndices[iconn][1];
+  localIndex const ei1  =  m_elementIndices[iconn][1];
+
+  // Will change when implementing collocation points. Will use fracture normal to project the permeability
+  real64 const t0 = m_weights[iconn][0] * LvArray::tensorOps::l2Norm< 3 >( coefficient[er0][esr0][ei0][0] );
+  // We consider the 3rd component of the permeability which is the normal one.
+  real64 const t1 = m_weights[iconn][1] * coefficient[er1][esr1][ei1][0][2];
+
+  real64 const sumOfTrans = t0+t1;
+  real64 const value = t0*t1/sumOfTrans;
+
+  weight[0][0] = value;
+  weight[0][1] = -value;
+
+  // We consider the 3rd component of the permeability which is the normal one.
+  real64 const dt0 = m_weights[iconn][0] * dCoeff_dVar[er0][esr0][ei0][0][0];
+  real64 const dt1 = m_weights[iconn][1] * dCoeff_dVar[er1][esr1][ei1][0][2];
+
+  dWeight_dVar[0][0] = ( dt0 * t1 * sumOfTrans - dt0 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+  dWeight_dVar[0][1] = ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+}
+
 GEOS_HOST_DEVICE
 inline void
 EmbeddedSurfaceToCellStencilWrapper::
diff --git a/src/coreComponents/finiteVolume/FaceElementToCellStencil.hpp b/src/coreComponents/finiteVolume/FaceElementToCellStencil.hpp
index 6920e52b3bf..e86e6724bed 100644
--- a/src/coreComponents/finiteVolume/FaceElementToCellStencil.hpp
+++ b/src/coreComponents/finiteVolume/FaceElementToCellStencil.hpp
@@ -106,6 +106,21 @@ class FaceElementToCellStencilWrapper : public StencilWrapperBase< TwoPointStenc
                        real64 ( &weight )[1][2],
                        real64 ( &dWeight_dVar )[1][2] ) const;
 
+/**
+ * @brief Compute half weigths and derivatives w.r.t to one variable.
+ * @param[in] iconn connection index
+ * @param[in] coefficient view accessor to the coefficient used to compute the weights
+ * @param[in] dCoeff_dVar view accessor to the derivative of the coefficient w.r.t to the variable
+ * @param[out] weight view weights
+ * @param[out] dWeight_dVar derivative of the weigths w.r.t to the variable
+ */
+  GEOS_HOST_DEVICE
+  void computeHalfWeights( localIndex iconn,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                           real64 ( &weight )[1][2],
+                           real64 ( &dWeight_dVar )[1][2] ) const;
+
   /**
    * @brief Compute weigths and derivatives w.r.t to one variable without coefficient
    * Used in ReactiveCompositionalMultiphaseOBL solver for thermal transmissibility computation:
@@ -297,6 +312,44 @@ inline void FaceElementToCellStencilWrapper::
   dWeight_dVar[0][1] = m_transMultiplier[iconn] * ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
 }
 
+GEOS_HOST_DEVICE
+inline void FaceElementToCellStencilWrapper::
+  computeHalfWeights( localIndex const iconn,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                      real64 ( & weight )[1][2],
+                      real64 ( & dWeight_dVar )[1][2] ) const
+{
+  localIndex const er0  =  m_elementRegionIndices[iconn][0];
+  localIndex const esr0 =  m_elementSubRegionIndices[iconn][0];
+  localIndex const ei0  =  m_elementIndices[iconn][0];
+
+  localIndex const er1  =  m_elementRegionIndices[iconn][1];
+  localIndex const esr1 =  m_elementSubRegionIndices[iconn][1];
+  localIndex const ei1  =  m_elementIndices[iconn][1];
+
+  real64 faceConormal[3];
+
+  // Will change when implementing collocation points.
+  LvArray::tensorOps::hadamardProduct< 3 >( faceConormal, coefficient[er0][esr0][ei0][0], m_faceNormal[iconn] );
+  real64 const t0 = m_weights[iconn][0] * LvArray::tensorOps::AiBi< 3 >( m_cellToFaceVec[iconn], faceConormal );
+  // We consider the 3rd component of the permeability which is the normal one.
+  real64 const t1 = m_weights[iconn][1] * coefficient[er1][esr1][ei1][0][2];
+
+  real64 const sumOfTrans = t0+t1;
+  real64 const value = m_transMultiplier[iconn]*t0*t1/sumOfTrans;
+
+  weight[0][0] = value;
+  weight[0][1] = -value;
+
+  // We consider the 3rd component of the permeability which is the normal one.
+  real64 const dt0 = m_weights[iconn][0] * dCoeff_dVar[er0][esr0][ei0][0][0];
+  real64 const dt1 = m_weights[iconn][1] * dCoeff_dVar[er1][esr1][ei1][0][2];
+
+  dWeight_dVar[0][0] = ( dt0 * t1 * sumOfTrans - dt0 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+  dWeight_dVar[0][1] = ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+}
+
 GEOS_HOST_DEVICE
 inline void
 FaceElementToCellStencilWrapper
diff --git a/src/coreComponents/finiteVolume/SurfaceElementStencil.hpp b/src/coreComponents/finiteVolume/SurfaceElementStencil.hpp
index 5de67fe2f11..22942a1a648 100644
--- a/src/coreComponents/finiteVolume/SurfaceElementStencil.hpp
+++ b/src/coreComponents/finiteVolume/SurfaceElementStencil.hpp
@@ -110,6 +110,21 @@ class SurfaceElementStencilWrapper : public StencilWrapperBase< SurfaceElementSt
                        real64 ( &weight )[maxNumConnections][2],
                        real64 ( &dWeight_dVar )[maxNumConnections][2] ) const;
 
+  /**
+   * @brief Compute weights and derivatives w.r.t to one variable.
+   * @param[in] iconn connection index
+   * @param[in] coefficient view accessor to the coefficient used to compute the weights
+   * @param[in] dCoeff_dVar view accessor to the derivative of the coefficient w.r.t to the variable
+   * @param[out] weight view weights
+   * @param[out] dWeight_dVar derivative of the weights w.r.t to the variable
+   */
+  GEOS_HOST_DEVICE
+  void computeHalfWeights( localIndex iconn,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                           CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                           real64 ( &weight )[maxNumConnections][2],
+                           real64 ( &dWeight_dVar )[maxNumConnections][2] ) const;
+
   /**
    * @brief Compute weights and derivatives w.r.t to one variable without coefficient
    * Used in ReactiveCompositionalMultiphaseOBL solver for thermal transmissibility computation:
@@ -364,6 +379,70 @@ SurfaceElementStencilWrapper::
   }
 }
 
+GEOS_HOST_DEVICE
+inline void
+SurfaceElementStencilWrapper::
+  computeHalfWeights( localIndex iconn,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & coefficient,
+                      CoefficientAccessor< arrayView3d< real64 const > > const & dCoeff_dVar,
+                      real64 ( & weight )[maxNumConnections][2],
+                      real64 ( & dWeight_dVar )[maxNumConnections][2] ) const
+{
+
+  real64 sumOfTrans = 0.0;
+  for( localIndex k=0; k<numPointsInFlux( iconn ); ++k )
+  {
+    localIndex const er  =  m_elementRegionIndices[iconn][k];
+    localIndex const esr =  m_elementSubRegionIndices[iconn][k];
+    localIndex const ei  =  m_elementIndices[iconn][k];
+
+    sumOfTrans += coefficient[er][esr][ei][0][0] * m_weights[iconn][k];
+  }
+
+  localIndex k[2];
+  localIndex connectionIndex = 0;
+  for( k[0]=0; k[0]<numPointsInFlux( iconn ); ++k[0] )
+  {
+    for( k[1]=k[0]+1; k[1]<numPointsInFlux( iconn ); ++k[1] )
+    {
+      localIndex const er0  =  m_elementRegionIndices[iconn][k[0]];
+      localIndex const esr0 =  m_elementSubRegionIndices[iconn][k[0]];
+      localIndex const ei0  =  m_elementIndices[iconn][k[0]];
+
+      localIndex const er1  =  m_elementRegionIndices[iconn][k[1]];
+      localIndex const esr1 =  m_elementSubRegionIndices[iconn][k[1]];
+      localIndex const ei1  =  m_elementIndices[iconn][k[1]];
+
+      real64 const t0 = m_weights[iconn][0] * coefficient[er0][esr0][ei0][0][0]; // this is a bit insane to access perm
+      real64 const t1 = m_weights[iconn][1] * coefficient[er1][esr1][ei1][0][0];
+
+      real64 const harmonicWeight   = t0*t1 / sumOfTrans;
+      real64 const arithmeticWeight = 0.25 * (t0+t1);
+
+      real64 const value = m_meanPermCoefficient * harmonicWeight + (1 - m_meanPermCoefficient) * arithmeticWeight;
+
+      weight[connectionIndex][0] = value;
+      weight[connectionIndex][1] = -value;
+
+      real64 const dt0 = m_weights[iconn][k[0]] * dCoeff_dVar[er0][esr0][ei0][0][0];
+      real64 const dt1 = m_weights[iconn][k[1]] * dCoeff_dVar[er1][esr1][ei1][0][0];
+
+      real64 dHarmonic[2];
+      dHarmonic[0] = ( dt0 * t1 * sumOfTrans - dt0 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+      dHarmonic[1] = ( t0 * dt1 * sumOfTrans - dt1 * t0 * t1 ) / ( sumOfTrans * sumOfTrans );
+
+      real64 dArithmetic[2];
+      dArithmetic[0] = 0.25 * dt0;
+      dArithmetic[1] = 0.25 * dt1;
+
+      dWeight_dVar[connectionIndex][0] = m_meanPermCoefficient * dHarmonic[0] + (1 - m_meanPermCoefficient) * dArithmetic[0];
+      dWeight_dVar[connectionIndex][1] = -( m_meanPermCoefficient * dHarmonic[1] + (1 - m_meanPermCoefficient) * dArithmetic[1] );
+
+      connectionIndex++;
+    }
+  }
+}
+
 GEOS_HOST_DEVICE
 inline void
 SurfaceElementStencilWrapper::
diff --git a/src/coreComponents/integrationTests/constitutiveTests/CMakeLists.txt b/src/coreComponents/integrationTests/constitutiveTests/CMakeLists.txt
index bbb94f47a59..7d2b4fc2fc8 100644
--- a/src/coreComponents/integrationTests/constitutiveTests/CMakeLists.txt
+++ b/src/coreComponents/integrationTests/constitutiveTests/CMakeLists.txt
@@ -1,6 +1,16 @@
 # Specify list of tests
 set( gtest_geosx_tests
-     testRelPermHysteresis.cpp )
+     # testCapillaryPressure.cpp
+     # testCO2BrinePVTModels.cpp
+     # testCO2SpycherPruessModels.cpp
+     # testDamage.cpp
+     # testMultiFluidCO2Brine.cpp
+     # testMultiFluidCompositionalMultiphase.cpp
+     # testMultiFluidDeadOil.cpp
+     # testMultiFluidLiveOil.cpp
+     # testRelPerm.cpp
+     testRelPermHysteresis.cpp
+   )
 
 set( gtest_triaxial_xmls
      testTriaxial_druckerPragerExtended.xml
diff --git a/src/coreComponents/integrationTests/constitutiveTests/testRelPermHysteresis.cpp b/src/coreComponents/integrationTests/constitutiveTests/testRelPermHysteresis.cpp
index aec4f323c85..8c5686c3fc3 100644
--- a/src/coreComponents/integrationTests/constitutiveTests/testRelPermHysteresis.cpp
+++ b/src/coreComponents/integrationTests/constitutiveTests/testRelPermHysteresis.cpp
@@ -44,49 +44,46 @@ TableRelativePermeabilityHysteresis & makeTableRelPermHysteresisTwoPhase( string
   array1d< real64_array > coordinates_dw;
 // Swc = 0.22
 // consistent with Swmaxd = 1-Sgcrd = 1-0 = 1
-  geos::testing::fillArray( coordinates_dw,
-                            {.22, .25, .3, .35, .4, .45, .5, .55, .6, .65, .66, .68, .72, .82, .91, 1.} );
+  geosx::testing::fill_array( coordinates_dw, {.22, .25, .3, .35, .4, .45, .5, .55, .6, .65, .66, .68, .72, .82, .91, 1.} );
 
   array1d< real64_array > coordinates_iw;
 // Swc = 0.22
 // consistent with Swmaxi = 1-Sgcri = 1-0.3 = 0.7
-  geos::testing::fillArray( coordinates_iw, {.22, .25, .3, .35, .4, .45, .5, .55, .6, .65, .66, .7} );
+  geosx::testing::fill_array( coordinates_iw, {.22, .25, .3, .35, .4, .45, .5, .55, .6, .65, .66, .7} );
 
   // Gas phase saturation, fifth column of Table 2
   array1d< real64_array > coordinates_dg;
   // Sgcrd = 0.0
   // consistent with Swc = 0.22
-  geos::testing::fillArray( coordinates_dg,
-                            {0.000, 0.010, 0.030, 0.050, 0.100, 0.150, 0.200, 0.250, 0.300, 0.350, 0.400, 0.450,
-                             0.500,
-                             0.550, 0.600, 0.650, 0.700, 0.750, 0.780} );
+  geosx::testing::fill_array( coordinates_dg,
+                              {0.000, 0.010, 0.030, 0.050, 0.100, 0.150, 0.200, 0.250, 0.300, 0.350, 0.400, 0.450, 0.500,
+                               0.550, 0.600, 0.650, 0.700, 0.750, 0.780} );
 
   array1d< real64_array > coordinates_ig;
   // Sgcri = 0.30;
   // consistent with Swc = 0.22
-  geos::testing::fillArray( coordinates_ig,
-                            {0.300, 0.350, 0.400, 0.450, 0.500, 0.550, 0.600, 0.650, 0.700, 0.750, 0.78} );
+  geosx::testing::fill_array( coordinates_ig, {0.300, 0.350, 0.400, 0.450, 0.500, 0.550, 0.600, 0.650, 0.700, 0.750, 0.78} );
 
 
   // then define the bounding drainage and imbibibition relative permeability
 
   // Water phase drainage relperm
   real64_array drainageValues_w;
-  geos::testing::fillArray( drainageValues_w, {0.00000, 0.00100, 0.00300, 0.01000, 0.01800, 0.03500, 0.04000, 0.05700,
-                                               0.08800, 0.14500, 0.16000, 0.19000, 0.26300, 0.45500, 0.69200, 1.} );
+  geosx::testing::fill_array( drainageValues_w, {0.00000, 0.00100, 0.00300, 0.01000, 0.01800, 0.03500, 0.04000, 0.05700,
+                                                 0.08800, 0.14500, 0.16000, 0.19000, 0.26300, 0.45500, 0.69200, 1.} );
   // Gas phase drainage relperm, seventh column of Table 2
   real64_array drainageValues_g;
-  geos::testing::fillArray( drainageValues_g, {0.00000, 0.00200, 0.00700, 0.01000, 0.02000, 0.04000, 0.07500,
-                                               0.12700, 0.18000, 0.24000, 0.31000, 0.37300, 0.46000, 0.55000,
-                                               0.64000, 0.73000, 0.82500, 0.92000, 1.00000} );
+  geosx::testing::fill_array( drainageValues_g, {0.00000, 0.00200, 0.00700, 0.01000, 0.02000, 0.04000, 0.07500,
+                                                 0.12700, 0.18000, 0.24000, 0.31000, 0.37300, 0.46000, 0.55000,
+                                                 0.64000, 0.73000, 0.82500, 0.92000, 1.00000} );
 
   real64_array imbibitionValues_w;
-  geos::testing::fillArray( imbibitionValues_w, {0, 0.0156, 0.0680, 0.1409, 0.2296, 0.3317, 0.4455, 0.5700,
-                                                 0.7044, 0.8479, 0.8776, 0.9382} );
+  geosx::testing::fill_array( imbibitionValues_w, {0, 0.0156, 0.0680, 0.1409, 0.2296, 0.3317, 0.4455, 0.5700,
+                                                   0.7044, 0.8479, 0.8776, 0.9382} );
 
   real64_array imbibitionValues_g;
-  geos::testing::fillArray( imbibitionValues_g, {0.0000, 0.03361965, 0.09509072, 0.17469281, 0.26895718,
-                                                 0.37587908, 0.49410588, 0.62264458, 0.76072577, 0.90773047, 1.} );
+  geosx::testing::fill_array( imbibitionValues_g, {0.0000, 0.03361965, 0.09509072, 0.17469281, 0.26895718,
+                                                   0.37587908, 0.49410588, 0.62264458, 0.76072577, 0.90773047, 1.} );
 
   initializeTable( "drainageWater_swg",
                    coordinates_dw,
diff --git a/src/coreComponents/integrationTests/fluidFlowTests/CMakeLists.txt b/src/coreComponents/integrationTests/fluidFlowTests/CMakeLists.txt
index 951cac7c502..9a89d938e2e 100644
--- a/src/coreComponents/integrationTests/fluidFlowTests/CMakeLists.txt
+++ b/src/coreComponents/integrationTests/fluidFlowTests/CMakeLists.txt
@@ -4,6 +4,7 @@ set( gtest_geosx_tests
      testThermalSinglePhaseFlow.cpp
      testTransmissibility.cpp
      testImmiscibleMultiphaseFlow.cpp
+     testImmiscibleInterfaceConditions.cpp
      testSinglePhaseMFDPolyhedral.cpp
      testSinglePhaseReactiveTransport.cpp )
 
diff --git a/src/coreComponents/integrationTests/fluidFlowTests/testImmiscibleInterfaceConditions.cpp b/src/coreComponents/integrationTests/fluidFlowTests/testImmiscibleInterfaceConditions.cpp
new file mode 100644
index 00000000000..b1816d04204
--- /dev/null
+++ b/src/coreComponents/integrationTests/fluidFlowTests/testImmiscibleInterfaceConditions.cpp
@@ -0,0 +1,764 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 TotalEnergies
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+#define phase0MinSat1 0.0
+#define phase1MinSat1 0.0
+#define phase0MinSat2 0.0
+#define phase1MinSat2 0.0
+
+
+#include <chrono>
+#include <iostream>
+
+#include "mainInterface/initialization.hpp"
+#include "mainInterface/GeosxState.hpp"
+#include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
+#include "physicsSolvers/PhysicsSolverManager.hpp"
+#include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp"
+#include "integrationTests/fluidFlowTests/testCompFlowUtils.hpp"
+#include "constitutive/unitTests/FluidModelTest.hpp"
+#include "constitutive/unitTests/FluidModelTest_impl.hpp"
+#include "common/initializeEnvironment.hpp"
+#include "constitutive/relativePermeability/unitTests/constitutiveTestHelpers.hpp"
+#include "functions/FunctionManager.hpp"
+#include "constitutive/capillaryPressure/CapillaryPressureFields.hpp"
+
+#include <conduit.hpp>
+
+
+
+using namespace geos;
+using namespace geos::dataRepository;
+using namespace geos::constitutive;
+using namespace geos::testing;
+
+CommandLineOptions g_commandLineOptions;
+
+TwoPhaseImmiscibleFluid * makeTwoPhaseImmiscibleFluid( TwoPhaseImmiscibleFluid & fluid )
+{
+  
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  // 1D table with linear interpolation
+  localIndex constexpr Naxis = 6;
+  localIndex constexpr NaxisSingle = 1;
+
+  real64_array densityCoordPhase0;
+  // fill( densityCoordPhase0, Feed< Naxis >{ 0.22, 0.3, 0.5, 0.6, 0.8, 1.0 } );
+  for (auto v : {0.0})
+    densityCoordPhase0.emplace_back(v);
+  real64_array densityValuesPhase0;
+  // fill( densityValuesPhase0, Feed< Naxis >{ 0.00603, 0.04224, 0.04224, 0.22423, 0.31311, 0.40203 } );
+  for (auto v : {1000.0})
+  densityValuesPhase0.emplace_back(v);
+
+  real64_array densityCoordPhase1;
+  // fill( densityCoordPhase1, Feed< Naxis >{ 1.22, 1.3, 1.5, 1.6, 1.8, 2.0 } );
+  for (auto v : {0.0})
+    densityCoordPhase1.emplace_back(v);
+  real64_array densityValuesPhase1;
+  // fill( densityValuesPhase1, Feed< Naxis >{ 0.00603, 0.04224, 0.04224, 0.22423, 0.31311, 0.40203 } );
+  for (auto v : {100.0})
+  densityValuesPhase1.emplace_back(v);
+
+  real64_array viscosityCoordPhase0;
+  // fill( viscosityCoordPhase0, Feed< Naxis >{ 0.22, 0.3, 0.5, 0.6, 0.8, 1.0 } );
+  for (auto v : {0.0})
+  viscosityCoordPhase0.emplace_back(v);
+  real64_array viscosityValuesPhase0;
+  // fill( viscosityValuesPhase0, Feed< Naxis >{ 40203, 31311, 22423, 15011, 4224, 603 } );
+  for (auto v : {0.001})
+  viscosityValuesPhase0.emplace_back(v);
+
+  real64_array viscosityCoordPhase1;
+  // fill( viscosityCoordPhase1, Feed< NaxisSingle >{ 0.22 } );
+  for (auto v : {0.0})
+  viscosityCoordPhase1.emplace_back(v);
+
+  real64_array viscosityValuesPhase1;
+  // fill( viscosityValuesPhase1, Feed< NaxisSingle >{ 45 } );
+  for (auto v : {0.001})
+  viscosityValuesPhase1.emplace_back(v);
+
+  TableFunction & table_density0 = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "densityTablePhase0" ) );
+  array1d<real64_array> coords_density0;
+  coords_density0.emplace_back(densityCoordPhase0);
+  table_density0.setTableCoordinates( coords_density0, { units::Dimensionless } );
+  table_density0.setTableValues( densityValuesPhase0, units::Dimensionless );
+  table_density0.reInitializeFunction();
+
+  table_density0.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  TableFunction & table_density1 = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "densityTablePhase1" ) );
+  array1d<real64_array> coords_density1;
+  coords_density1.emplace_back(densityCoordPhase1);
+  table_density1.setTableCoordinates( coords_density1, { units::Dimensionless } );
+  table_density1.setTableValues( densityValuesPhase1, units::Dimensionless );
+  table_density1.reInitializeFunction();
+
+  table_density1.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  TableFunction & table_viscosity0 = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "viscosityTablePhase0" ) );
+  array1d<real64_array> coords_viscosity0;
+  coords_viscosity0.emplace_back(viscosityCoordPhase0);
+  table_viscosity0.setTableCoordinates( coords_viscosity0, { units::Dimensionless } );
+  table_viscosity0.setTableValues( viscosityValuesPhase0, units::Dimensionless );
+  table_viscosity0.reInitializeFunction();
+
+  table_viscosity0.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  TableFunction & table_viscosity1 = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "viscosityTablePhase1" ) );
+  array1d<real64_array> coords_viscosity1;
+  coords_viscosity1.emplace_back(viscosityCoordPhase1);
+  table_viscosity1.setTableCoordinates( coords_viscosity1, { units::Dimensionless } );
+  table_viscosity1.setTableValues( viscosityValuesPhase1, units::Dimensionless );
+  table_viscosity1.reInitializeFunction();
+
+  table_viscosity1.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+
+  // createTable( "densityTablePhase0", densityCoordPhase0, densityValuesPhase0 );
+  // createTable( "densityTablePhase1", densityCoordPhase1, densityValuesPhase1 );
+  // createTable( "viscosityTablePhase0", viscosityCoordPhase0, viscosityValuesPhase0 );
+  // createTable( "viscosityTablePhase1", viscosityCoordPhase1, viscosityValuesPhase1 );
+
+  // 2) Set up the constitutive model
+
+  string_array & phaseNames = fluid.getReference< string_array >( TwoPhaseImmiscibleFluid::viewKeyStruct::phaseNamesString() );
+  phaseNames.emplace_back( "water" );
+  phaseNames.emplace_back( "gas" );
+
+  string_array & densityTableNames = fluid.getReference< string_array >( TwoPhaseImmiscibleFluid::viewKeyStruct::densityTableNamesString() );
+  densityTableNames.emplace_back( "densityTablePhase0" );
+  densityTableNames.emplace_back( "densityTablePhase1" );
+
+  string_array & viscosityTableNames = fluid.getReference< string_array >( TwoPhaseImmiscibleFluid::viewKeyStruct::viscosityTableNamesString() );
+  viscosityTableNames.emplace_back( "viscosityTablePhase0" );
+  viscosityTableNames.emplace_back( "viscosityTablePhase1" );
+
+  fluid.postInputInitializationRecursive();
+  fluid.initialize(); // to test all the checks
+
+  return &fluid;
+}
+
+CapillaryPressureBase & makeJFunctionCapPressureTwoPhase( string const & name, Group & parent )
+{
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  // 1) First, define the tables
+
+  // // 1D table, various interpolation methods
+  // localIndex const Naxis = 12;
+
+  // // Setup table
+  // array1d< real64_array > coordinates;
+  // coordinates.resize( 1 );
+  // coordinates[0].resize( Naxis );
+
+  // coordinates[0][0] = 0.0;
+  // coordinates[0][1] = 0.05;
+  // coordinates[0][2] = 0.15;
+  // coordinates[0][3] = 0.25;
+  // coordinates[0][4] = 0.35;
+  // coordinates[0][5] = 0.45;
+  // coordinates[0][6] = 0.55;
+  // coordinates[0][7] = 0.65;
+  // coordinates[0][8] = 0.75;
+  // coordinates[0][9] = 0.85;
+  // coordinates[0][10] = 0.95;
+  // coordinates[0][11] = 1.0;
+
+  // real64_array values( Naxis );
+  // values[0] = 4.331729359;
+  // values[1] = 3.523266264;
+  // values[2] = 2.677103439;
+  // values[3] = 2.356150157;
+  // values[4] = 2.166062360;
+  // values[5] = 2.034158727;
+  // values[6] = 1.934627222;
+  // values[7] = 1.855494313;
+  // values[8] = 1.790286970;
+  // values[9] = 1.735134860;
+  // values[10] = 1.687551617;
+  // values[11] = 1.666049754;
+
+
+  localIndex const Naxis = 2;
+
+  // Setup table
+  array1d< real64_array > coordinates;
+  coordinates.resize( 1 );
+  coordinates[0].resize( Naxis );
+
+  coordinates[0][0] = 0.0;
+  coordinates[0][1] = 1.0;
+
+  real64_array values( Naxis );
+  values[0] = 4.331729359;
+  values[1] = 1.666049754;
+
+
+  TableFunction & table_w = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "water_jFunction" ) );
+  table_w.setTableCoordinates( coordinates, { units::Dimensionless } );
+  table_w.setTableValues( values, units::Dimensionless );
+  table_w.reInitializeFunction();
+
+  table_w.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  // 2) Then set up the constitutive model
+
+  JFunctionCapillaryPressure & capPressure = parent.registerGroup< JFunctionCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  auto & waterTableName = capPressure.getReference< string >( JFunctionCapillaryPressure::viewKeyStruct::wettingNonWettingJFuncTableNameString() );
+  waterTableName = "water_jFunction";
+
+  auto & surfaceTension = capPressure.getReference< real64 >( JFunctionCapillaryPressure::viewKeyStruct::wettingNonWettingSurfaceTensionString() );
+  //surfaceTension = 23.86955676433857e-3;
+  surfaceTension = 0.02;
+
+  auto & permeabilityDirection =
+    capPressure.getReference< JFunctionCapillaryPressure::PermeabilityDirection >( JFunctionCapillaryPressure::viewKeyStruct::permeabilityDirectionString() );
+  permeabilityDirection = JFunctionCapillaryPressure::PermeabilityDirection::XY;
+
+  capPressure.postInputInitializationRecursive();
+  capPressure.initialize(); // to test all the checks
+
+  return capPressure;
+}
+
+CapillaryPressureBase & makeTableCapPressureTwoPhase1( string const & name, Group & parent )
+{
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  // 1) First, define the tables
+
+  // 1D table, various interpolation methods
+  localIndex Naxis = 12;
+
+  // Setup table
+  array1d< real64_array > coordinates;
+  coordinates.resize( 1 );
+  coordinates[0].resize( Naxis );
+  coordinates[0][0] = 0.0;
+  coordinates[0][1] = 0.05;
+  coordinates[0][2] = 0.15;
+  coordinates[0][3] = 0.25;
+  coordinates[0][4] = 0.35;
+  coordinates[0][5] = 0.45;
+  coordinates[0][6] = 0.55;
+  coordinates[0][7] = 0.65;
+  coordinates[0][8] = 0.75;
+  coordinates[0][9] = 0.85;
+  coordinates[0][10] = 0.95;
+  coordinates[0][11] = 1.0;
+
+  real64_array values( Naxis );
+  values[0] = 130000.0;
+  values[1] = 90572.79;
+  values[2] = 49307.11;
+  values[3] = 33654.85;
+  values[4] = 24384.64;
+  values[5] = 17951.96;
+  values[6] = 13098;
+  values[7] = 9238.84;
+  values[8] = 6058.81;
+  values[9] = 3369.14;
+  values[10] = 1048.6;
+  values[11] = 0.0;
+
+  // localIndex const Naxis = 2;
+
+  // // Setup table
+  // array1d< real64_array > coordinates;
+  // coordinates.resize( 1 );
+  // coordinates[0].resize( Naxis );
+
+  // coordinates[0][0] = 0.0;
+  // coordinates[0][1] = 1.0;
+
+  // real64_array values( Naxis );
+  // values[0] = 129999.999994362;
+  // values[1] = 50000.0000139914;
+
+
+  TableFunction & table_w = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "water_pc" ) );
+  table_w.setTableCoordinates( coordinates, { units::Dimensionless } );
+  table_w.setTableValues( values, units::Pressure );
+  table_w.reInitializeFunction();
+
+  table_w.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  // 2) Then set up the constitutive model
+
+  TableCapillaryPressure & capPressure = parent.registerGroup< TableCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  auto & waterTableName = capPressure.getReference< string >( TableCapillaryPressure::viewKeyStruct::wettingNonWettingCapPresTableNameString() );
+  waterTableName = "water_pc";
+
+  capPressure.postInputInitializationRecursive();
+  capPressure.initialize(); // to test all the checks
+  return capPressure;
+}
+
+CapillaryPressureBase & makeTableCapPressureTwoPhase2( string const & name, Group & parent )
+{
+  FunctionManager & functionManager = FunctionManager::getInstance();
+
+  // 1) First, define the tables
+
+  // 1D table, various interpolation methods
+  localIndex Naxis = 12;
+
+  // Setup table
+  array1d< real64_array > coordinates;
+  coordinates.resize( 1 );
+  coordinates[0].resize( Naxis );
+  coordinates[0][0] = 0.0;
+  coordinates[0][1] = 0.05;
+  coordinates[0][2] = 0.15;
+  coordinates[0][3] = 0.25;
+  coordinates[0][4] = 0.35;
+  coordinates[0][5] = 0.45;
+  coordinates[0][6] = 0.55;
+  coordinates[0][7] = 0.65;
+  coordinates[0][8] = 0.75;
+  coordinates[0][9] = 0.85;
+  coordinates[0][10] = 0.95;
+  coordinates[0][11] = 1.0;
+
+  real64_array values( Naxis );
+  values[0] = 195000.0;
+  values[1] = 135859.25;
+  values[2] = 73960.67;
+  values[3] = 50482.28;
+  values[4] = 36576.96;
+  values[5] = 26927.94;
+  values[6] = 19647;
+  values[7] = 13858.26;
+  values[8] = 9088.2;
+  values[9] = 5053.72;
+  values[10] = 1572.9;
+  values[11] = 0.0;
+
+  // localIndex const Naxis = 2;
+
+  // // Setup table
+  // array1d< real64_array > coordinates;
+  // coordinates.resize( 1 );
+  // coordinates[0].resize( Naxis );
+
+  // coordinates[0][0] = 0.0;
+  // coordinates[0][1] = 1.0;
+
+  // real64_array values( Naxis );
+  // values[0] = 129999.999994362;
+  // values[1] = 50000.0000139914;
+
+
+  TableFunction & table_w = dynamicCast< TableFunction & >( *functionManager.createChild( "TableFunction", "water_pc" ) );
+  table_w.setTableCoordinates( coordinates, { units::Dimensionless } );
+  table_w.setTableValues( values, units::Pressure );
+  table_w.reInitializeFunction();
+
+  table_w.setInterpolationMethod( TableFunction::InterpolationType::Linear );
+
+  // 2) Then set up the constitutive model
+
+  TableCapillaryPressure & capPressure = parent.registerGroup< TableCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  auto & waterTableName = capPressure.getReference< string >( TableCapillaryPressure::viewKeyStruct::wettingNonWettingCapPresTableNameString() );
+  waterTableName = "water_pc";
+
+  capPressure.postInputInitializationRecursive();
+  capPressure.initialize(); // to test all the checks
+  return capPressure;
+}
+
+CapillaryPressureBase & makeBrooksCoreyCapPressureTwoPhase1( string const & name, Group & parent )
+{
+  BrooksCoreyCapillaryPressure & capPressure = parent.registerGroup< BrooksCoreyCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  array1d< real64 > & phaseMinSat = capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseMinVolumeFractionString() );
+  phaseMinSat.resize( 2 );
+  phaseMinSat[0] = phase0MinSat1; phaseMinSat[1] = phase1MinSat1;
+
+  array1d< real64 > & phaseCapPressureExpInv =
+    capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseCapPressureExponentInvString() );
+  phaseCapPressureExpInv.resize( 2 );
+  phaseCapPressureExpInv[0] = 4; phaseCapPressureExpInv[1] = 1;
+
+  array1d< real64 > & phaseEntryPressure = capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseEntryPressureString() );
+  phaseEntryPressure.resize( 2 );
+  phaseEntryPressure[0] = 4.0e3; phaseEntryPressure[1] = 0;
+
+  real64 & capPressureEpsilon = capPressure.getReference< real64 >( BrooksCoreyCapillaryPressure::viewKeyStruct::capPressureEpsilonString() );
+  capPressureEpsilon = 1.0e-8;
+
+  capPressure.postInputInitializationRecursive();
+  return capPressure;
+}
+
+CapillaryPressureBase & makeBrooksCoreyCapPressureTwoPhase2( string const & name, Group & parent )
+{
+  BrooksCoreyCapillaryPressure & capPressure = parent.registerGroup< BrooksCoreyCapillaryPressure >( name );
+
+  string_array & phaseNames = capPressure.getReference< string_array >( CapillaryPressureBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  array1d< real64 > & phaseMinSat = capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseMinVolumeFractionString() );
+  phaseMinSat.resize( 2 );
+  phaseMinSat[0] = phase0MinSat2; phaseMinSat[1] = phase1MinSat2;
+
+  array1d< real64 > & phaseCapPressureExpInv =
+    capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseCapPressureExponentInvString() );
+  phaseCapPressureExpInv.resize( 2 );
+  phaseCapPressureExpInv[0] = 4; phaseCapPressureExpInv[1] = 1;
+
+  array1d< real64 > & phaseEntryPressure = capPressure.getReference< array1d< real64 > >( BrooksCoreyCapillaryPressure::viewKeyStruct::phaseEntryPressureString() );
+  phaseEntryPressure.resize( 2 );
+  phaseEntryPressure[0] = 2.0e3; phaseEntryPressure[1] = 0;
+
+  real64 & capPressureEpsilon = capPressure.getReference< real64 >( BrooksCoreyCapillaryPressure::viewKeyStruct::capPressureEpsilonString() );
+  capPressureEpsilon = 1e-8;
+
+  capPressure.postInputInitializationRecursive();
+  return capPressure;
+}
+
+RelativePermeabilityBase & makeBrooksCoreyRelPerm( string const & name, Group & parent )
+{
+  BrooksCoreyRelativePermeability & relPerm = parent.registerGroup< BrooksCoreyRelativePermeability >( name );
+
+  string_array & phaseNames = relPerm.getReference< string_array >( RelativePermeabilityBase::viewKeyStruct::phaseNamesString() );
+  phaseNames.resize( 2 );
+  phaseNames[0] = "water"; phaseNames[1] = "gas";
+
+  array1d< real64 > & phaseMinSat = relPerm.getReference< array1d< real64 > >( BrooksCoreyRelativePermeability::viewKeyStruct::phaseMinVolumeFractionString() );
+  phaseMinSat.resize( 2 );
+  phaseMinSat[0] = phase0MinSat1; phaseMinSat[1] = phase1MinSat1;
+
+  array1d< real64 > & phaseRelPermExp = relPerm.getReference< array1d< real64 > >( BrooksCoreyRelativePermeability::viewKeyStruct::phaseRelPermExponentString() );
+  phaseRelPermExp.resize( 2 );
+  phaseRelPermExp[0] = 2.0; phaseRelPermExp[1] = 2.0;
+
+  array1d< real64 > & phaseRelPermMaxVal = relPerm.getReference< array1d< real64 > >( BrooksCoreyRelativePermeability::viewKeyStruct::phaseRelPermMaxValueString() );
+  phaseRelPermMaxVal.resize( 2 );
+  phaseRelPermMaxVal[0] = 1.0; phaseRelPermMaxVal[1] = 1.0;
+
+  relPerm.postInputInitializationRecursive();
+  return relPerm;
+}
+
+class ImmiscibleInterfaceConditionsTest : public FluidModelTest< TwoPhaseImmiscibleFluid, 2 >
+{
+public:
+  ImmiscibleInterfaceConditionsTest(): state( std::make_unique< CommandLineOptions >( g_commandLineOptions )), 
+  m_parent( "TestParentGroup", m_node )
+
+  {}
+
+protected:
+
+  static real64 constexpr time = 0.0;
+  static real64 constexpr dt = 1e4;
+  static real64 constexpr eps = std::numeric_limits< real64 >::epsilon();
+
+  GeosxState state;
+  ImmiscibleMultiphaseFlow *solver;
+  conduit::Node m_node;
+  dataRepository::Group m_parent;
+};
+
+real64 constexpr ImmiscibleInterfaceConditionsTest::time;
+real64 constexpr ImmiscibleInterfaceConditionsTest::dt;
+real64 constexpr ImmiscibleInterfaceConditionsTest::eps;
+
+
+
+TEST_F( ImmiscibleInterfaceConditionsTest, LocalNonlinearSolverConvergence )
+{
+
+  // using Base = FluidModelTest< TwoPhaseImmiscibleFluid, 2 >;
+  createFluid( "fluid", [this]( TwoPhaseImmiscibleFluid & fluid ){
+    makeTwoPhaseImmiscibleFluid( fluid );
+ 
+  // getting constitutive models:
+    RelativePermeabilityBase & relPerm = makeBrooksCoreyRelPerm( "relPerm" , this->m_parent);
+    RelativePermeabilityBase * relPermPtr = &relPerm;
+    // CapillaryPressureBase & capPressure0 =  makeJFunctionCapPressureTwoPhase( "capPressure0", this->m_parent );
+    // CapillaryPressureBase * capPressurePtr0 = &capPressure0;
+
+    CapillaryPressureBase & capPressure0 =  makeTableCapPressureTwoPhase1( "capPressure0", this->m_parent );
+    CapillaryPressureBase * capPressurePtr0 = &capPressure0;
+
+    CapillaryPressureBase & capPressure1 =  makeTableCapPressureTwoPhase2( "capPressure1", this->m_parent );
+    CapillaryPressureBase * capPressurePtr1 = &capPressure1;
+    // CapillaryPressureBase & capPressure0 =  makeBrooksCoreyCapPressureTwoPhase1( "capPressure0", this->m_parent );
+    // CapillaryPressureBase * capPressurePtr0 = &capPressure0;
+
+    // CapillaryPressureBase & capPressure1 =  makeBrooksCoreyCapPressureTwoPhase2( "capPressure1", this->m_parent );
+    // CapillaryPressureBase * capPressurePtr1 = &capPressure1;
+    
+  std::vector< RelativePermeabilityBase * > relPerms = {relPermPtr, relPermPtr};
+  std::vector< CapillaryPressureBase * > capPressures = {capPressurePtr0, capPressurePtr1};
+  std::vector< TwoPhaseImmiscibleFluid * > fluids = { &fluid, &fluid };
+    // real64 uT = 3.2864545889999906e-05;
+  
+   real64 uT = 3.3e-2;
+// real64 uT = 1e-7;
+  stdVector< real64 > saturations = {0.2, 0.4};
+  stdVector< real64 > trappedSats1 = {phase0MinSat1, phase1MinSat1};
+  stdVector< real64 > trappedSats2 = {phase0MinSat2, phase1MinSat2};
+  stdVector< real64 > pressures = {1e7, 1e7};
+  stdVector< real64 > JFMultipliers = {45016.662822296035, 30011.108548197357};
+  stdVector< fields::cappres::ModeIndexType > modes = {static_cast<fields::cappres::ModeIndexType>(0), static_cast<fields::cappres::ModeIndexType>(0)};
+  stdVector< real64 > transHats = {1.9738466000000002e-12, 4.4411548500000007e-12};
+  stdVector< real64 > dTransHats_dP = {0.0, 0.0};
+  stdVector< real64 > gravCoefHats = {490.5, 490.5};
+  stdVector< real64 > gravCoefs = {465.97500000000002, 515.02499999999998};
+  stdVector< real64 > cellCenterDuT = {0.0, 0.0, 0.0, 0.0}; // duT_dP[0], duT_dP[1], duT_dS[0], duT_dS[1]
+  stdVector< real64 > cellCenterDens = {1000.0, 800.0}; // density for each phase
+  stdVector< real64 > cellCenterDens_dP = {0.0, 0.0, 0.0, 0.0}; // dDens_dP[0][0], dDens_dP[0][1], dDens_dP[1][0], dDens_dP[1][1]
+  stdVector< real64 > phaseMaxHistVolFrac1 = {0.0, 0.0};
+  stdVector< real64 > phaseMinHistVolFrac1 = {0.0, 0.0};
+  stdVector< real64 > phaseMaxHistVolFrac2 = {0.0, 0.0};
+  stdVector< real64 > phaseMinHistVolFrac2 = {0.0, 0.0};
+
+  stdVector< real64 > phi = {0.0, 0.0};
+  stdVector< real64 > grad_phi_P = {0.0, 0.0, 0.0, 0.0};
+  stdVector< real64 > grad_phi_S = {0.0, 0.0, 0.0, 0.0};
+  bool converged = false;
+
+  std::ofstream outFile( "local_solver_results.csv" );
+
+
+          // Write data to the file
+          outFile << "Si";
+          outFile << ",";
+          outFile << "Sj";
+          outFile << ",";
+          outFile << "Fw_alpha";
+          outFile << ",";
+          outFile << "Fn_alpha";
+          outFile << ",";
+          outFile << "Residual_initial";
+          outFile << ",";
+          outFile << "Pc_int";
+          outFile << ",";
+          outFile << "Residual";
+          outFile << ",";
+          outFile << "newton";
+          outFile << std::endl;
+
+          real64 const start_sat = 0.0;
+          real64 const end_sat   = 1.0;
+          real64 const dS        = 1e-2;
+              // real64 Si = 0.0;
+              //  real64 Sj = 0.9;
+          
+          for( real64 Si = start_sat; Si <= end_sat + 1e-8; Si += dS )
+          {
+            for( real64 Sj = start_sat; Sj <= end_sat + 1e-8; Sj += dS )
+            {
+              saturations[0] = Si;
+              saturations[1] = Sj;
+
+              auto t0 = std::chrono::high_resolution_clock::now();
+
+// Call the GEOS local solver
+    geos::immiscibleMultiphaseKernels::local_solver( uT, saturations, pressures, JFMultipliers, trappedSats1, trappedSats2, modes, transHats, dTransHats_dP, gravCoefHats, gravCoefs,
+      cellCenterDuT, cellCenterDens, cellCenterDens_dP, relPerms, capPressures, fluids, phi, grad_phi_P, grad_phi_S, converged,
+      phaseMaxHistVolFrac1, phaseMinHistVolFrac1, phaseMaxHistVolFrac2, phaseMinHistVolFrac2 );
+
+auto t1 = std::chrono::high_resolution_clock::now();
+std::chrono::duration<double> elapsed = t1 - t0;
+// std::cout << "Local solver time: " << elapsed.count() << " s" << std::endl;
+EXPECT_TRUE( converged ) << "Local solver diverged for saturations Si=" << Si << ", Sj=" << Sj;
+
+                  // Write data to the file
+                  outFile << GEOS_FMT( "{:10.10e}", saturations[0] );
+                  outFile << GEOS_FMT( ",{:10.10e}", saturations[1] );
+                  outFile << GEOS_FMT( ",{:10.10e}", phi[0] );
+                  outFile << GEOS_FMT( ",{:10.10e}", phi[1] );
+                  outFile << GEOS_FMT( ",{:10.10e}", grad_phi_P[0] );
+                  outFile << GEOS_FMT( ",{:10.10e}", grad_phi_P[1] );
+                  outFile << GEOS_FMT( ",{:10.10e}", grad_phi_P[2] );
+                  outFile << GEOS_FMT( ",{:10.10e}", grad_phi_P[3] );
+                  outFile << std::endl;
+                  phi[0] = 0;
+                  phi[1] = 0;
+                  grad_phi_P[0] = 0;
+                  grad_phi_P[1] = 0;
+                  grad_phi_P[2] = 0;
+                  grad_phi_P[3] = 0;
+                  grad_phi_S[0] = 0;
+                  grad_phi_S[1] = 0;
+                  grad_phi_S[2] = 0;
+                  grad_phi_S[3] = 0;
+
+  }
+}
+
+  outFile.close();
+
+} );
+}
+
+TEST_F( ImmiscibleInterfaceConditionsTest, LocalSolverResults )
+{
+
+  // using Base = FluidModelTest< TwoPhaseImmiscibleFluid, 2 >;
+  createFluid( "fluid", [this]( TwoPhaseImmiscibleFluid & fluid ){
+    makeTwoPhaseImmiscibleFluid( fluid );
+ 
+  // getting constitutive models:
+    RelativePermeabilityBase & relPerm = makeBrooksCoreyRelPerm( "relPerm" , this->m_parent);
+    RelativePermeabilityBase * relPermPtr = &relPerm;
+
+    CapillaryPressureBase & capPressure0 =  makeBrooksCoreyCapPressureTwoPhase1( "capPressure0", this->m_parent );
+    CapillaryPressureBase * capPressurePtr0 = &capPressure0;
+
+    CapillaryPressureBase & capPressure1 =  makeBrooksCoreyCapPressureTwoPhase2( "capPressure1", this->m_parent );
+    CapillaryPressureBase * capPressurePtr1 = &capPressure1;
+    
+  std::vector< RelativePermeabilityBase * > relPerms = {relPermPtr, relPermPtr};
+  std::vector< CapillaryPressureBase * > capPressures = {capPressurePtr0, capPressurePtr1};
+  std::vector< TwoPhaseImmiscibleFluid * > fluids = { &fluid, &fluid };
+  
+   real64 uT = 0.000001889581158;
+
+  stdVector< real64 > saturations = {0.6, 0.3};
+  stdVector< real64 > trappedSats1 = {phase0MinSat1, phase1MinSat1};
+  stdVector< real64 > trappedSats2 = {phase0MinSat2, phase1MinSat2};
+  stdVector< real64 > pressures = {1e7, 1e7};
+  stdVector< real64 > JFMultipliers = {45016.662822296035, 30011.108548197357};
+  stdVector< fields::cappres::ModeIndexType > modes = {static_cast<fields::cappres::ModeIndexType>(0), static_cast<fields::cappres::ModeIndexType>(0)};
+  stdVector< real64 > transHats = {2.0e-12, 8.0e-12};
+  stdVector< real64 > dTransHats_dP = {0.0, 0.0};
+  stdVector< real64 > gravCoefHats = {49.05, 49.05};
+  stdVector< real64 > gravCoefs = {46.5975, 51.5025};
+  stdVector< real64 > cellCenterDuT = {8.32E-10, -8.32E-10, 0.0000063429744518, -0.0000012971521486}; // duT_dP[0], duT_dP[1], duT_dS[0], duT_dS[1]
+  stdVector< real64 > cellCenterDens = {1000.0, 100.0}; // density for each phase
+  stdVector< real64 > cellCenterDens_dP = {0.0, 0.0, 0.0, 0.0}; // dDens_dP[0][0], dDens_dP[0][1], dDens_dP[1][0], dDens_dP[1][1]
+  stdVector< real64 > phaseMaxHistVolFrac1 = {0.0, 0.0};
+  stdVector< real64 > phaseMinHistVolFrac1 = {0.0, 0.0};
+  stdVector< real64 > phaseMaxHistVolFrac2 = {0.0, 0.0};
+  stdVector< real64 > phaseMinHistVolFrac2 = {0.0, 0.0};
+
+  stdVector< real64 > phi = {0.0, 0.0};
+  stdVector< real64 > grad_phi_P = {0.0, 0.0, 0.0, 0.0};
+  stdVector< real64 > grad_phi_S = {0.0, 0.0, 0.0, 0.0};
+  bool converged = false;
+
+
+
+// Call the GEOS local solver
+    geos::immiscibleMultiphaseKernels::local_solver( uT, saturations, pressures, JFMultipliers, trappedSats1, trappedSats2, modes, transHats, dTransHats_dP, gravCoefHats, gravCoefs,
+      cellCenterDuT, cellCenterDens, cellCenterDens_dP, relPerms, capPressures, fluids, phi, grad_phi_P, grad_phi_S, converged,
+      phaseMaxHistVolFrac1, phaseMinHistVolFrac1, phaseMaxHistVolFrac2, phaseMinHistVolFrac2 );
+
+  real64 const tolerance_eps = std::sqrt( std::numeric_limits< real64 >::epsilon() );
+  real64 const tol = 1e-4;
+  real64 const abs_tolerance = tolerance_eps * tol;
+
+  EXPECT_NEAR( phi[0], 1.676451024635667e-03, abs_tolerance );
+  EXPECT_NEAR( phi[1], 2.131301333609180e-05, abs_tolerance );
+  EXPECT_NEAR( grad_phi_P[0], 5.760000000000000e-07, abs_tolerance );
+  EXPECT_NEAR( grad_phi_P[1], -5.760000000000000e-07, abs_tolerance );
+  EXPECT_NEAR( grad_phi_P[2], 2.560000000000001e-08, abs_tolerance );
+  EXPECT_NEAR( grad_phi_P[3], -2.560000000000001e-08, abs_tolerance );
+  EXPECT_NEAR( grad_phi_S[0], 7.268012258072125e-03, abs_tolerance );
+  EXPECT_NEAR( grad_phi_S[1], -8.980284105794445e-04, abs_tolerance );
+  EXPECT_NEAR( grad_phi_S[2], -9.250378062747074e-05, abs_tolerance );
+  EXPECT_NEAR( grad_phi_S[3], -3.991237380353088e-05, abs_tolerance );
+
+
+} );
+}
+
+
+
+int main( int argc, char * *argv )
+{
+  ::testing::InitGoogleTest( &argc, argv );
+  g_commandLineOptions = *geos::basicSetup( argc, argv );
+  int const result = RUN_ALL_TESTS();
+  geos::basicCleanup();
+  return result;
+}
+
+// maybe needed later on
+// TEST_F( CapillaryPressureTest, numericalDerivatives_jFunctionCapPressureTwoPhase )
+// {
+//   initialize( makeJFunctionCapPressureTwoPhase( "capPressure", m_parent ) );
+
+//   // here, we have to apply a special treatment to this test
+//   // to make sure that the J-function multiplier is initialized using initializeRockState
+//   // this requires calling allocateConstitutiveData in advance (it will be called again later, in the "test" function)
+
+//   // setup some values for porosity and permeability
+//   array2d< real64 > porosity;
+//   porosity.resize( 1, 1 );
+//   porosity[0][0] = 0.13496794266569806;
+//   array3d< real64 > permeability;
+//   permeability.resize( 1, 1, 3 );
+//   permeability[0][0][0] = 0.1722194e-15;
+//   permeability[0][0][1] = 0.3423156e-15;
+//   permeability[0][0][2] = 0.2324191e-15;
+
+//   // initialize the J-function multiplier (done on GPU if GPU is available)
+//   m_model->allocateConstitutiveData( m_parent, 1 );
+//   m_model->initializeRockState( porosity.toViewConst(), permeability.toViewConst() );
+
+//   // move the multiplier back to the CPU since the test is performed on the CPU
+//   auto & jFuncMultiplier =
+//     m_model->getReference< array2d< real64 > >( fields::cappres::jFuncMultiplier::key() );
+//   jFuncMultiplier.move( hostMemorySpace, false );
+
+//   // we are ready to proceed to the test
+
+//   real64 const eps = std::sqrt( std::numeric_limits< real64 >::epsilon() );
+//   real64 const tol = 1e-4;
+
+//   real64 const start_sat = 0.3;
+//   real64 const end_sat   = 0.9;
+//   real64 const dS        = 1e-1;
+//   array1d< real64 > sat( 2 );
+//   sat[0] = start_sat; sat[1] = 1-sat[0];
+//   while( sat[0] <= end_sat )
+//   {
+//     test( sat, eps, tol );
+//     sat[0] += dS;
+//     sat[1] = 1 - sat[0];
+//   }
+
+// }
\ No newline at end of file
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/CMakeLists.txt b/src/coreComponents/physicsSolvers/fluidFlow/CMakeLists.txt
index 6eb55e9775a..df14131a19a 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/CMakeLists.txt
+++ b/src/coreComponents/physicsSolvers/fluidFlow/CMakeLists.txt
@@ -29,8 +29,6 @@ set( fluidFlowSolvers_headers
      ImmiscibleMultiphaseFlow.hpp
      ImmiscibleMultiphaseFlowFields.hpp
      LogLevelsInfo.hpp
-     ReactiveCompositionalMultiphaseOBL.hpp
-     ReactiveCompositionalMultiphaseOBLFields.hpp
      SourceFluxStatistics.hpp
      SinglePhaseBase.hpp
      SinglePhaseBaseFields.hpp
@@ -65,18 +63,6 @@ set( fluidFlowSolvers_headers
      kernels/singlePhase/ThermalFluxComputeKernel.hpp
      kernels/singlePhase/proppant/ProppantBaseKernels.hpp
      kernels/singlePhase/proppant/ProppantFluxKernels.hpp
-     kernels/singlePhase/reactive/AccumulationKernels.hpp
-     kernels/singlePhase/reactive/DirichletFluxComputeKernel.hpp
-     kernels/singlePhase/reactive/FluidUpdateKernel.hpp
-     kernels/singlePhase/reactive/FluxComputeKernel.hpp
-     kernels/singlePhase/reactive/KernelLaunchSelectors.hpp
-     kernels/singlePhase/reactive/ReactionUpdateKernel.hpp
-     kernels/singlePhase/reactive/ResidualNormKernel.hpp
-     kernels/singlePhase/reactive/SourceFluxComputeKernel.hpp
-     kernels/singlePhase/reactive/ThermalAccumulationKernels.hpp
-     kernels/singlePhase/reactive/ThermalDirichletFluxComputeKernel.hpp
-     kernels/singlePhase/reactive/ThermalFluxComputeKernel.hpp
-     kernels/singlePhase/reactive/ThermalSourceFluxComputeKernel.hpp
      kernels/compositional/AccumulationKernel.hpp
      kernels/compositional/AquiferBCKernel.hpp
      kernels/compositional/PPUPhaseFlux.hpp
@@ -104,7 +90,6 @@ set( fluidFlowSolvers_headers
      kernels/compositional/PotGrad.hpp
      kernels/compositional/PPUPhaseFlux.hpp
      kernels/compositional/PropertyKernelBase.hpp
-     kernels/compositional/ReactiveCompositionalMultiphaseOBLKernels.hpp
      kernels/compositional/RelativePermeabilityUpdateKernel.hpp
      kernels/compositional/ResidualNormKernel.hpp
      kernels/compositional/SolidInternalEnergyUpdateKernel.hpp
@@ -145,14 +130,12 @@ set( fluidFlowSolvers_sources
      CompositionalMultiphaseStatistics.cpp
      CompositionalMultiphaseHybridFVM.cpp
      ImmiscibleMultiphaseFlow.cpp
-     ReactiveCompositionalMultiphaseOBL.cpp
      FlowSolverBase.cpp
      SinglePhaseBase.cpp
      SinglePhaseStatistics.cpp
      SinglePhaseFVM.cpp
      SinglePhaseHybridFVM.cpp
      SinglePhaseProppantBase.cpp
-     SinglePhaseReactiveTransport.cpp
      SourceFluxStatistics.cpp
      StencilDataCollection.cpp
      kernels/singlePhase/proppant/ProppantFluxKernels.cpp
@@ -174,8 +157,10 @@ file( READ "${CMAKE_CURRENT_LIST_DIR}/kernelSpecs.json" kernelSpecs )
 set( kernelTemplateFileList "" )
 
 # Keep only the templates that are unrelated to hybrid flux/dirichlet
+if( ENABLE_HPCREACT AND EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/../constitutive/HPCReact/CMakeLists.txt" )
 list( APPEND kernelTemplateFileList
       ReactiveCompositionalMultiphaseOBLKernels.cpp.template )
+endif()
 
 foreach( kernelTemplateFile ${kernelTemplateFileList} )
   get_filename_component( jsonKey ${kernelTemplateFile} NAME_WE )
@@ -188,6 +173,31 @@ foreach( kernelTemplateFile ${kernelTemplateFileList} )
   list(APPEND fluidFlowSolvers_sources ${sourceFiles})
 endforeach()
 
+# Conditionally add reactive transport files when HPCReact is available
+if( ENABLE_HPCREACT AND EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/../constitutive/HPCReact/CMakeLists.txt" )
+  list( APPEND fluidFlowSolvers_headers
+       ReactiveCompositionalMultiphaseOBL.hpp
+       ReactiveCompositionalMultiphaseOBLFields.hpp
+       kernels/singlePhase/reactive/AccumulationKernels.hpp
+       kernels/singlePhase/reactive/DirichletFluxComputeKernel.hpp
+       kernels/singlePhase/reactive/FluidUpdateKernel.hpp
+       kernels/singlePhase/reactive/FluxComputeKernel.hpp
+       kernels/singlePhase/reactive/KernelLaunchSelectors.hpp
+       kernels/singlePhase/reactive/ReactionUpdateKernel.hpp
+       kernels/singlePhase/reactive/ResidualNormKernel.hpp
+       kernels/singlePhase/reactive/SourceFluxComputeKernel.hpp
+       kernels/singlePhase/reactive/ThermalAccumulationKernels.hpp
+       kernels/singlePhase/reactive/ThermalDirichletFluxComputeKernel.hpp
+       kernels/singlePhase/reactive/ThermalFluxComputeKernel.hpp
+       kernels/singlePhase/reactive/ThermalSourceFluxComputeKernel.hpp
+       kernels/compositional/ReactiveCompositionalMultiphaseOBLKernels.hpp
+       SinglePhaseReactiveTransport.hpp )
+  
+  list( APPEND fluidFlowSolvers_sources
+       ReactiveCompositionalMultiphaseOBL.cpp
+       SinglePhaseReactiveTransport.cpp )
+endif()
+
 # TODO: The two kernels below have non-matching file names and JSON keys.
 #       Either fix them to follow pattern, or come up with another mechanism.
 
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/CompositionalMultiphaseBase.cpp b/src/coreComponents/physicsSolvers/fluidFlow/CompositionalMultiphaseBase.cpp
index ec8268e0079..d71740eb5fe 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/CompositionalMultiphaseBase.cpp
+++ b/src/coreComponents/physicsSolvers/fluidFlow/CompositionalMultiphaseBase.cpp
@@ -998,12 +998,24 @@ void CompositionalMultiphaseBase::initializeFluidState( MeshLevel & mesh,
     // We postpone the other constitutive models for now
 
     // Now, we initialize and update each constitutive model one by one
-
     // initialized phase volume fraction
     arrayView2d< real64 const, compflow::USD_PHASE > const phaseVolFrac =
-      subRegion.template getField< flow::phaseVolumeFraction >();
+      subRegion.template getField< fields::flow::phaseVolumeFraction >();
 
-    // Initialize/update the relative permeability model using the initial phase volume fraction
+    // 4.2 Save the computed porosity into the old porosity
+    //
+    // Note:
+    // - This must be called after updatePorosityAndPermeability
+    // - This step depends on porosity
+    string const & solidName = subRegion.template getReference< string >( viewKeyStruct::solidNamesString() );
+    CoupledSolidBase const & porousMaterial = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
+    porousMaterial.initializeState();
+
+    // 4.3 Initialize/update the relative permeability model using the initial phase volume fraction
+    //     This is needed to handle relative permeability hysteresis
+    //     Also, initialize the fluid model (to compute the initial total mass density, needed to compute the body force increment in
+    // coupled simulations)
+    //
     // Note:
     // - This must be called after updatePhaseVolumeFraction
     // - This step depends on phaseVolFraction
@@ -2858,6 +2870,7 @@ void CompositionalMultiphaseBase::implicitStepComplete( real64 const & time,
         CapillaryPressureBase const & capPressureMaterial =
           getConstitutiveModel< CapillaryPressureBase >( subRegion, capPressName );
         capPressureMaterial.saveConvergedRockState( porosity, permeability );
+        capPressureMaterial.saveConvergedPhaseVolFractionState(phaseVolFrac);
       }
 
       // Step 6: if the thermal option is on, send the converged porosity and phase volume fraction to the thermal conductivity model
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/CompositionalMultiphaseBase.hpp b/src/coreComponents/physicsSolvers/fluidFlow/CompositionalMultiphaseBase.hpp
index 227055bf3ed..a03fbf63a99 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/CompositionalMultiphaseBase.hpp
+++ b/src/coreComponents/physicsSolvers/fluidFlow/CompositionalMultiphaseBase.hpp
@@ -20,6 +20,11 @@
 #ifndef GEOS_PHYSICSSOLVERS_FLUIDFLOW_COMPOSITIONALMULTIPHASEBASE_HPP_
 #define GEOS_PHYSICSSOLVERS_FLUIDFLOW_COMPOSITIONALMULTIPHASEBASE_HPP_
 
+#include "common/DataLayouts.hpp"
+#include "constitutive/fluid/multifluid/Layouts.hpp"
+#include "constitutive/relativePermeability/Layouts.hpp"
+#include "constitutive/capillaryPressure/Layouts.hpp"
+#include "fieldSpecification/FieldSpecificationManager.hpp"
 #include "physicsSolvers/fluidFlow/FlowSolverBase.hpp"
 #include "common/DataLayouts.hpp"
 #include "constitutive/fluid/multifluid/Layouts.hpp"
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.cpp b/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.cpp
index a198a78cb17..5fc1155a274 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.cpp
+++ b/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.cpp
@@ -17,402 +17,585 @@
  * @file ImmiscibleMultiphaseFlow.cpp
  */
 
-#include "ImmiscibleMultiphaseFlow.hpp"
-
-#include "FlowSolverBaseFields.hpp"
-#include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlowFields.hpp"
-#include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
-#include "physicsSolvers/fluidFlow/CompositionalMultiphaseUtilities.hpp"
-#include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp"
-#include "physicsSolvers/fluidFlow/kernels/compositional/RelativePermeabilityUpdateKernel.hpp"
-#include "physicsSolvers/fluidFlow/kernels/compositional/CapillaryPressureUpdateKernel.hpp"
-#include "constitutive/capillaryPressure/CapillaryPressureSelector.hpp"
-#include "constitutive/relativePermeability/RelativePermeabilitySelector.hpp"
-
-#include "fieldSpecification/EquilibriumInitialCondition.hpp"
-#include "fieldSpecification/SourceFluxBoundaryCondition.hpp"
-#include "physicsSolvers/fluidFlow/SourceFluxStatistics.hpp"
-#include "physicsSolvers/LogLevelsInfo.hpp"
-
-#include "constitutive/ConstitutivePassThru.hpp"
-#include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
-
-#include <cmath>
-
-#if defined( __INTEL_COMPILER )
-#pragma GCC optimize "O0"
-#endif
-
-namespace geos
-{
-
-using namespace dataRepository;
-using namespace constitutive;
-using namespace fields::immiscibleMultiphaseFlow;
-using namespace immiscibleMultiphaseKernels;
-
-
-ImmiscibleMultiphaseFlow::ImmiscibleMultiphaseFlow( const string & name,
-                                                    Group * const parent )
-  :
-  FlowSolverBase( name, parent ),
-  m_numPhases( 2 ),
-  m_hasCapPressure( false ),
-  m_useTotalMassEquation ( 1 )
-{
-  this->registerWrapper( viewKeyStruct::inputTemperatureString(), &m_inputTemperature ).
-    setInputFlag( InputFlags::REQUIRED ).
-    setDescription( "Temperature" );
-
-  this->registerWrapper( viewKeyStruct::useTotalMassEquationString(), &m_useTotalMassEquation ).
-    setSizedFromParent( 0 ).
-    setInputFlag( InputFlags::OPTIONAL ).
-    setApplyDefaultValue( 1 ).
-    setDescription( "Flag indicating whether total mass equation is used" );
-
-  this->registerWrapper( viewKeyStruct::gravityDensitySchemeString(), &m_gravityDensityScheme ).
-    setSizedFromParent( 0 ).
-    setInputFlag( InputFlags::OPTIONAL ).
-    setApplyDefaultValue( GravityDensityScheme::ArithmeticAverage ).
-    setDescription( "Scheme for density treatment in gravity" );
-
-  this->registerWrapper( viewKeyStruct::solutionChangeScalingFactorString(), &m_solutionChangeScalingFactor ).
-    setSizedFromParent( 0 ).
-    setInputFlag( InputFlags::OPTIONAL ).
-    setApplyDefaultValue( 0.5 ).
-    setDescription( "Damping factor for solution change targets" );
-  this->registerWrapper( viewKeyStruct::targetRelativePresChangeString(), &m_targetRelativePresChange ).
-    setSizedFromParent( 0 ).
-    setInputFlag( InputFlags::OPTIONAL ).
-    setApplyDefaultValue( 0.2 ).
-    setDescription( "Target (relative) change in pressure in a time step (expected value between 0 and 1)" );
-  this->registerWrapper( viewKeyStruct::targetPhaseVolFracChangeString(), &m_targetPhaseVolFracChange ).
-    setSizedFromParent( 0 ).
-    setInputFlag( InputFlags::OPTIONAL ).
-    setApplyDefaultValue( 0.2 ).
-    setDescription( "Target (absolute) change in the phase volume fraction within a single time step." );
-}
-
-void ImmiscibleMultiphaseFlow::postInputInitialization()
-{
-  FlowSolverBase::postInputInitialization();
-}
-
-void ImmiscibleMultiphaseFlow::registerDataOnMesh( Group & meshBodies )
-{
-  FlowSolverBase::registerDataOnMesh( meshBodies );
-
-  // 0. Find a "reference" fluid model name (at this point, models are already attached to subregions)
-  forDiscretizationOnMeshTargets( meshBodies, [&]( string const &,
-                                                   MeshLevel & mesh,
-                                                   string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions( regionNames,
-                                                [&]( localIndex const,
-                                                     ElementSubRegionBase & subRegion )
-    {
-      // If at least one region has a capillary pressure model, consider it enabled for all
-      string const capPresName = getConstitutiveName< CapillaryPressureBase >( subRegion );
-      if( !capPresName.empty() )
-      {
-        m_hasCapPressure = true;
-      }
-    } );
-  } );
-
-  m_numDofPerCell = m_numPhases;
-
-  // 2. Register and resize all fields as necessary
-  forDiscretizationOnMeshTargets( meshBodies, [&]( string const &,
-                                                   MeshLevel & mesh,
-                                                   string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions( regionNames,
-                                                [&]( localIndex const,
-                                                     ElementSubRegionBase & subRegion )
-    {
-      if( m_hasCapPressure )
+ #include "ImmiscibleMultiphaseFlow.hpp"
+
+ #include "FlowSolverBaseFields.hpp"
+ #include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlowFields.hpp"
+ #include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
+ #include "physicsSolvers/fluidFlow/CompositionalMultiphaseUtilities.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/CapillaryPressureUpdateKernel.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/compositional/ThermalAccumulationKernel.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/compositional/RelativePermeabilityUpdateKernel.hpp"
+ #include "constitutive/ConstitutiveManager.hpp"
+ #include "constitutive/capillaryPressure/CapillaryPressureFields.hpp"
+ #include "constitutive/capillaryPressure/CapillaryPressureSelector.hpp"
+ #include "constitutive/relativePermeability/RelativePermeabilitySelector.hpp"
+ 
+ #include "fieldSpecification/EquilibriumInitialCondition.hpp"
+ #include "fieldSpecification/SourceFluxBoundaryCondition.hpp"
+ #include "physicsSolvers/fluidFlow/SourceFluxStatistics.hpp"
+ #include "physicsSolvers/LogLevelsInfo.hpp"
+ 
+ #include "constitutive/ConstitutivePassThru.hpp"
+ #include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
+ 
+ #include <cmath>
+ 
+ #if defined( __INTEL_COMPILER )
+ #pragma GCC optimize "O0"
+ #endif
+ 
+ namespace geos
+ {
+ 
+ using namespace dataRepository;
+ using namespace constitutive;
+ using namespace fields::immiscibleMultiphaseFlow;
+ using namespace immiscibleMultiphaseKernels;
+ 
+ 
+ ImmiscibleMultiphaseFlow::ImmiscibleMultiphaseFlow( const string & name,
+                                                     Group * const parent )
+   :
+   FlowSolverBase( name, parent ),
+   m_numPhases( 2 ),
+   m_hasCapPressure( false ),
+   m_useTotalMassEquation ( 1 )
+ {
+   this->registerWrapper( viewKeyStruct::inputTemperatureString(), &m_inputTemperature ).
+     setInputFlag( InputFlags::REQUIRED ).
+     setDescription( "Temperature" );
+ 
+   this->registerWrapper( viewKeyStruct::useTotalMassEquationString(), &m_useTotalMassEquation ).
+     setSizedFromParent( 0 ).
+     setInputFlag( InputFlags::OPTIONAL ).
+     setApplyDefaultValue( 1 ).
+     setDescription( "Flag indicating whether total mass equation is used" );
+ 
+   this->registerWrapper( viewKeyStruct::gravityDensitySchemeString(), &m_gravityDensityScheme ).
+     setSizedFromParent( 0 ).
+     setInputFlag( InputFlags::OPTIONAL ).
+     setApplyDefaultValue( GravityDensityScheme::ArithmeticAverage ).
+     setDescription( "Scheme for density treatment in gravity" );
+ 
+   this->registerWrapper( viewKeyStruct::solutionChangeScalingFactorString(), &m_solutionChangeScalingFactor ).
+     setSizedFromParent( 0 ).
+     setInputFlag( InputFlags::OPTIONAL ).
+     setApplyDefaultValue( 0.5 ).
+     setDescription( "Damping factor for solution change targets" );
+   this->registerWrapper( viewKeyStruct::targetRelativePresChangeString(), &m_targetRelativePresChange ).
+     setSizedFromParent( 0 ).
+     setInputFlag( InputFlags::OPTIONAL ).
+     setApplyDefaultValue( 0.2 ).
+     setDescription( "Target (relative) change in pressure in a time step (expected value between 0 and 1)" );
+   this->registerWrapper( viewKeyStruct::targetPhaseVolFracChangeString(), &m_targetPhaseVolFracChange ).
+     setSizedFromParent( 0 ).
+     setInputFlag( InputFlags::OPTIONAL ).
+     setApplyDefaultValue( 0.2 ).
+     setDescription( "Target (absolute) change in phase volume fraction in a time step" );
+ 
+   this->registerWrapper( viewKeyStruct::interfaceFaceSetNamesString(),
+                          &m_interfaceFaceSetNames ).
+     setInputFlag( InputFlags::OPTIONAL ).
+     setDescription( "Names of the interface face sets" );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::postInputInitialization()
+ {
+   FlowSolverBase::postInputInitialization();
+ }
+ 
+ void ImmiscibleMultiphaseFlow::registerDataOnMesh( Group & meshBodies )
+ {
+   FlowSolverBase::registerDataOnMesh( meshBodies );
+ 
+   // 0. Find a "reference" fluid model name (at this point, models are already attached to subregions)
+   forDiscretizationOnMeshTargets( meshBodies, [&]( string const &,
+                                                    MeshLevel & mesh,
+                                                    string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions( regionNames,
+                                                 [&]( localIndex const,
+                                                      ElementSubRegionBase & subRegion )
+     {
+       // If at least one region has a capillary pressure model, consider it enabled for all
+       string const capPresName = getConstitutiveName< CapillaryPressureBase >( subRegion );
+       if( !capPresName.empty() )
+       {
+         m_hasCapPressure = true;
+       }
+     } );
+   } );
+ 
+   m_numDofPerCell = m_numPhases;
+ 
+   // 2. Register and resize all fields as necessary
+   forDiscretizationOnMeshTargets( meshBodies, [&]( string const &,
+                                                    MeshLevel & mesh,
+                                                    string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions( regionNames,
+                                                 [&]( localIndex const,
+                                                      ElementSubRegionBase & subRegion )
+     {
+       if( m_hasCapPressure )
+       {
+         subRegion.registerWrapper< string >( viewKeyStruct::capPressureNamesString() ).
+           setPlotLevel( PlotLevel::NOPLOT ).
+           setRestartFlags( RestartFlags::NO_WRITE ).
+           setSizedFromParent( 0 ).
+           setDescription( "Name of the capillary pressure constitutive model to use" ).
+           reference();
+ 
+         string & capPresName = subRegion.getReference< string >( viewKeyStruct::capPressureNamesString() );
+         capPresName = getConstitutiveName< CapillaryPressureBase >( subRegion );
+         GEOS_THROW_IF( capPresName.empty(),
+                        GEOS_FMT( "{}: Capillary pressure model not found on subregion {}",
+                                  getDataContext(), subRegion.getDataContext() ),
+                        InputError );
+       }
+ 
+       // The resizing of the arrays needs to happen here, before the call to initializePreSubGroups,
+       // to make sure that the dimensions are properly set before the timeHistoryOutput starts its initialization.
+       subRegion.registerField< phaseVolumeFraction >( getName() ).
+         reference().resizeDimension< 1 >( m_numPhases );
+ 
+       subRegion.registerField< phaseVolumeFraction_n >( getName() ).
+         reference().resizeDimension< 1 >( m_numPhases );
+ 
+       subRegion.registerField< bcPhaseVolumeFraction >( getName() ).
+         reference().resizeDimension< 1 >( m_numPhases );
+ 
+       subRegion.registerField< phaseMass >( getName() ).
+         reference().resizeDimension< 1 >( m_numPhases );
+ 
+       subRegion.registerField< phaseMass_n >( getName() ).
+         reference().resizeDimension< 1 >( m_numPhases );
+ 
+       subRegion.registerField< phaseMobility >( getName() ).
+         reference().resizeDimension< 1 >( m_numPhases );
+ 
+       subRegion.registerField< dPhaseMobility >( getName() ).
+         reference().resizeDimension< 1, 2 >( m_numPhases, m_numPhases ); // dP, dS
+ 
+     } );
+ 
+   } );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::setConstitutiveNames( ElementSubRegionBase & subRegion ) const
+ {
+   setConstitutiveName< TwoPhaseImmiscibleFluid >( subRegion, viewKeyStruct::fluidNamesString(), "two phase immiscible fluid" );
+ 
+   setConstitutiveName< RelativePermeabilityBase >( subRegion, viewKeyStruct::relPermNamesString(), "relative permeability" );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::initializePreSubGroups()
+ {
+   m_linearSolverParameters.get().mgr.strategy = LinearSolverParameters::MGR::StrategyType::immiscibleMultiphaseFVM;
+ 
+   FlowSolverBase::initializePreSubGroups();
+ 
+   DomainPartition & domain = this->getGroupByPath< DomainPartition >( "/Problem/domain" );
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions( regionNames,
+                                                 [&]( localIndex const,
+                                                      ElementSubRegionBase & subRegion )
+     {
+       arrayView1d< real64 > const temp = subRegion.getField< fields::flow::temperature >();
+       temp.setValues< parallelHostPolicy >( m_inputTemperature );
+     } );
+   } );
+ 
+   // ***** Create FaceElements *****
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & meshLevel,
+                                                                string_array const & GEOS_UNUSED_PARAM( regionNames ))
+   {
+ 
+     FaceManager const & faceManager = meshLevel.getFaceManager();
+     Group const & faceSetGroup = faceManager.sets();
+     ElementRegionManager & elemManager = meshLevel.getElemManager();
+     m_interfaceConstitutivePairs.resize( m_interfaceFaceSetNames.size() );
+ 
+     // this is the FaceElement Level
+     for( size_t surfaceRegionIndex=0; surfaceRegionIndex < m_interfaceFaceSetNames.size(); ++surfaceRegionIndex )
+     {
+       string const & faceSetName = m_interfaceFaceSetNames[surfaceRegionIndex];
+       SortedArrayView< localIndex const > const & faceSet = faceSetGroup.getReference< SortedArray< localIndex > >( faceSetName );
+       SurfaceElementRegion & faceRegion = elemManager.getRegion< SurfaceElementRegion >( faceSetName );
+ 
+       for( localIndex const faceIndex : faceSet )
+       {
+         localIndex const faceIndices[2] = { faceIndex, faceIndex };
+         faceRegion.addToSurfaceMesh( &faceManager, faceIndices );
+       }
+ 
+       FaceElementSubRegion const & faceSubRegion = faceRegion.getUniqueSubRegion< FaceElementSubRegion >();
+      FixedToManyElementRelation const & faceElementsToCells = faceSubRegion.getToCellRelation();
+
+      // Precompute numRegions once (it's constant for all face elements)
+      localIndex const numRegions = elemManager.numRegions();
+      constexpr int MAX_REASONABLE_REGION_INDEX = 100000;
+
+      std::function< std::tuple< CellElementSubRegion *, CellElementSubRegion * >(localIndex) > getSubregions = [&]( localIndex surfaceSubRegionIndex ) -> std::tuple< CellElementSubRegion *,
+                                                                                                                                                                        CellElementSubRegion * >
       {
-        subRegion.registerWrapper< string >( viewKeyStruct::capPressureNamesString() ).
-          setPlotLevel( PlotLevel::NOPLOT ).
-          setRestartFlags( RestartFlags::NO_WRITE ).
-          setSizedFromParent( 0 ).
-          setDescription( "Name of the capillary pressure constitutive model to use" ).
-          reference();
-
-        string & capPresName = subRegion.getReference< string >( viewKeyStruct::capPressureNamesString() );
-        capPresName = getConstitutiveName< CapillaryPressureBase >( subRegion );
-        GEOS_THROW_IF( capPresName.empty(),
-                       GEOS_FMT( "{}: Capillary pressure model not found on subregion {}",
-                                 getDataContext(), subRegion.getDataContext() ),
-                       InputError );
-      }
-
-      // The resizing of the arrays needs to happen here, before the call to initializePreSubGroups,
-      // to make sure that the dimensions are properly set before the timeHistoryOutput starts its initialization.
-      subRegion.registerField< phaseVolumeFraction >( getName() ).
-        reference().resizeDimension< 1 >( m_numPhases );
-
-      subRegion.registerField< phaseVolumeFraction_n >( getName() ).
-        reference().resizeDimension< 1 >( m_numPhases );
-
-      subRegion.registerField< bcPhaseVolumeFraction >( getName() ).
-        reference().resizeDimension< 1 >( m_numPhases );
-
-      subRegion.registerField< phaseMass >( getName() ).
-        reference().resizeDimension< 1 >( m_numPhases );
-
-      subRegion.registerField< phaseMass_n >( getName() ).
-        reference().resizeDimension< 1 >( m_numPhases );
 
-      subRegion.registerField< phaseMobility >( getName() ).
-        reference().resizeDimension< 1 >( m_numPhases );
-
-      subRegion.registerField< dPhaseMobility >( getName() ).
-        reference().resizeDimension< 1, 2 >( m_numPhases, m_numPhases ); // dP, dS
-
-    } );
-
-  } );
-}
-
-void ImmiscibleMultiphaseFlow::setConstitutiveNames( ElementSubRegionBase & subRegion ) const
-{
-  setConstitutiveName< TwoPhaseImmiscibleFluid >( subRegion, viewKeyStruct::fluidNamesString(), "two phase immiscible fluid" );
-
-  setConstitutiveName< RelativePermeabilityBase >( subRegion, viewKeyStruct::relPermNamesString(), "relative permeability" );
-}
-
-void ImmiscibleMultiphaseFlow::initializePreSubGroups()
-{
-  m_linearSolverParameters.get().mgr.strategy = LinearSolverParameters::MGR::StrategyType::immiscibleMultiphaseFVM;
-
-  FlowSolverBase::initializePreSubGroups();
-
-  DomainPartition & domain = this->getGroupByPath< DomainPartition >( "/Problem/domain" );
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions( regionNames,
-                                                [&]( localIndex const,
-                                                     ElementSubRegionBase & subRegion )
-    {
-      arrayView1d< real64 > const temp = subRegion.getField< fields::flow::temperature >();
-      temp.setValues< parallelHostPolicy >( m_inputTemperature );
-    } );
-  } );
-}
-
-
-void ImmiscibleMultiphaseFlow::updateFluidModel( ObjectManagerBase & dataGroup ) const
-{
-  GEOS_MARK_FUNCTION;
+        int regionIdx0 = faceElementsToCells.m_toElementRegion[surfaceSubRegionIndex][0];
+        int regionIdx1 = faceElementsToCells.m_toElementRegion[surfaceSubRegionIndex][1];
+        int subRegionIdx0 = faceElementsToCells.m_toElementSubRegion[surfaceSubRegionIndex][0];
+        int subRegionIdx1 = faceElementsToCells.m_toElementSubRegion[surfaceSubRegionIndex][1];
 
-  arrayView1d< real64 const > const pres = dataGroup.getField< fields::flow::pressure >();
-
-  TwoPhaseImmiscibleFluid & fluid = getConstitutiveModel< TwoPhaseImmiscibleFluid >( dataGroup, dataGroup.getReference< string >( viewKeyStruct::fluidNamesString() ) );
-
-  constitutiveUpdatePassThru( fluid, [&] ( auto & castedFluid )
-  {
-    using FluidType = TYPEOFREF( castedFluid );
-    typename FluidType::KernelWrapper fluidWrapper = castedFluid.createKernelWrapper();
-
-    FluidUpdateKernel::launch< parallelDevicePolicy<> >( dataGroup.size(), fluidWrapper, pres );
-  } );
-}
-
-
-void ImmiscibleMultiphaseFlow::updateRelPermModel( ObjectManagerBase & dataGroup ) const
-{
-  GEOS_MARK_FUNCTION;
-
-
-  GEOS_UNUSED_VAR( dataGroup );
-
-  arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
-    dataGroup.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-
-  string const & relPermName = dataGroup.getReference< string >( viewKeyStruct::relPermNamesString() );
-  RelativePermeabilityBase & relPerm = getConstitutiveModel< RelativePermeabilityBase >( dataGroup, relPermName );
+        // Fast validation checks (ordered from cheapest to most expensive)
+        if( regionIdx0 < 0 || regionIdx1 < 0 || 
+            subRegionIdx0 < 0 || subRegionIdx1 < 0 )
+        {
+          return std::make_tuple( nullptr, nullptr );
+        }
+        
+        if( regionIdx0 > MAX_REASONABLE_REGION_INDEX || regionIdx1 > MAX_REASONABLE_REGION_INDEX )
+        {
+          return std::make_tuple( nullptr, nullptr );
+        }
+        
+        if( static_cast< localIndex >( regionIdx0 ) >= numRegions || 
+            static_cast< localIndex >( regionIdx1 ) >= numRegions )
+        {
+          return std::make_tuple( nullptr, nullptr );
+        }
 
-  constitutive::constitutiveUpdatePassThru( relPerm, [&] ( auto & castedRelPerm )
-  {
-    typename TYPEOFREF( castedRelPerm ) ::KernelWrapper relPermWrapper = castedRelPerm.createKernelWrapper();
+        // Try to get regions - they might not exist on this MPI rank even if index is in range
+        ElementRegionBase * region0BasePtr = nullptr;
+        ElementRegionBase * region1BasePtr = nullptr;
+        
+        try
+        {
+          region0BasePtr = &elemManager.getRegion< ElementRegionBase >( regionIdx0 );
+          region1BasePtr = &elemManager.getRegion< ElementRegionBase >( regionIdx1 );
+        }
+        catch( std::exception const & )
+        {
+          return std::make_tuple( nullptr, nullptr );
+        }
+        
+        // Check if they are CellElementRegion (interface conditions only apply to cell-to-cell interfaces)
+        CellElementRegion * cellRegion0 = dynamic_cast< CellElementRegion * >( region0BasePtr );
+        CellElementRegion * cellRegion1 = dynamic_cast< CellElementRegion * >( region1BasePtr );
+        
+        if( cellRegion0 == nullptr || cellRegion1 == nullptr )
+        {
+          return std::make_tuple( nullptr, nullptr );
+        }
 
-    isothermalCompositionalMultiphaseBaseKernels::
-      RelativePermeabilityUpdateKernel::
-      launch< parallelDevicePolicy<> >( dataGroup.size(),
-                                        relPermWrapper,
-                                        phaseVolFrac );
-  } );
-}
+        // Validate subregion indices before accessing
+        if( static_cast< localIndex >( subRegionIdx0 ) >= cellRegion0->numSubRegions() ||
+            static_cast< localIndex >( subRegionIdx1 ) >= cellRegion1->numSubRegions() )
+        {
+          return std::make_tuple( nullptr, nullptr );
+        }
 
-void ImmiscibleMultiphaseFlow::updateCapPressureModel( ObjectManagerBase & dataGroup ) const
+        CellElementSubRegion * subRegion0 = &cellRegion0->getSubRegion< CellElementSubRegion >( subRegionIdx0 );
+        CellElementSubRegion * subRegion1 = &cellRegion1->getSubRegion< CellElementSubRegion >( subRegionIdx1 );
+        return std::make_tuple( subRegion0, subRegion1 );
+      };
+ 
+      //  std::tuple< CellElementSubRegion *, CellElementSubRegion * > subRegionPair = getSubregions( surfaceRegionIndex );
+      //  CellElementSubRegion * subRegion0 = std::get< 0 >( subRegionPair );
+      //  CellElementSubRegion * subRegion1 = std::get< 1 >( subRegionPair );
+ 
+      //  // get constitutives by type and name: relPerms, capPressures, Fluids (three pointers)
+      //  std::string & relPermName0 = subRegion0->getReference< std::string >( viewKeyStruct::relPermNamesString());
+      //  std::string & relPermName1 = subRegion1->getReference< std::string >( viewKeyStruct::relPermNamesString());
+      //  RelativePermeabilityBase * relPerm0 = &getConstitutiveModel< RelativePermeabilityBase >( *subRegion0, relPermName0 );
+      //  RelativePermeabilityBase * relPerm1 = &getConstitutiveModel< RelativePermeabilityBase >( *subRegion1, relPermName1 );
+ 
+      //  std::string & cappresName0 = subRegion0->getReference< std::string >( viewKeyStruct::capPressureNamesString());
+      //  std::string & cappresName1 = subRegion1->getReference< std::string >( viewKeyStruct::capPressureNamesString());
+      //  CapillaryPressureBase * capPressure0 = &getConstitutiveModel< CapillaryPressureBase >( *subRegion0, cappresName0 );
+      //  CapillaryPressureBase * capPressure1 = &getConstitutiveModel< CapillaryPressureBase >( *subRegion1, cappresName1 );
+ 
+      //  std::string & fluidName0 = subRegion0->getReference< std::string >( viewKeyStruct::fluidNamesString() );
+      //  std::string & fluidName1 = subRegion1->getReference< std::string >( viewKeyStruct::fluidNamesString() );
+ 
+      //  TwoPhaseImmiscibleFluid * fluid0 = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( *subRegion0, fluidName0 );
+      //  TwoPhaseImmiscibleFluid * fluid1 = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( *subRegion1, fluidName1 );
+ 
+      //  m_interfaceConstitutivePairs[surfaceRegionIndex][0] = std::make_tuple( relPerm0, capPressure0, fluid0 );
+      //  m_interfaceConstitutivePairs[surfaceRegionIndex][1] = std::make_tuple( relPerm1, capPressure1, fluid1 );
+ // Find a representative face element that connects two CellElementRegion objects
+// (not SurfaceElementRegion, which we don't handle for interface conditions)
+CellElementSubRegion * subRegion0 = nullptr;
+CellElementSubRegion * subRegion1 = nullptr;
+bool foundValidFei = false;
+
+// Single loop to find a valid face element (avoids redundant scanning)
+for( localIndex i = 0; i < faceElementsToCells.size(); ++i )
 {
-  GEOS_MARK_FUNCTION;
-
-  if( m_hasCapPressure )
+  // Quick check: must have two adjacent cells with non-negative region indices
+  if( faceElementsToCells.m_toElementRegion[i].size() >= 2 &&
+      faceElementsToCells.m_toElementRegion[i][0] >= 0 &&
+      faceElementsToCells.m_toElementRegion[i][1] >= 0 )
   {
-    arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
-      dataGroup.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-
-    string const & cappresName = dataGroup.getReference< string >( viewKeyStruct::capPressureNamesString() );
-    CapillaryPressureBase & capPressure = getConstitutiveModel< CapillaryPressureBase >( dataGroup, cappresName );
-
-    constitutive::constitutiveUpdatePassThru( capPressure, [&] ( auto & castedCapPres )
+    std::tuple< CellElementSubRegion *, CellElementSubRegion * > subRegionPair = getSubregions( i );
+    CellElementSubRegion * testSubRegion0 = std::get< 0 >( subRegionPair );
+    CellElementSubRegion * testSubRegion1 = std::get< 1 >( subRegionPair );
+    
+    if( testSubRegion0 != nullptr && testSubRegion1 != nullptr )
     {
-      typename TYPEOFREF( castedCapPres ) ::KernelWrapper capPresWrapper = castedCapPres.createKernelWrapper();
-
-      isothermalCompositionalMultiphaseBaseKernels::
-        CapillaryPressureUpdateKernel::
-        launch< parallelDevicePolicy<> >( dataGroup.size(),
-                                          capPresWrapper,
-                                          phaseVolFrac );
-    } );
+      subRegion0 = testSubRegion0;
+      subRegion1 = testSubRegion1;
+      foundValidFei = true;
+      break;
+    }
   }
 }
 
-
-void ImmiscibleMultiphaseFlow::updateFluidState( ElementSubRegionBase & subRegion ) const
-{
-  GEOS_MARK_FUNCTION;
-
-  updateFluidModel( subRegion );
-  updateVolumeConstraint( subRegion );
-  updatePhaseMass( subRegion );
-  updateRelPermModel( subRegion );
-  updatePhaseMobility( subRegion );
-  updateCapPressureModel( subRegion );
-}
-
-
-void ImmiscibleMultiphaseFlow::updatePhaseMass( ElementSubRegionBase & subRegion ) const
+// If no valid face element connecting two CellElementRegion objects, skip this surface region
+if( !foundValidFei )
 {
-  GEOS_MARK_FUNCTION;
-
-  string const & solidName = subRegion.getReference< string >( viewKeyStruct::solidNamesString() );
-  string const & fluidName = subRegion.getReference< string >( viewKeyStruct::fluidNamesString() );
-
-  TwoPhaseImmiscibleFluid const & fluid = getConstitutiveModel< TwoPhaseImmiscibleFluid >( subRegion, fluidName );
-  CoupledSolidBase const & solid = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
-
-  arrayView1d< real64 const > const volume = subRegion.getElementVolume();
-  arrayView2d< real64 const > const porosity = solid.getPorosity();
-
-  arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac= subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-  arrayView3d< real64 const, multifluid::USD_PHASE > phaseDens = fluid.phaseDensity();
-  arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseMass = subRegion.getField< fields::immiscibleMultiphaseFlow::phaseMass >();
-
-  // Might be needed for geomechanics????? if so, need to change the accumulation as well?
-  //arrayView1d< real64 > const deltaVolume = subRegion.getField< fields::flow::deltaVolume >();
-
-  forAll< parallelDevicePolicy<> >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const ei )
-  {
-    real64 const poreVolume = volume[ei] * porosity[ei][0];
-    for( integer ip = 0; ip < 2; ++ip )
-    {
-      phaseMass[ei][ip] = poreVolume * phaseVolFrac[ei][ip] * phaseDens[ei][0][ip];
-    }
-  } );
+  continue;
 }
 
-
-void ImmiscibleMultiphaseFlow::updatePhaseMobility( ObjectManagerBase & dataGroup ) const
-{
-  GEOS_MARK_FUNCTION;
-
-  // note that the phase mobility computed here also includes phase density
-  string const & fluidName = dataGroup.getReference< string >( viewKeyStruct::fluidNamesString() );
-  TwoPhaseImmiscibleFluid const & fluid = getConstitutiveModel< TwoPhaseImmiscibleFluid >( dataGroup, fluidName );
-
-  string const & relpermName = dataGroup.getReference< string >( viewKeyStruct::relPermNamesString() );
-  RelativePermeabilityBase const & relperm = getConstitutiveModel< RelativePermeabilityBase >( dataGroup, relpermName );
-
-  immiscibleMultiphaseKernels::
-    PhaseMobilityKernelFactory::
-    createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
-                                               dataGroup,
-                                               fluid,
-                                               relperm );
-}
-
-void ImmiscibleMultiphaseFlow::initializeFluidState( MeshLevel & mesh,
-                                                     string_array const & regionNames )
-{
-  GEOS_MARK_FUNCTION;
-
-  mesh.getElemManager().forElementSubRegions( regionNames,
-                                              [&]( localIndex const,
-                                                   ElementSubRegionBase & subRegion )
-  {
-    // 2. Assume global component fractions have been prescribed.
-    // Initialize constitutive state to get fluid density.
-    updateFluidModel( subRegion );
-
-  } );
-
-  // for some reason CUDA does not want the host_device lambda to be defined inside the generic lambda
-  // I need the exact type of the subRegion for updateSolidflowProperties to work well.
-  mesh.getElemManager().forElementSubRegions< CellElementSubRegion,
-                                              SurfaceElementSubRegion >( regionNames, [&]( localIndex const,
-                                                                                           auto & subRegion )
-  {
-    // 4. Initialize/update dependent state quantities
-
-    // 4.1 Update the constitutive models that only depend on
-    //      - the primary variables
-    //      - the fluid constitutive quantities (as they have already been updated)
-    // We postpone the other constitutive models for now
-    // In addition, to avoid multiplying permeability/porosity bay netToGross in the assembly kernel, we do it once and for all here
-    arrayView1d< real64 const > const netToGross = subRegion.template getField< fields::flow::netToGross >();
-    CoupledSolidBase const & porousSolid =
-      getConstitutiveModel< CoupledSolidBase >( subRegion, subRegion.template getReference< string >( viewKeyStruct::solidNamesString() ) );
-    PermeabilityBase const & permeabilityModel =
-      getConstitutiveModel< PermeabilityBase >( subRegion, subRegion.template getReference< string >( viewKeyStruct::permeabilityNamesString() ) );
-    permeabilityModel.scaleHorizontalPermeability( netToGross );
-    porousSolid.scaleReferencePorosity( netToGross );
-    saveConvergedState( subRegion ); // necessary for a meaningful porosity update in sequential schemes
-    updatePorosityAndPermeability( subRegion );
-
-    // Now, we initialize and update each constitutive model one by one
-
-    // 4.2 Save the computed porosity into the old porosity
-    //
-    // Note:
-    // - This must be called after updatePorosityAndPermeability
-    // - This step depends on porosity
-    string const & solidName = subRegion.template getReference< string >( viewKeyStruct::solidNamesString() );
-    CoupledSolidBase const & porousMaterial = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
-    porousMaterial.initializeState();
-
-    // 4.3 Initialize/update the relative permeability model using the initial phase volume fraction
-    //     This is needed to handle relative permeability hysteresis
-    //     Also, initialize the fluid model
-    //
-    // Note:
-    // - This must be called after updateVolumeConstraint
-    // - This step depends on phaseVolFraction
-
-    // initialized phase volume fraction
-    arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
-      subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-
-    string const & relpermName = subRegion.template getReference< string >( viewKeyStruct::relPermNamesString() );
-    RelativePermeabilityBase & relPermMaterial =
-      getConstitutiveModel< RelativePermeabilityBase >( subRegion, relpermName );
-    relPermMaterial.saveConvergedPhaseVolFractionState( phaseVolFrac ); // this needs to happen before calling updateRelPermModel
-    updateRelPermModel( subRegion );
-    relPermMaterial.saveConvergedState(); // this needs to happen after calling updateRelPermModel
-
-    // 4.4 Then, we initialize/update the capillary pressure model
-    //
-    // Note:
-    // - This must be called after updatePorosityAndPermeability
-    // - This step depends on porosity and permeability
-    if( m_hasCapPressure )
-    {
+// get constitutives by type and name: relPerms, capPressures, Fluids (three pointers)
+std::string & relPermName0 = subRegion0->getReference< std::string >( viewKeyStruct::relPermNamesString());
+std::string & relPermName1 = subRegion1->getReference< std::string >( viewKeyStruct::relPermNamesString());
+RelativePermeabilityBase * relPerm0 = &getConstitutiveModel< RelativePermeabilityBase >( *subRegion0, relPermName0 );
+RelativePermeabilityBase * relPerm1 = &getConstitutiveModel< RelativePermeabilityBase >( *subRegion1, relPermName1 );
+
+std::string & cappresName0 = subRegion0->getReference< std::string >( viewKeyStruct::capPressureNamesString());
+std::string & cappresName1 = subRegion1->getReference< std::string >( viewKeyStruct::capPressureNamesString());
+CapillaryPressureBase * capPressure0 = &getConstitutiveModel< CapillaryPressureBase >( *subRegion0, cappresName0 );
+CapillaryPressureBase * capPressure1 = &getConstitutiveModel< CapillaryPressureBase >( *subRegion1, cappresName1 );
+
+std::string & fluidName0 = subRegion0->getReference< std::string >( viewKeyStruct::fluidNamesString() );
+std::string & fluidName1 = subRegion1->getReference< std::string >( viewKeyStruct::fluidNamesString() );
+
+TwoPhaseImmiscibleFluid * fluid0 = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( *subRegion0, fluidName0 );
+TwoPhaseImmiscibleFluid * fluid1 = &getConstitutiveModel< TwoPhaseImmiscibleFluid >( *subRegion1, fluidName1 );
+
+m_interfaceConstitutivePairs[surfaceRegionIndex][0] = std::make_tuple( relPerm0, capPressure0, fluid0 );
+m_interfaceConstitutivePairs[surfaceRegionIndex][1] = std::make_tuple( relPerm1, capPressure1, fluid1 );
+
+     }
+   } );
+ 
+ }
+ 
+ 
+ void ImmiscibleMultiphaseFlow::updateFluidModel( ObjectManagerBase & dataGroup ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   arrayView1d< real64 const > const pres = dataGroup.getField< fields::flow::pressure >();
+ 
+   TwoPhaseImmiscibleFluid & fluid = getConstitutiveModel< TwoPhaseImmiscibleFluid >( dataGroup, dataGroup.getReference< string >( viewKeyStruct::fluidNamesString() ) );
+ 
+   constitutiveUpdatePassThru( fluid, [&] ( auto & castedFluid )
+   {
+     using FluidType = TYPEOFREF( castedFluid );
+     typename FluidType::KernelWrapper fluidWrapper = castedFluid.createKernelWrapper();
+ 
+     FluidUpdateKernel::launch< parallelDevicePolicy<> >( dataGroup.size(), fluidWrapper, pres );
+   } );
+ }
+ 
+ 
+ void ImmiscibleMultiphaseFlow::updateRelPermModel( ObjectManagerBase & dataGroup ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+ 
+   GEOS_UNUSED_VAR( dataGroup );
+ 
+   arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
+     dataGroup.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+ 
+   string const & relPermName = dataGroup.getReference< string >( viewKeyStruct::relPermNamesString() );
+   RelativePermeabilityBase & relPerm = getConstitutiveModel< RelativePermeabilityBase >( dataGroup, relPermName );
+ 
+   constitutive::constitutiveUpdatePassThru( relPerm, [&] ( auto & castedRelPerm )
+   {
+     typename TYPEOFREF( castedRelPerm ) ::KernelWrapper relPermWrapper = castedRelPerm.createKernelWrapper();
+ 
+     isothermalCompositionalMultiphaseBaseKernels::
+       RelativePermeabilityUpdateKernel::
+       launch< parallelDevicePolicy<> >( dataGroup.size(),
+                                         relPermWrapper,
+                                         phaseVolFrac );
+   } );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::updateCapPressureModel( ObjectManagerBase & dataGroup ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   if( m_hasCapPressure )
+   {
+     arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
+       dataGroup.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+ 
+     string const & cappresName = dataGroup.getReference< string >( viewKeyStruct::capPressureNamesString() );
+     CapillaryPressureBase & capPressure = getConstitutiveModel< CapillaryPressureBase >( dataGroup, cappresName );
+ 
+     constitutive::constitutiveUpdatePassThru( capPressure, [&] ( auto & castedCapPres )
+     {
+       typename TYPEOFREF( castedCapPres ) ::KernelWrapper capPresWrapper = castedCapPres.createKernelWrapper();
+ 
+       // isothermalCompositionalMultiphaseBaseKernels::
+       immiscibleMultiphaseKernels::
+         CapillaryPressureUpdateKernel::
+         launch< parallelDevicePolicy<> >( dataGroup.size(),
+                                           capPresWrapper,
+                                           phaseVolFrac );
+     } );
+   }
+ }
+ 
+ 
+ void ImmiscibleMultiphaseFlow::updateFluidState( ElementSubRegionBase & subRegion ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   updateFluidModel( subRegion );
+   updateVolumeConstraint( subRegion );
+   updatePhaseMass( subRegion );
+   updateRelPermModel( subRegion );
+   updatePhaseMobility( subRegion );
+   updateCapPressureModel( subRegion );
+ }
+ 
+ 
+ void ImmiscibleMultiphaseFlow::updatePhaseMass( ElementSubRegionBase & subRegion ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   string const & solidName = subRegion.getReference< string >( viewKeyStruct::solidNamesString() );
+   string const & fluidName = subRegion.getReference< string >( viewKeyStruct::fluidNamesString() );
+ 
+   TwoPhaseImmiscibleFluid const & fluid = getConstitutiveModel< TwoPhaseImmiscibleFluid >( subRegion, fluidName );
+   CoupledSolidBase const & solid = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
+ 
+   arrayView1d< real64 const > const volume = subRegion.getElementVolume();
+   arrayView2d< real64 const > const porosity = solid.getPorosity();
+ 
+   arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac= subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+   arrayView3d< real64 const, multifluid::USD_PHASE > phaseDens = fluid.phaseDensity();
+   arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseMass = subRegion.getField< fields::immiscibleMultiphaseFlow::phaseMass >();
+ 
+   // Might be needed for geomechanics????? if so, need to change the accumulation as well?
+   //arrayView1d< real64 > const deltaVolume = subRegion.getField< fields::flow::deltaVolume >();
+ 
+   forAll< parallelDevicePolicy<> >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const ei )
+   {
+     real64 const poreVolume = volume[ei] * porosity[ei][0];
+     for( integer ip = 0; ip < 2; ++ip )
+     {
+       phaseMass[ei][ip] = poreVolume * phaseVolFrac[ei][ip] * phaseDens[ei][0][ip];
+     }
+   } );
+ }
+ 
+ 
+ void ImmiscibleMultiphaseFlow::updatePhaseMobility( ObjectManagerBase & dataGroup ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   // note that the phase mobility computed here also includes phase density
+   string const & fluidName = dataGroup.getReference< string >( viewKeyStruct::fluidNamesString() );
+   TwoPhaseImmiscibleFluid const & fluid = getConstitutiveModel< TwoPhaseImmiscibleFluid >( dataGroup, fluidName );
+ 
+   string const & relpermName = dataGroup.getReference< string >( viewKeyStruct::relPermNamesString() );
+   RelativePermeabilityBase const & relperm = getConstitutiveModel< RelativePermeabilityBase >( dataGroup, relpermName );
+ 
+   immiscibleMultiphaseKernels::
+     PhaseMobilityKernelFactory::
+     createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
+                                                dataGroup,
+                                                fluid,
+                                                relperm );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::initializeFluidState( MeshLevel & mesh,
+                                                      string_array const & regionNames )
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   mesh.getElemManager().forElementSubRegions( regionNames,
+                                               [&]( localIndex const,
+                                                    ElementSubRegionBase & subRegion )
+   {
+     // 2. Assume global component fractions have been prescribed.
+     // Initialize constitutive state to get fluid density.
+     updateFluidModel( subRegion );
+ 
+   } );
+ 
+   // for some reason CUDA does not want the host_device lambda to be defined inside the generic lambda
+   // I need the exact type of the subRegion for updateSolidflowProperties to work well.
+   mesh.getElemManager().forElementSubRegions< CellElementSubRegion,
+                                               SurfaceElementSubRegion >( regionNames, [&]( localIndex const,
+                                                                                            auto & subRegion )
+   {
+     // 4. Initialize/update dependent state quantities
+ 
+     // 4.1 Update the constitutive models that only depend on
+     //      - the primary variables
+     //      - the fluid constitutive quantities (as they have already been updated)
+     // We postpone the other constitutive models for now
+     // In addition, to avoid multiplying permeability/porosity bay netToGross in the assembly kernel, we do it once and for all here
+     arrayView1d< real64 const > const netToGross = subRegion.template getField< fields::flow::netToGross >();
+     CoupledSolidBase const & porousSolid =
+       getConstitutiveModel< CoupledSolidBase >( subRegion, subRegion.template getReference< string >( viewKeyStruct::solidNamesString() ) );
+     PermeabilityBase const & permeabilityModel =
+       getConstitutiveModel< PermeabilityBase >( subRegion, subRegion.template getReference< string >( viewKeyStruct::permeabilityNamesString() ) );
+     permeabilityModel.scaleHorizontalPermeability( netToGross );
+     porousSolid.scaleReferencePorosity( netToGross );
+     saveConvergedState( subRegion ); // necessary for a meaningful porosity update in sequential schemes
+     updatePorosityAndPermeability( subRegion );
+ 
+     // Now, we initialize and update each constitutive model one by one
+ 
+     // 4.2 Save the computed porosity into the old porosity
+     //
+     // Note:
+     // - This must be called after updatePorosityAndPermeability
+     // - This step depends on porosity
+     string const & solidName = subRegion.template getReference< string >( viewKeyStruct::solidNamesString() );
+     CoupledSolidBase const & porousMaterial = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
+     porousMaterial.initializeState();
+ 
+     // 4.3 Initialize/update the relative permeability model using the initial phase volume fraction
+     //     This is needed to handle relative permeability hysteresis
+     //     Also, initialize the fluid model
+     //
+     // Note:
+     // - This must be called after updateVolumeConstraint
+     // - This step depends on phaseVolFraction
+ 
+     // initialized phase volume fraction
+     arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
+       subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+ 
+     string const & relpermName = subRegion.template getReference< string >( viewKeyStruct::relPermNamesString() );
+     RelativePermeabilityBase & relPermMaterial =
+       getConstitutiveModel< RelativePermeabilityBase >( subRegion, relpermName );
+     relPermMaterial.saveConvergedPhaseVolFractionState( phaseVolFrac ); // this needs to happen before calling updateRelPermModel
+     updateRelPermModel( subRegion );
+     relPermMaterial.saveConvergedState(); // this needs to happen after calling updateRelPermModel
+ 
+     // 4.4 Then, we initialize/update the capillary pressure model
+     //
+     // Note:
+     // - This must be called after updatePorosityAndPermeability
+     // - This step depends on porosity and permeability
+     if( m_hasCapPressure )
+     {
       // initialized porosity
       arrayView2d< real64 const > const porosity = porousMaterial.getPorosity();
 
@@ -425,854 +608,939 @@ void ImmiscibleMultiphaseFlow::initializeFluidState( MeshLevel & mesh,
       CapillaryPressureBase const & capPressureMaterial =
         getConstitutiveModel< CapillaryPressureBase >( subRegion, capPressureName );
       capPressureMaterial.initializeRockState( porosity, permeability ); // this needs to happen before calling updateCapPressureModel
+      capPressureMaterial.saveConvergedPhaseVolFractionState( phaseVolFrac );
       updateCapPressureModel( subRegion );
-    }
-
-    // 4.5 Update the phase mobility
-    //
-    // Note:
-    // - This must be called after updateRelPermModel
-    // - This step depends phaseRelPerm
-    updatePhaseMobility( subRegion );
-
-  } );
-
-  // 5. Save initial pressure
-  mesh.getElemManager().forElementSubRegions( regionNames, [&]( localIndex const,
-                                                                ElementSubRegionBase & subRegion )
-  {
-    arrayView1d< real64 const > const pres = subRegion.getField< fields::flow::pressure >();
-    arrayView1d< real64 > const initPres = subRegion.getField< fields::flow::initialPressure >();
-    arrayView1d< real64 const > const temp = subRegion.getField< fields::flow::temperature >();
-    arrayView1d< real64 > const initTemp = subRegion.template getField< fields::flow::initialTemperature >();
-    initPres.setValues< parallelDevicePolicy<> >( pres );
-    initTemp.setValues< parallelDevicePolicy<> >( temp );
-
-    // TODO: Missing updatePhaseMass?
-  } );
-}
-
-
-void ImmiscibleMultiphaseFlow::initializePostInitialConditionsPreSubGroups()
-{
-  GEOS_MARK_FUNCTION;
-
-  FlowSolverBase::initializePostInitialConditionsPreSubGroups();
-
-  DomainPartition & domain = this->getGroupByPath< DomainPartition >( "/Problem/domain" );
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & regionNames )
-  {
-    FieldIdentifiers fieldsToBeSync;
-    fieldsToBeSync.addElementFields( { fields::flow::pressure::key(),
-                                       fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() },
-                                     regionNames );
-
-    CommunicationTools::getInstance().synchronizeFields( fieldsToBeSync, mesh, domain.getNeighbors(), false );
-  } );
-
-  initializeState( domain );
-}
-
-
-void
-ImmiscibleMultiphaseFlow::implicitStepSetup( real64 const & GEOS_UNUSED_PARAM( time_n ),
-                                             real64 const & GEOS_UNUSED_PARAM( dt ),
-                                             DomainPartition & domain )
-{
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions< CellElementSubRegion,
-                                                SurfaceElementSubRegion >( regionNames,
-                                                                           [&]( localIndex const,
-                                                                                auto & subRegion )
-    {
-      saveConvergedState( subRegion );
-
-      // update porosity, permeability
-      updatePorosityAndPermeability( subRegion );
-      // update all fluid properties
-      updateVolumeConstraint( subRegion );
-      updateFluidState( subRegion );
-
-      // after the update, save the new saturation
-      arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
-        subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-
-      arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolFrac_n =
-        subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction_n >();
-      phaseVolFrac_n.setValues< parallelDevicePolicy<> >( phaseVolFrac );
-
-      arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const & phaseMass =
-        subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseMass >();
-
-      arrayView2d< real64, immiscibleFlow::USD_PHASE > const & phaseMass_n =
-        subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseMass_n >();
-      phaseMass_n.setValues< parallelDevicePolicy<> >( phaseMass );
-
-    } );
-  } );
-}
-
-void ImmiscibleMultiphaseFlow::assembleSystem( real64 const GEOS_UNUSED_PARAM( time_n ),
-                                               real64 const dt,
-                                               DomainPartition & domain,
-                                               DofManager const & dofManager,
-                                               CRSMatrixView< real64, globalIndex const > const & localMatrix,
-                                               arrayView1d< real64 > const & localRhs )
-{
-  GEOS_MARK_FUNCTION;
-
-  assembleAccumulationTerm( domain,
-                            dofManager,
-                            localMatrix,
-                            localRhs );
-
-
-  assembleFluxTerms( dt,
-                     domain,
-                     dofManager,
-                     localMatrix,
-                     localRhs );
-}
-
-
-
-void ImmiscibleMultiphaseFlow::assembleAccumulationTerm( DomainPartition & domain,
-                                                         DofManager const & dofManager,
-                                                         CRSMatrixView< real64, globalIndex const > const & localMatrix,
-                                                         arrayView1d< real64 > const & localRhs ) const
-{
-  GEOS_MARK_FUNCTION;
-
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel const & mesh,
-                                                               string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions( regionNames,
-                                                [&]( localIndex const,
-                                                     ElementSubRegionBase const & subRegion )
-    {
-      string const dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
-      string const & solidName = subRegion.getReference< string >( viewKeyStruct::solidNamesString() );
-      string const & fluidName = subRegion.getReference< string >( viewKeyStruct::fluidNamesString() );
-
-      TwoPhaseImmiscibleFluid const & fluid = getConstitutiveModel< TwoPhaseImmiscibleFluid >( subRegion, fluidName );
-      CoupledSolidBase const & solid = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
-
-      immiscibleMultiphaseKernels::
-        AccumulationKernelFactory::
-        createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
-                                                   dofManager.rankOffset(),
-                                                   m_useTotalMassEquation,
-                                                   dofKey,
-                                                   subRegion,
-                                                   fluid,
-                                                   solid,
-                                                   localMatrix,
-                                                   localRhs );
-
-    } );
-  } );
-}
-
-void ImmiscibleMultiphaseFlow::assembleFluxTerms( real64 const dt,
-                                                  DomainPartition const & domain,
-                                                  DofManager const & dofManager,
-                                                  CRSMatrixView< real64, globalIndex const > const & localMatrix,
-                                                  arrayView1d< real64 > const & localRhs ) const
-{
-  GEOS_MARK_FUNCTION;
-
-  NumericalMethodsManager const & numericalMethodManager = domain.getNumericalMethodManager();
-  FiniteVolumeManager const & fvManager = numericalMethodManager.getFiniteVolumeManager();
-  FluxApproximationBase const & fluxApprox = fvManager.getFluxApproximation( m_discretizationName );
-
-  string const & dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&] ( string const &,
+     }
+ 
+     // 4.5 Update the phase mobility
+     //
+     // Note:
+     // - This must be called after updateRelPermModel
+     // - This step depends phaseRelPerm
+     updatePhaseMobility( subRegion );
+ 
+   } );
+ 
+   // 5. Save initial pressure
+   mesh.getElemManager().forElementSubRegions( regionNames, [&]( localIndex const,
+                                                                 ElementSubRegionBase & subRegion )
+   {
+     arrayView1d< real64 const > const pres = subRegion.getField< fields::flow::pressure >();
+     arrayView1d< real64 > const initPres = subRegion.getField< fields::flow::initialPressure >();
+     arrayView1d< real64 const > const temp = subRegion.getField< fields::flow::temperature >();
+     arrayView1d< real64 > const initTemp = subRegion.template getField< fields::flow::initialTemperature >();
+     initPres.setValues< parallelDevicePolicy<> >( pres );
+     initTemp.setValues< parallelDevicePolicy<> >( temp );
+ 
+     // TODO: Missing updatePhaseMass?
+   } );
+ }
+ 
+ 
+ void ImmiscibleMultiphaseFlow::initializePostInitialConditionsPreSubGroups()
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   FlowSolverBase::initializePostInitialConditionsPreSubGroups();
+ 
+   DomainPartition & domain = this->getGroupByPath< DomainPartition >( "/Problem/domain" );
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & regionNames )
+   {
+     FieldIdentifiers fieldsToBeSync;
+     fieldsToBeSync.addElementFields( { fields::flow::pressure::key(),
+                                        fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() },
+                                      regionNames );
+ 
+     CommunicationTools::getInstance().synchronizeFields( fieldsToBeSync, mesh, domain.getNeighbors(), false );
+   } );
+ 
+   // Retrieve the numerical methods and finite volume manager
+   FiniteVolumeManager const & fvManager = domain.getNumericalMethodManager().getFiniteVolumeManager();
+   FluxApproximationBase const & fluxApprox = fvManager.getFluxApproximation( m_discretizationName );
+   const geos::string flux_approximation_name = fluxApprox.getName();
+ 
+   // Clear the existing mapping between connector indices and interface region indices
+   m_interfaceRegionByConnector.clear();
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( std::string const &,
+                                                                MeshLevel & meshLevel,
+                                                                string_array const & GEOS_UNUSED_PARAM( regionNames ))
+   {
+     // Access the face manager and retrieve the face set group for the current mesh level
+     FaceManager const & faceManager = meshLevel.getFaceManager();
+     Group const & faceSetGroup = faceManager.sets();
+ 
+     // Access the connector indices map (face index → connector index)
+     Group & stencilGroup =
+       meshLevel.getGroup( FluxApproximationBase::groupKeyStruct::stencilMeshGroupString())
+         .getGroup( flux_approximation_name );
+     CellElementStencilTPFA & stencil =
+       stencilGroup.getReference< CellElementStencilTPFA >(
+         FluxApproximationBase::viewKeyStruct::cellStencilString());
+     unordered_map< localIndex, localIndex > const & connectorIndices = stencil.getConnectorIndices();
+ 
+     // for all interface face sets to map connector indices to their corresponding interface region indices
+     for( size_t surfaceRegionIndex = 0; surfaceRegionIndex < m_interfaceFaceSetNames.size(); ++surfaceRegionIndex )
+     {
+       // Iterate over each face and associate its connector index
+       std::string const & faceSetName = m_interfaceFaceSetNames[surfaceRegionIndex];
+       for( localIndex kf : faceSetGroup.getReference< SortedArray< localIndex > >( faceSetName ))
+       {
+         auto it = connectorIndices.find( kf );
+         if( it != connectorIndices.end())
+         {
+           // Map the connector index to the corresponding surface region index
+           m_interfaceRegionByConnector[it->second] = surfaceRegionIndex;
+         }
+       }
+     }
+   } );
+ 
+ 
+   initializeState( domain );
+ }
+ 
+ 
+ void
+ ImmiscibleMultiphaseFlow::implicitStepSetup( real64 const & GEOS_UNUSED_PARAM( time_n ),
+                                              real64 const & GEOS_UNUSED_PARAM( dt ),
+                                              DomainPartition & domain )
+ {
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions< CellElementSubRegion,
+                                                 SurfaceElementSubRegion >( regionNames,
+                                                                            [&]( localIndex const,
+                                                                                 auto & subRegion )
+     {
+       saveConvergedState( subRegion );
+ 
+       // update porosity, permeability
+       updatePorosityAndPermeability( subRegion );
+       // update all fluid properties
+       updateVolumeConstraint( subRegion );
+       updateFluidState( subRegion );
+ 
+       // after the update, save the new saturation
+       arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
+         subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+ 
+       arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolFrac_n =
+         subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction_n >();
+       phaseVolFrac_n.setValues< parallelDevicePolicy<> >( phaseVolFrac );
+ 
+       arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const & phaseMass =
+         subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseMass >();
+ 
+       arrayView2d< real64, immiscibleFlow::USD_PHASE > const & phaseMass_n =
+         subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseMass_n >();
+       phaseMass_n.setValues< parallelDevicePolicy<> >( phaseMass );
+ 
+     } );
+   } );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::assembleSystem( real64 const GEOS_UNUSED_PARAM( time_n ),
+                                                real64 const dt,
+                                                DomainPartition & domain,
+                                                DofManager const & dofManager,
+                                                CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                                                arrayView1d< real64 > const & localRhs )
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   assembleAccumulationTerm( domain,
+                             dofManager,
+                             localMatrix,
+                             localRhs );
+ 
+ 
+   assembleFluxTerms( dt,
+                      domain,
+                      dofManager,
+                      localMatrix,
+                      localRhs );
+ }
+ 
+ 
+ 
+ void ImmiscibleMultiphaseFlow::assembleAccumulationTerm( DomainPartition & domain,
+                                                          DofManager const & dofManager,
+                                                          CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                                                          arrayView1d< real64 > const & localRhs ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
                                                                 MeshLevel const & mesh,
-                                                                string_array const & )
-  {
-    fluxApprox.forAllStencils( mesh, [&]( auto & stencil )
-    {
-      typename TYPEOFREF( stencil ) ::KernelWrapper stencilWrapper = stencil.createKernelWrapper();
-      immiscibleMultiphaseKernels::
-        FluxComputeKernelFactory::createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
-                                                                             dofManager.rankOffset(),
-                                                                             dofKey,
-                                                                             m_hasCapPressure,
-                                                                             m_useTotalMassEquation,
-                                                                             m_gravityDensityScheme == GravityDensityScheme::PhasePresence,
-                                                                             getName(),
-                                                                             mesh.getElemManager(),
-                                                                             stencilWrapper,
-                                                                             dt,
-                                                                             localMatrix.toViewConstSizes(),
-                                                                             localRhs.toView() );
-    } );
-  } );
-}
-
-void ImmiscibleMultiphaseFlow::setupDofs( DomainPartition const & domain,
-                                          DofManager & dofManager ) const
-{
-  GEOS_UNUSED_VAR( domain, dofManager );
-  // add a field for the cell-centered degrees of freedom
-  dofManager.addField( viewKeyStruct::elemDofFieldString(),
-                       FieldLocation::Elem,
-                       m_numDofPerCell,
-                       getMeshTargets() );
-
-  //// this call with instruct GEOS to reorder the dof numbers
-  //dofManager.setLocalReorderingType( viewKeyStruct::elemDofFieldString(),
-  //                                   DofManager::LocalReorderingType::ReverseCutHillMcKee );
-
-  NumericalMethodsManager const & numericalMethodManager = domain.getNumericalMethodManager();
-  FiniteVolumeManager const & fvManager = numericalMethodManager.getFiniteVolumeManager();
-  FluxApproximationBase const & fluxApprox = fvManager.getFluxApproximation( m_discretizationName );
-  dofManager.addCoupling( viewKeyStruct::elemDofFieldString(), fluxApprox );
-}
-
-void ImmiscibleMultiphaseFlow::applyBoundaryConditions( real64 const time_n,
-                                                        real64 const dt,
-                                                        DomainPartition & domain,
-                                                        DofManager const & dofManager,
-                                                        CRSMatrixView< real64, globalIndex const > const & localMatrix,
-                                                        arrayView1d< real64 > const & localRhs )
-{
-  GEOS_MARK_FUNCTION;
-
-  // apply pressure boundary conditions.
-  applyDirichletBC( time_n, dt, dofManager, domain, localMatrix.toViewConstSizes(), localRhs.toView() );
-
-  // apply flux boundary conditions
-  applySourceFluxBC( time_n, dt, dofManager, domain, localMatrix.toViewConstSizes(), localRhs.toView() );
-}
-
-
-namespace
-{
-char const bcLogMessage[] =
-  "ImmiscibleMultiphaseFlow {}: at time {}s, "
-  "the <{}> boundary condition '{}' is applied to the element set '{}' in subRegion '{}'. "
-  "\nThe scale of this boundary condition is {} and multiplies the value of the provided function (if any). "
-  "\nThe total number of target elements (including ghost elements) is {}. "
-  "\nNote that if this number is equal to zero for all subRegions, the boundary condition will not be applied on this element set.";
-}
-
-bool ImmiscibleMultiphaseFlow::validateDirichletBC( DomainPartition & domain,
-                                                    real64 const time ) const
-{
-  constexpr integer MAX_NP = 2;
-  FieldSpecificationManager & fsManager = FieldSpecificationManager::getInstance();
-
-  bool bcConsistent = true;
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & )
-  {
-    // map: regionName -> subRegionName -> setName -> numPhases to check pressure/phase are present consistent
-    map< string, map< string, map< string, ComponentMask< MAX_NP > > > > bcPresCompStatusMap;
-
-    // 1. Check pressure Dirichlet BCs
-    fsManager.apply< ElementSubRegionBase >( time,
-                                             mesh,
-                                             fields::flow::pressure::key(),
-                                             [&]( FieldSpecificationBase const &,
-                                                  string const & setName,
-                                                  SortedArrayView< localIndex const > const &,
-                                                  ElementSubRegionBase & subRegion,
-                                                  string const & )
-    {
-      // Check whether pressure has already been applied to this set
-      string const & subRegionName = subRegion.getName();
-      string const & regionName = subRegion.getParent().getParent().getName();
-
-      auto & subRegionSetMap = bcPresCompStatusMap[regionName][subRegionName];
-      if( subRegionSetMap.count( setName ) > 0 )
-      {
-        bcConsistent = false;
-        GEOS_WARNING( BCMessage::pressureConflict( regionName, subRegionName, setName,
-                                                   fields::flow::pressure::key() ) );
-      }
-      subRegionSetMap[setName].setNumComp( m_numPhases );
-    } );
-    // 2. Check saturation Dirichlet BCs
-    fsManager.apply< ElementSubRegionBase >( time,
-                                             mesh,
-                                             fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key(),
-                                             [&] ( FieldSpecificationBase const & fs,
-                                                   string const & setName,
-                                                   SortedArrayView< localIndex const > const &,
-                                                   ElementSubRegionBase & subRegion,
-                                                   string const & )
+                                                                string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions( regionNames,
+                                                 [&]( localIndex const,
+                                                      ElementSubRegionBase const & subRegion )
+     {
+       string const dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
+       string const & solidName = subRegion.getReference< string >( viewKeyStruct::solidNamesString() );
+       string const & fluidName = subRegion.getReference< string >( viewKeyStruct::fluidNamesString() );
+ 
+       TwoPhaseImmiscibleFluid const & fluid = getConstitutiveModel< TwoPhaseImmiscibleFluid >( subRegion, fluidName );
+       CoupledSolidBase const & solid = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
+ 
+       immiscibleMultiphaseKernels::
+         AccumulationKernelFactory::
+         createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
+                                                    dofManager.rankOffset(),
+                                                    m_useTotalMassEquation,
+                                                    dofKey,
+                                                    subRegion,
+                                                    fluid,
+                                                    solid,
+                                                    localMatrix,
+                                                    localRhs );
+ 
+     } );
+   } );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::assembleFluxTerms( real64 const dt,
+                                                   DomainPartition & domain,
+                                                   DofManager const & dofManager,
+                                                   CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                                                   arrayView1d< real64 > const & localRhs ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   NumericalMethodsManager const & numericalMethodManager = domain.getNumericalMethodManager();
+   FiniteVolumeManager const & fvManager = numericalMethodManager.getFiniteVolumeManager();
+   FluxApproximationBase const & fluxApprox = fvManager.getFluxApproximation( m_discretizationName );
+ 
+   string const & dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
+ 
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&] ( string const &,
+                                                                 MeshLevel & mesh,
+                                                                 string_array const & regionNames )
+   {
+    if( m_hasCapPressure )
     {
-      string const & subRegionName = subRegion.getName(   );
-      string const & regionName = subRegion.getParent().getParent().getName();
-      integer const comp = fs.getComponent();
-
-      auto & subRegionSetMap = bcPresCompStatusMap[regionName][subRegionName];
-      if( subRegionSetMap.count( setName ) == 0 )
+      // Get the first subregion to pass to the kernel factory (only used for domainSize, not for filtering connections)
+      ElementSubRegionBase const * firstSubRegion = nullptr;
+      mesh.getElemManager().forElementSubRegions( regionNames,
+                                                   [&]( localIndex const,
+                                                        ElementSubRegionBase const & subRegion )
       {
-        bcConsistent = false;
-        GEOS_WARNING( BCMessage::missingPressure( regionName, subRegionName, setName,
-                                                  fields::flow::pressure::key() ) );
-      }
-      if( comp < 0 || comp >= m_numPhases )
-      {
-        bcConsistent = false;
-        GEOS_WARNING( BCMessage::invalidComponentIndex( comp, fs.getName(),
-                                                        fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() ) );
-        return; // can't check next part with invalid component id
-      }
-
-      ComponentMask< MAX_NP > & compMask = subRegionSetMap[setName];
-      if( compMask[comp] )
-      {
-        bcConsistent = false;
-        fsManager.forSubGroups< EquilibriumInitialCondition >( [&] ( EquilibriumInitialCondition const & bc )
+        if( firstSubRegion == nullptr )
         {
-          string_array const & componentNames = bc.getComponentNames();
-          GEOS_WARNING( BCMessage::conflictingComposition( comp, componentNames[comp],
-                                                           regionName, subRegionName, setName,
-                                                           fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() ) );
-        } );
-      }
-      compMask.set( comp );
-    } );
+          firstSubRegion = &subRegion;
+        }
+      } );
 
-    // 3.2 Check consistency between composition BC applied to sets
-    // Note: for a temperature-only boundary condition, this loop does not do anything
-    for( auto const & regionEntry : bcPresCompStatusMap )
-    {
-      for( auto const & subRegionEntry : regionEntry.second )
+      fluxApprox.forAllStencils( mesh, [&]( auto & stencil )
       {
-        for( auto const & setEntry : subRegionEntry.second )
-        {
-          ComponentMask< MAX_NP > const & compMask = setEntry.second;
-
-          fsManager.forSubGroups< EquilibriumInitialCondition >( [&] ( EquilibriumInitialCondition const & fs )
-          {
-            string_array const & componentNames = fs.getComponentNames();
-            for( size_t ic = 0; ic < componentNames.size(); ic++ )
-            {
-              if( !compMask[ic] )
-              {
-                bcConsistent = false;
-                GEOS_WARNING( BCMessage::notAppliedOnRegion( ic, componentNames[ic],
-                                                             regionEntry.first, subRegionEntry.first, setEntry.first,
-                                                             fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() ) );
-              }
-            }
-          } );
-        }
-      }
+        typename TYPEOFREF( stencil ) ::KernelWrapper stencilWrapper = stencil.createKernelWrapper();
+        immiscibleMultiphaseKernels::
+          FluxComputeKernelFactory::createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
+                                                                               dofManager.rankOffset(),
+                                                                               dofKey,
+                                                                               m_hasCapPressure,
+                                                                               m_useTotalMassEquation,
+                                                                               m_gravityDensityScheme == GravityDensityScheme::PhasePresence,
+                                                                               getName(),
+                                                                               mesh.getElemManager(),
+                                                                               stencilWrapper,
+                                                                               m_interfaceFaceSetNames,
+                                                                               m_interfaceConstitutivePairs,
+                                                                               m_interfaceRegionByConnector,
+                                                                               *firstSubRegion,
+                                                                               dt,
+                                                                               localMatrix.toViewConstSizes(),
+                                                                               localRhs.toView() );
+      } );
     }
-  } );
-
-  return bcConsistent;
-}
-
-void ImmiscibleMultiphaseFlow::applyDirichletBC( real64 const time_n,
-                                                 real64 const dt,
-                                                 DofManager const & dofManager,
-                                                 DomainPartition & domain,
-                                                 CRSMatrixView< real64, globalIndex const > const & localMatrix,
-                                                 arrayView1d< real64 > const & localRhs ) const
-{
-  GEOS_MARK_FUNCTION;
-
-  // Only validate BC at the beginning of Newton loop
-  if( m_nonlinearSolverParameters.m_numNewtonIterations == 0 )
-  {
-    bool const bcConsistent = validateDirichletBC( domain, time_n + dt );
-    GEOS_ERROR_IF( !bcConsistent, GEOS_FMT( "ImmiscibleMultiphaseFlow {}: inconsistent boundary conditions", getDataContext() ) );
-  }
-
-  FieldSpecificationManager & fsManager = FieldSpecificationManager::getInstance();
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & )
-  {
-
-    // 1. Apply pressure Dirichlet BCs, store in a separate field
-    applyFieldValue< ElementSubRegionBase >( time_n, dt, mesh, bcLogMessage,
-                                             fields::flow::pressure::key(), fields::flow::bcPressure::key() );
-    // 2. Apply saturation BC (phase volume fraction) and store in a separate field
-    applyFieldValue< ElementSubRegionBase >( time_n, dt, mesh, bcLogMessage,
-                                             fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key(),
-                                             fields::immiscibleMultiphaseFlow::bcPhaseVolumeFraction::key() );
-
-    globalIndex const rankOffset = dofManager.rankOffset();
-    string const dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
-
-    // 3. Call constitutive update
-    fsManager.apply< ElementSubRegionBase >( time_n + dt,
-                                             mesh,
-                                             fields::flow::pressure::key(),
-                                             [&] ( FieldSpecificationBase const &,
-                                                   string const &,
-                                                   SortedArrayView< localIndex const > const & targetSet,
+     else
+     {
+       fluxApprox.forAllStencils( mesh, [&]( auto & stencil )
+       {
+         typename TYPEOFREF( stencil ) ::KernelWrapper stencilWrapper = stencil.createKernelWrapper();
+         immiscibleMultiphaseKernels::
+           FluxComputeKernelFactory::createAndLaunch< parallelDevicePolicy<> >( m_numPhases,
+                                                                                dofManager.rankOffset(),
+                                                                                dofKey,
+                                                                                m_hasCapPressure,
+                                                                                m_useTotalMassEquation,
+                                                                                m_gravityDensityScheme == GravityDensityScheme::PhasePresence,
+                                                                                getName(),
+                                                                                mesh.getElemManager(),
+                                                                                stencilWrapper,
+                                                                                dt,
+                                                                                localMatrix.toViewConstSizes(),
+                                                                                localRhs.toView() );
+       } );
+     }
+ 
+   } );
+ }
+ 
+ // Ryan: Looks like this will need to be overwritten as well...
+ // I have left the CompositionalMultiphaseFVM implementation for reference
+ void ImmiscibleMultiphaseFlow::setupDofs( DomainPartition const & domain,
+                                           DofManager & dofManager ) const
+ {
+   GEOS_UNUSED_VAR( domain, dofManager );
+   // add a field for the cell-centered degrees of freedom
+   dofManager.addField( viewKeyStruct::elemDofFieldString(),
+                        FieldLocation::Elem,
+                        m_numDofPerCell,
+                        getMeshTargets() );
+ 
+   //// this call with instruct GEOS to reorder the dof numbers
+   //dofManager.setLocalReorderingType( viewKeyStruct::elemDofFieldString(),
+   //                                   DofManager::LocalReorderingType::ReverseCutHillMcKee );
+ 
+   NumericalMethodsManager const & numericalMethodManager = domain.getNumericalMethodManager();
+   FiniteVolumeManager const & fvManager = numericalMethodManager.getFiniteVolumeManager();
+   FluxApproximationBase const & fluxApprox = fvManager.getFluxApproximation( m_discretizationName );
+   dofManager.addCoupling( viewKeyStruct::elemDofFieldString(), fluxApprox );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::applyBoundaryConditions( real64 const time_n,
+                                                         real64 const dt,
+                                                         DomainPartition & domain,
+                                                         DofManager const & dofManager,
+                                                         CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                                                         arrayView1d< real64 > const & localRhs )
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   // apply pressure boundary conditions.
+   applyDirichletBC( time_n, dt, dofManager, domain, localMatrix.toViewConstSizes(), localRhs.toView() );
+ 
+   // apply flux boundary conditions
+   applySourceFluxBC( time_n, dt, dofManager, domain, localMatrix.toViewConstSizes(), localRhs.toView() );
+ }
+ 
+ 
+ namespace
+ {
+ char const bcLogMessage[] =
+   "ImmiscibleMultiphaseFlow {}: at time {}s, "
+   "the <{}> boundary condition '{}' is applied to the element set '{}' in subRegion '{}'. "
+   "\nThe scale of this boundary condition is {} and multiplies the value of the provided function (if any). "
+   "\nThe total number of target elements (including ghost elements) is {}. "
+   "\nNote that if this number is equal to zero for all subRegions, the boundary condition will not be applied on this element set.";
+ }
+ 
+ bool ImmiscibleMultiphaseFlow::validateDirichletBC( DomainPartition & domain,
+                                                     real64 const time ) const
+ {
+   constexpr integer MAX_NP = 2;
+   FieldSpecificationManager & fsManager = FieldSpecificationManager::getInstance();
+ 
+   bool bcConsistent = true;
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & )
+   {
+     // map: regionName -> subRegionName -> setName -> numPhases to check pressure/phase are present consistent
+     map< string, map< string, map< string, ComponentMask< MAX_NP > > > > bcPresCompStatusMap;
+ 
+     // 1. Check pressure Dirichlet BCs
+     fsManager.apply< ElementSubRegionBase >( time,
+                                              mesh,
+                                              fields::flow::pressure::key(),
+                                              [&]( FieldSpecificationBase const &,
+                                                   string const & setName,
+                                                   SortedArrayView< localIndex const > const &,
                                                    ElementSubRegionBase & subRegion,
                                                    string const & )
-    {
-
-      arrayView1d< real64 const > const bcPres =
-        subRegion.getReference< array1d< real64 > >( fields::flow::bcPressure::key() );
-      arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const bcPhaseVolFraction =
-        subRegion.getReference< array2d< real64, immiscibleFlow::LAYOUT_PHASE > >(
-          fields::immiscibleMultiphaseFlow::bcPhaseVolumeFraction::key() );
-
-      arrayView1d< integer const > const ghostRank =
-        subRegion.getReference< array1d< integer > >( ObjectManagerBase::viewKeyStruct::ghostRankString() );
-      arrayView1d< globalIndex const > const dofNumber =
-        subRegion.getReference< array1d< globalIndex > >( dofKey );
-      arrayView1d< real64 const > const pres =
-        subRegion.getReference< array1d< real64 > >( fields::flow::pressure::key() );
-      arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFraction =
-        subRegion.getReference< array2d< real64, immiscibleFlow::LAYOUT_PHASE > >(
-          fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() );
-
-      integer const numPhase = m_numPhases;
-
-
-      forAll< parallelDevicePolicy<> >( targetSet.size(), [=] GEOS_HOST_DEVICE ( localIndex const a )
-      {
-        localIndex const ei = targetSet[a];
-        if( ghostRank[ei] >= 0 )
-        {
-          return;
-        }
-
-        globalIndex const dofIndex = dofNumber[ei];
-        localIndex const localRow = dofIndex - rankOffset;
-        real64 rhsValue;
-
-        // 3.1. Apply pressure value to the matrix/rhs
-        FieldSpecificationEqual::SpecifyFieldValue( dofIndex,
-                                                    rankOffset,
-                                                    localMatrix,
-                                                    rhsValue,
-                                                    bcPres[ei],
-                                                    pres[ei] );
-        localRhs[localRow] = rhsValue;
-
-        // 3.2. For each phase, apply target saturation value
-        for( integer ip = 0; ip < numPhase-1; ++ip )
-        {
-          FieldSpecificationEqual::SpecifyFieldValue( dofIndex + ip + 1,
-                                                      rankOffset,
-                                                      localMatrix,
-                                                      rhsValue,
-                                                      bcPhaseVolFraction[ei][ip],
-                                                      phaseVolFraction[ei][ip] );
-          localRhs[localRow + ip + 1] = rhsValue;
-        }
-      } );
-    } );
-  } );
-}
-
-void ImmiscibleMultiphaseFlow::applySourceFluxBC( real64 const time,
+     {
+       // Check whether pressure has already been applied to this set
+       string const & subRegionName = subRegion.getName();
+       string const & regionName = subRegion.getParent().getParent().getName();
+ 
+       auto & subRegionSetMap = bcPresCompStatusMap[regionName][subRegionName];
+       if( subRegionSetMap.count( setName ) > 0 )
+       {
+         bcConsistent = false;
+         GEOS_WARNING( BCMessage::pressureConflict( regionName, subRegionName, setName,
+                                                    fields::flow::pressure::key() ) );
+       }
+       subRegionSetMap[setName].setNumComp( m_numPhases );
+     } );
+     // 2. Check saturation Dirichlet BCs
+     fsManager.apply< ElementSubRegionBase >( time,
+                                              mesh,
+                                              fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key(),
+                                              [&] ( FieldSpecificationBase const & fs,
+                                                    string const & setName,
+                                                    SortedArrayView< localIndex const > const &,
+                                                    ElementSubRegionBase & subRegion,
+                                                    string const & )
+     {
+       string const & subRegionName = subRegion.getName(   );
+       string const & regionName = subRegion.getParent().getParent().getName();
+       integer const comp = fs.getComponent();
+ 
+       auto & subRegionSetMap = bcPresCompStatusMap[regionName][subRegionName];
+       if( subRegionSetMap.count( setName ) == 0 )
+       {
+         bcConsistent = false;
+         GEOS_WARNING( BCMessage::missingPressure( regionName, subRegionName, setName,
+                                                   fields::flow::pressure::key() ) );
+       }
+       if( comp < 0 || comp >= m_numPhases )
+       {
+         bcConsistent = false;
+         GEOS_WARNING( BCMessage::invalidComponentIndex( comp, fs.getName(),
+                                                         fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() ) );
+         return; // can't check next part with invalid component id
+       }
+ 
+       ComponentMask< MAX_NP > & compMask = subRegionSetMap[setName];
+       if( compMask[comp] )
+       {
+         bcConsistent = false;
+         fsManager.forSubGroups< EquilibriumInitialCondition >( [&] ( EquilibriumInitialCondition const & bc )
+         {
+           string_array const & componentNames = bc.getComponentNames();
+           GEOS_WARNING( BCMessage::conflictingComposition( comp, componentNames[comp],
+                                                            regionName, subRegionName, setName,
+                                                            fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() ) );
+         } );
+       }
+       compMask.set( comp );
+     } );
+ 
+     // 3.2 Check consistency between composition BC applied to sets
+     // Note: for a temperature-only boundary condition, this loop does not do anything
+     for( auto const & regionEntry : bcPresCompStatusMap )
+     {
+       for( auto const & subRegionEntry : regionEntry.second )
+       {
+         for( auto const & setEntry : subRegionEntry.second )
+         {
+           ComponentMask< MAX_NP > const & compMask = setEntry.second;
+ 
+           fsManager.forSubGroups< EquilibriumInitialCondition >( [&] ( EquilibriumInitialCondition const & fs )
+           {
+             string_array const & componentNames = fs.getComponentNames();
+             for( size_t ic = 0; ic < componentNames.size(); ic++ )
+             {
+               if( !compMask[ic] )
+               {
+                 bcConsistent = false;
+                 GEOS_WARNING( BCMessage::notAppliedOnRegion( ic, componentNames[ic],
+                                                              regionEntry.first, subRegionEntry.first, setEntry.first,
+                                                              fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() ) );
+               }
+             }
+           } );
+         }
+       }
+     }
+   } );
+ 
+   return bcConsistent;
+ }
+ 
+ void ImmiscibleMultiphaseFlow::applyDirichletBC( real64 const time_n,
                                                   real64 const dt,
                                                   DofManager const & dofManager,
                                                   DomainPartition & domain,
                                                   CRSMatrixView< real64, globalIndex const > const & localMatrix,
                                                   arrayView1d< real64 > const & localRhs ) const
-{
-  GEOS_MARK_FUNCTION;
-
-  FieldSpecificationManager & fsManager = FieldSpecificationManager::getInstance();
-
-  string const dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
-
-  // Step 1: count individual source flux boundary conditions
-
-  stdMap< string, localIndex > bcNameToBcId;
-  localIndex bcCounter = 0;
-
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   // Only validate BC at the beginning of Newton loop
+   if( m_nonlinearSolverParameters.m_numNewtonIterations == 0 )
+   {
+     bool const bcConsistent = validateDirichletBC( domain, time_n + dt );
+     GEOS_ERROR_IF( !bcConsistent, GEOS_FMT( "ImmiscibleMultiphaseFlow {}: inconsistent boundary conditions", getDataContext() ) );
+   }
+ 
+   FieldSpecificationManager & fsManager = FieldSpecificationManager::getInstance();
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & )
+   {
+ 
+     // 1. Apply pressure Dirichlet BCs, store in a separate field
+     applyFieldValue< ElementSubRegionBase >( time_n, dt, mesh, bcLogMessage,
+                                              fields::flow::pressure::key(), fields::flow::bcPressure::key() );
+     // 2. Apply saturation BC (phase volume fraction) and store in a separate field
+     applyFieldValue< ElementSubRegionBase >( time_n, dt, mesh, bcLogMessage,
+                                              fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key(),
+                                              fields::immiscibleMultiphaseFlow::bcPhaseVolumeFraction::key() );
+ 
+     globalIndex const rankOffset = dofManager.rankOffset();
+     string const dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
+ 
+     // 3. Call constitutive update
+     fsManager.apply< ElementSubRegionBase >( time_n + dt,
+                                              mesh,
+                                              fields::flow::pressure::key(),
+                                              [&] ( FieldSpecificationBase const &,
+                                                    string const &,
+                                                    SortedArrayView< localIndex const > const & targetSet,
+                                                    ElementSubRegionBase & subRegion,
+                                                    string const & )
+     {
+ 
+       arrayView1d< real64 const > const bcPres =
+         subRegion.getReference< array1d< real64 > >( fields::flow::bcPressure::key() );
+       arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const bcPhaseVolFraction =
+         subRegion.getReference< array2d< real64, immiscibleFlow::LAYOUT_PHASE > >(
+           fields::immiscibleMultiphaseFlow::bcPhaseVolumeFraction::key() );
+ 
+       arrayView1d< integer const > const ghostRank =
+         subRegion.getReference< array1d< integer > >( ObjectManagerBase::viewKeyStruct::ghostRankString() );
+       arrayView1d< globalIndex const > const dofNumber =
+         subRegion.getReference< array1d< globalIndex > >( dofKey );
+       arrayView1d< real64 const > const pres =
+         subRegion.getReference< array1d< real64 > >( fields::flow::pressure::key() );
+       arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFraction =
+         subRegion.getReference< array2d< real64, immiscibleFlow::LAYOUT_PHASE > >(
+           fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() );
+ 
+       integer const numPhase = m_numPhases;
+ 
+ 
+       forAll< parallelDevicePolicy<> >( targetSet.size(), [=] GEOS_HOST_DEVICE ( localIndex const a )
+       {
+         localIndex const ei = targetSet[a];
+         if( ghostRank[ei] >= 0 )
+         {
+           return;
+         }
+ 
+         globalIndex const dofIndex = dofNumber[ei];
+         localIndex const localRow = dofIndex - rankOffset;
+         real64 rhsValue;
+ 
+         // 3.1. Apply pressure value to the matrix/rhs
+         FieldSpecificationEqual::SpecifyFieldValue( dofIndex,
+                                                     rankOffset,
+                                                     localMatrix,
+                                                     rhsValue,
+                                                     bcPres[ei],
+                                                     pres[ei] );
+         localRhs[localRow] = rhsValue;
+ 
+         // 3.2. For each phase, apply target saturation value
+         for( integer ip = 0; ip < numPhase-1; ++ip )
+         {
+           FieldSpecificationEqual::SpecifyFieldValue( dofIndex + ip + 1,
+                                                       rankOffset,
+                                                       localMatrix,
+                                                       rhsValue,
+                                                       bcPhaseVolFraction[ei][ip],
+                                                       phaseVolFraction[ei][ip] );
+           localRhs[localRow + ip + 1] = rhsValue;
+         }
+       } );
+     } );
+   } );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::applySourceFluxBC( real64 const time,
+                                                   real64 const dt,
+                                                   DofManager const & dofManager,
+                                                   DomainPartition & domain,
+                                                   CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                                                   arrayView1d< real64 > const & localRhs ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   FieldSpecificationManager & fsManager = FieldSpecificationManager::getInstance();
+ 
+   string const dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
+ 
+   // Step 1: count individual source flux boundary conditions
+ 
+   stdMap< string, localIndex > bcNameToBcId;
+   localIndex bcCounter = 0;
+ 
   fsManager.forSubGroups< SourceFluxBoundaryCondition >( [&] ( SourceFluxBoundaryCondition const & bc )
   {
     // collect all the bc names to idx
     bcNameToBcId.insert( {bc.getName(), bcCounter} );
     bcCounter++;
   } );
-
-  if( bcCounter == 0 )
-  {
-    return;
-  }
-
-  // Step 2: count the set size for each source flux (each source flux may have multiple target sets)
-
-  array1d< globalIndex > bcAllSetsSize( bcNameToBcId.size() );
-
-  computeSourceFluxSizeScalingFactor( time,
-                                      dt,
-                                      domain,
-                                      bcNameToBcId,
-                                      bcAllSetsSize.toView() );
-
-  // Step 3: we are ready to impose the boundary condition, normalized by the set size
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & )
-  {
-
-    fsManager.apply< ElementSubRegionBase,
-                     SourceFluxBoundaryCondition >( time + dt,
-                                                    mesh,
-                                                    SourceFluxBoundaryCondition::catalogName(),
-                                                    [&]( SourceFluxBoundaryCondition const & fs,
-                                                         string const & setName,
-                                                         SortedArrayView< localIndex const > const & targetSet,
-                                                         ElementSubRegionBase & subRegion,
-                                                         string const & )
-    {
-      if( fs.getLogLevel() >= 1 && m_nonlinearSolverParameters.m_numNewtonIterations == 0 )
-      {
-        globalIndex const numTargetElems = MpiWrapper::sum< globalIndex >( targetSet.size() );
-        GEOS_LOG_RANK_0( GEOS_FMT( bcLogMessage,
-                                   getName(), time+dt, fs.getCatalogName(), fs.getName(),
-                                   setName, subRegion.getName(), fs.getScale(), numTargetElems ) );
-      }
-
-      if( targetSet.size() == 0 )
-      {
-        return;
-      }
-      if( !subRegion.hasWrapper( dofKey ) )
-      {
-        if( fs.getLogLevel() >= 1 )
-        {
-          GEOS_LOG_RANK( GEOS_FMT( "{}: trying to apply SourceFlux, but its targetSet named '{}' intersects with non-simulated region named '{}'.",
-                                   getDataContext(), setName, subRegion.getName() ) );
-        }
-        return;
-      }
-
-      arrayView1d< globalIndex const > const dofNumber = subRegion.getReference< array1d< globalIndex > >( dofKey );
-      arrayView1d< integer const > const ghostRank = subRegion.ghostRank();
-
-      // Step 3.1: get the values of the source boundary condition that need to be added to the rhs
-
-      array1d< globalIndex > dofArray( targetSet.size() );
-      array1d< real64 > rhsContributionArray( targetSet.size() );
-      arrayView1d< real64 > rhsContributionArrayView = rhsContributionArray.toView();
-      localIndex const rankOffset = dofManager.rankOffset();
-
-      RAJA::ReduceSum< parallelDeviceReduce, real64 > massProd( 0.0 );
-
-      // note that the dofArray will not be used after this step (simpler to use dofNumber instead)
-      fs.computeRhsContribution< FieldSpecificationAdd,
-                                 parallelDevicePolicy<> >( targetSet.toViewConst(),
-                                                           time + dt,
-                                                           dt,
-                                                           subRegion,
-                                                           dofNumber,
-                                                           rankOffset,
-                                                           localMatrix,
-                                                           dofArray.toView(),
-                                                           rhsContributionArrayView,
-                                                           [] GEOS_HOST_DEVICE ( localIndex const )
-      {
-        return 0.0;
-      } );
-
-      // Step 3.2: we are ready to add the right-hand side contributions, taking into account our equation layout
-
-      // get the normalizer
-      real64 const sizeScalingFactor = bcAllSetsSize[bcNameToBcId.at( fs.getName())];
-      integer const fluidPhaseId = fs.getComponent();
-      integer const numFluidPhases = m_numPhases;
-      integer useTotalMassEquation = m_useTotalMassEquation;
-      forAll< parallelDevicePolicy<> >( targetSet.size(), [sizeScalingFactor,
-                                                           targetSet,
-                                                           rankOffset,
-                                                           ghostRank,
-                                                           fluidPhaseId,
-                                                           numFluidPhases,
-                                                           useTotalMassEquation,
-                                                           dofNumber,
-                                                           rhsContributionArrayView,
-                                                           localRhs,
-                                                           massProd] GEOS_HOST_DEVICE ( localIndex const a )
-      {
-        // we need to filter out ghosts here, because targetSet may contain them
-        localIndex const ei = targetSet[a];
-        if( ghostRank[ei] >= 0 )
-        {
-          return;
-        }
-
-        real64 const rhsValue = rhsContributionArrayView[a] / sizeScalingFactor; // scale the contribution by the sizeScalingFactor here!
-        massProd += rhsValue;
-        if( useTotalMassEquation > 0 )
-        {
-          // for all "fluid components", we add the value to the total mass balance equation
-          globalIndex const totalMassBalanceRow = dofNumber[ei] - rankOffset;
-          localRhs[totalMassBalanceRow] += rhsValue;
-          if( fluidPhaseId < numFluidPhases - 1 )
-          {
-            globalIndex const compMassBalanceRow = totalMassBalanceRow + fluidPhaseId + 1; // component mass bal equations are shifted
-            localRhs[compMassBalanceRow] += rhsValue;
-          }
-        }
-        else
-        {
-          globalIndex const compMassBalanceRow = dofNumber[ei] - rankOffset + fluidPhaseId;
-          localRhs[compMassBalanceRow] += rhsValue;
-        }
-      } );
-
-      SourceFluxStatsAggregator::forAllFluxStatWrappers( subRegion, fs.getName(),
-                                                         [&]( SourceFluxStatsAggregator::WrappedStats & wrapper )
-      {
-        // set the new sub-region statistics for this timestep
-        array1d< real64 > massProdArr{ m_numPhases };
-        massProdArr[fluidPhaseId] = massProd.get();
-        wrapper.gatherTimeStepStats( time, dt, massProdArr.toViewConst(), targetSet.size() );
-      } );
-    } );
-  } );
-}
-
-real64 ImmiscibleMultiphaseFlow::calculateResidualNorm( real64 const & GEOS_UNUSED_PARAM( time_n ),
-                                                        real64 const & GEOS_UNUSED_PARAM( dt ),
-                                                        DomainPartition const & domain,
-                                                        DofManager const & dofManager,
-                                                        arrayView1d< real64 const > const & localRhs )
-{
-  GEOS_MARK_FUNCTION;
-  array1d< real64 > localResidualNorm;
-  array1d< real64 > localResidualNormalizer;
-  localResidualNorm.resize( numNorm );
-  localResidualNormalizer.resize( numNorm );
-
-  physicsSolverBaseKernels::NormType const normType = getNonlinearSolverParameters().normType();
-
-  globalIndex const rankOffset = dofManager.rankOffset();
-  string const dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel const & mesh,
-                                                               string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions( regionNames,
-                                                [&]( localIndex const,
-                                                     ElementSubRegionBase const & subRegion )
-    {
-      real64 subRegionResidualNorm[numNorm]{};
-      real64 subRegionResidualNormalizer[numNorm]{};
-
-      string const & solidName = subRegion.getReference< string >( viewKeyStruct::solidNamesString() );
-      CoupledSolidBase const & solid = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
-
-      // step 1: compute the norm in the subRegion
-
-      real64 subRegionFlowResidualNorm[1]{};
-      real64 subRegionFlowResidualNormalizer[1]{};
-
-      immiscibleMultiphaseKernels::
-        ResidualNormKernelFactory::createAndLaunch< parallelDevicePolicy<> >( normType,
-                                                                              2,
-                                                                              rankOffset,
-                                                                              dofKey,
-                                                                              localRhs,
-                                                                              subRegion,
-                                                                              solid,
-                                                                              m_nonlinearSolverParameters.m_minNormalizer,
-                                                                              subRegionFlowResidualNorm,
-                                                                              subRegionFlowResidualNormalizer );
-      subRegionResidualNorm[0] = subRegionFlowResidualNorm[0];
-      subRegionResidualNormalizer[0] = subRegionFlowResidualNormalizer[0];
-
-      // step 2: first reduction across meshBodies/regions/subRegions
-      if( normType == physicsSolverBaseKernels::NormType::Linf )
-      {
-        physicsSolverBaseKernels::LinfResidualNormHelper::
-          updateLocalNorm< numNorm >( subRegionResidualNorm, localResidualNorm );
-      }
-      else
-      {
-        physicsSolverBaseKernels::L2ResidualNormHelper::
-          updateLocalNorm< numNorm >( subRegionResidualNorm, subRegionResidualNormalizer, localResidualNorm, localResidualNormalizer );
-      }
-    } );
-  } );
-
-  real64 residualNorm = 0.0;
-  residualNorm = localResidualNorm[0];
-  if( normType == physicsSolverBaseKernels::NormType::Linf )
-  {
-    physicsSolverBaseKernels::LinfResidualNormHelper::computeGlobalNorm( localResidualNorm[0], residualNorm );
-  }
-  else
-  {
-    physicsSolverBaseKernels::L2ResidualNormHelper::computeGlobalNorm( localResidualNorm[0], localResidualNormalizer[0], residualNorm );
-  }
-
+ 
+   if( bcCounter == 0 )
+   {
+     return;
+   }
+ 
+   // Step 2: count the set size for each source flux (each source flux may have multiple target sets)
+ 
+   array1d< globalIndex > bcAllSetsSize( bcNameToBcId.size() );
+ 
+   computeSourceFluxSizeScalingFactor( time,
+                                       dt,
+                                       domain,
+                                       bcNameToBcId,
+                                       bcAllSetsSize.toView() );
+ 
+   // Step 3: we are ready to impose the boundary condition, normalized by the set size
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & )
+   {
+ 
+     fsManager.apply< ElementSubRegionBase,
+                      SourceFluxBoundaryCondition >( time + dt,
+                                                     mesh,
+                                                     SourceFluxBoundaryCondition::catalogName(),
+                                                     [&]( SourceFluxBoundaryCondition const & fs,
+                                                          string const & setName,
+                                                          SortedArrayView< localIndex const > const & targetSet,
+                                                          ElementSubRegionBase & subRegion,
+                                                          string const & )
+     {
+       if( fs.getLogLevel() >= 1 && m_nonlinearSolverParameters.m_numNewtonIterations == 0 )
+       {
+         globalIndex const numTargetElems = MpiWrapper::sum< globalIndex >( targetSet.size() );
+         GEOS_LOG_RANK_0( GEOS_FMT( bcLogMessage,
+                                    getName(), time+dt, fs.getCatalogName(), fs.getName(),
+                                    setName, subRegion.getName(), fs.getScale(), numTargetElems ) );
+       }
+ 
+       if( targetSet.size() == 0 )
+       {
+         return;
+       }
+       if( !subRegion.hasWrapper( dofKey ) )
+       {
+         if( fs.getLogLevel() >= 1 )
+         {
+           GEOS_LOG_RANK( GEOS_FMT( "{}: trying to apply SourceFlux, but its targetSet named '{}' intersects with non-simulated region named '{}'.",
+                                    getDataContext(), setName, subRegion.getName() ) );
+         }
+         return;
+       }
+ 
+       arrayView1d< globalIndex const > const dofNumber = subRegion.getReference< array1d< globalIndex > >( dofKey );
+       arrayView1d< integer const > const ghostRank = subRegion.ghostRank();
+ 
+       // Step 3.1: get the values of the source boundary condition that need to be added to the rhs
+ 
+       array1d< globalIndex > dofArray( targetSet.size() );
+       array1d< real64 > rhsContributionArray( targetSet.size() );
+       arrayView1d< real64 > rhsContributionArrayView = rhsContributionArray.toView();
+       localIndex const rankOffset = dofManager.rankOffset();
+ 
+       RAJA::ReduceSum< parallelDeviceReduce, real64 > massProd( 0.0 );
+ 
+       // note that the dofArray will not be used after this step (simpler to use dofNumber instead)
+       fs.computeRhsContribution< FieldSpecificationAdd,
+                                  parallelDevicePolicy<> >( targetSet.toViewConst(),
+                                                            time + dt,
+                                                            dt,
+                                                            subRegion,
+                                                            dofNumber,
+                                                            rankOffset,
+                                                            localMatrix,
+                                                            dofArray.toView(),
+                                                            rhsContributionArrayView,
+                                                            [] GEOS_HOST_DEVICE ( localIndex const )
+       {
+         return 0.0;
+       } );
+ 
+       // Step 3.2: we are ready to add the right-hand side contributions, taking into account our equation layout
+ 
+       // get the normalizer
+       real64 const sizeScalingFactor = bcAllSetsSize[bcNameToBcId.at( fs.getName())];
+       integer const fluidPhaseId = fs.getComponent();
+       integer const numFluidPhases = m_numPhases;
+       integer useTotalMassEquation = m_useTotalMassEquation;
+       forAll< parallelDevicePolicy<> >( targetSet.size(), [sizeScalingFactor,
+                                                            targetSet,
+                                                            rankOffset,
+                                                            ghostRank,
+                                                            fluidPhaseId,
+                                                            numFluidPhases,
+                                                            useTotalMassEquation,
+                                                            dofNumber,
+                                                            rhsContributionArrayView,
+                                                            localRhs,
+                                                            massProd] GEOS_HOST_DEVICE ( localIndex const a )
+       {
+         // we need to filter out ghosts here, because targetSet may contain them
+         localIndex const ei = targetSet[a];
+         if( ghostRank[ei] >= 0 )
+         {
+           return;
+         }
+ 
+         real64 const rhsValue = rhsContributionArrayView[a] / sizeScalingFactor; // scale the contribution by the sizeScalingFactor here!
+         massProd += rhsValue;
+         if( useTotalMassEquation > 0 )
+         {
+           // for all "fluid components", we add the value to the total mass balance equation
+           globalIndex const totalMassBalanceRow = dofNumber[ei] - rankOffset;
+           localRhs[totalMassBalanceRow] += rhsValue;
+           if( fluidPhaseId < numFluidPhases - 1 )
+           {
+             globalIndex const compMassBalanceRow = totalMassBalanceRow + fluidPhaseId + 1; // component mass bal equations are shifted
+             localRhs[compMassBalanceRow] += rhsValue;
+           }
+         }
+         else
+         {
+           globalIndex const compMassBalanceRow = dofNumber[ei] - rankOffset + fluidPhaseId;
+           localRhs[compMassBalanceRow] += rhsValue;
+         }
+       } );
+ 
+       SourceFluxStatsAggregator::forAllFluxStatWrappers( subRegion, fs.getName(),
+                                                          [&]( SourceFluxStatsAggregator::WrappedStats & wrapper )
+       {
+         // set the new sub-region statistics for this timestep
+         array1d< real64 > massProdArr{ m_numPhases };
+         massProdArr[fluidPhaseId] = massProd.get();
+         wrapper.gatherTimeStepStats( time, dt, massProdArr.toViewConst(), targetSet.size() );
+       } );
+     } );
+   } );
+ }
+ 
+ real64 ImmiscibleMultiphaseFlow::calculateResidualNorm( real64 const & GEOS_UNUSED_PARAM( time_n ),
+                                                         real64 const & GEOS_UNUSED_PARAM( dt ),
+                                                         DomainPartition const & domain,
+                                                         DofManager const & dofManager,
+                                                         arrayView1d< real64 const > const & localRhs )
+ {
+   GEOS_MARK_FUNCTION;
+   array1d< real64 > localResidualNorm;
+   array1d< real64 > localResidualNormalizer;
+   localResidualNorm.resize( numNorm );
+   localResidualNormalizer.resize( numNorm );
+ 
+   physicsSolverBaseKernels::NormType const normType = getNonlinearSolverParameters().normType();
+ 
+   globalIndex const rankOffset = dofManager.rankOffset();
+   string const dofKey = dofManager.getKey( viewKeyStruct::elemDofFieldString() );
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel const & mesh,
+                                                                string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions( regionNames,
+                                                 [&]( localIndex const,
+                                                      ElementSubRegionBase const & subRegion )
+     {
+       real64 subRegionResidualNorm[numNorm]{};
+       real64 subRegionResidualNormalizer[numNorm]{};
+ 
+       string const & solidName = subRegion.getReference< string >( viewKeyStruct::solidNamesString() );
+       CoupledSolidBase const & solid = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
+ 
+       // step 1: compute the norm in the subRegion
+ 
+       real64 subRegionFlowResidualNorm[1]{};
+       real64 subRegionFlowResidualNormalizer[1]{};
+ 
+       immiscibleMultiphaseKernels::
+         ResidualNormKernelFactory::createAndLaunch< parallelDevicePolicy<> >( normType,
+                                                                               2,
+                                                                               rankOffset,
+                                                                               dofKey,
+                                                                               localRhs,
+                                                                               subRegion,
+                                                                               solid,
+                                                                               m_nonlinearSolverParameters.m_minNormalizer,
+                                                                               subRegionFlowResidualNorm,
+                                                                               subRegionFlowResidualNormalizer );
+       subRegionResidualNorm[0] = subRegionFlowResidualNorm[0];
+       subRegionResidualNormalizer[0] = subRegionFlowResidualNormalizer[0];
+ 
+       // step 2: first reduction across meshBodies/regions/subRegions
+       if( normType == physicsSolverBaseKernels::NormType::Linf )
+       {
+         physicsSolverBaseKernels::LinfResidualNormHelper::
+           updateLocalNorm< numNorm >( subRegionResidualNorm, localResidualNorm );
+       }
+       else
+       {
+         physicsSolverBaseKernels::L2ResidualNormHelper::
+           updateLocalNorm< numNorm >( subRegionResidualNorm, subRegionResidualNormalizer, localResidualNorm, localResidualNormalizer );
+       }
+     } );
+   } );
+ 
+   real64 residualNorm = 0.0;
+   residualNorm = localResidualNorm[0];
+   if( normType == physicsSolverBaseKernels::NormType::Linf )
+   {
+     physicsSolverBaseKernels::LinfResidualNormHelper::computeGlobalNorm( localResidualNorm[0], residualNorm );
+   }
+   else
+   {
+     physicsSolverBaseKernels::L2ResidualNormHelper::computeGlobalNorm( localResidualNorm[0], localResidualNormalizer[0], residualNorm );
+   }
+ 
   GEOS_LOG_LEVEL_RANK_0_NLR( logInfo::ResidualNorm, GEOS_FMT( "        ( R{} ) = ( {:4.2e} )",
                                                               coupledSolverAttributePrefix(), residualNorm ))
-
-  getConvergenceStats().setResidualValue( GEOS_FMT( "R{}", coupledSolverAttributePrefix()), residualNorm );
-
-  return residualNorm;
-}
-
-void ImmiscibleMultiphaseFlow::applySystemSolution( DofManager const & dofManager,
-                                                    arrayView1d< real64 const > const & localSolution,
-                                                    real64 const scalingFactor,
-                                                    real64 const dt,
-                                                    DomainPartition & domain )
-{
-  GEOS_UNUSED_VAR( dt );
-
-  DofManager::CompMask pressureMask( m_numDofPerCell, 0, 1 );
-
-  // 1. apply the pressure update
-  dofManager.addVectorToField( localSolution,
-                               viewKeyStruct::elemDofFieldString(),
-                               fields::flow::pressure::key(),
-                               scalingFactor,
-                               pressureMask );
-
-  // 2. apply the phaseVolumeFraction update
-  dofManager.addVectorToField( localSolution,
-                               viewKeyStruct::elemDofFieldString(),
-                               fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key(),
-                               scalingFactor,
-                               ~pressureMask );
-
-  // 3. synchronize
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&] ( string const &,
+ 
+   return residualNorm;
+ }
+ 
+ void ImmiscibleMultiphaseFlow::applySystemSolution( DofManager const & dofManager,
+                                                     arrayView1d< real64 const > const & localSolution,
+                                                     real64 const scalingFactor,
+                                                     real64 const dt,
+                                                     DomainPartition & domain )
+ {
+   GEOS_UNUSED_VAR( dt );
+ 
+   DofManager::CompMask pressureMask( m_numDofPerCell, 0, 1 );
+ 
+   // 1. apply the pressure update
+   dofManager.addVectorToField( localSolution,
+                                viewKeyStruct::elemDofFieldString(),
+                                fields::flow::pressure::key(),
+                                scalingFactor,
+                                pressureMask );
+ 
+   // 2. apply the phaseVolumeFraction update
+   dofManager.addVectorToField( localSolution,
+                                viewKeyStruct::elemDofFieldString(),
+                                fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key(),
+                                scalingFactor,
+                                ~pressureMask );
+ 
+   // 3. synchronize
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&] ( string const &,
+                                                                 MeshLevel & mesh,
+                                                                 string_array const & regionNames )
+   {
+     std::vector< string > fields{ fields::flow::pressure::key(), fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() };
+ 
+     FieldIdentifiers fieldsToBeSync;
+     fieldsToBeSync.addElementFields( fields, regionNames );
+ 
+     CommunicationTools::getInstance().synchronizeFields( fieldsToBeSync, mesh, domain.getNeighbors(), true );
+   } );
+ }
+ 
+ 
+ void ImmiscibleMultiphaseFlow::updateVolumeConstraint( ElementSubRegionBase & subRegion ) const
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolumeFraction = subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+ 
+   forAll< parallelDevicePolicy<> >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const ei )
+   {
+     phaseVolumeFraction[ei][0] = fmin( 1.0, fmax( phaseVolumeFraction[ei][0], 0.0 )); ;
+     phaseVolumeFraction[ei][1] = 1.0 - phaseVolumeFraction[ei][0];
+   } );
+ }
+ 
+ 
+ void ImmiscibleMultiphaseFlow::resetStateToBeginningOfStep( DomainPartition & domain )
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
                                                                 MeshLevel & mesh,
                                                                 string_array const & regionNames )
-  {
-    stdVector< string > fields{ fields::flow::pressure::key(), fields::immiscibleMultiphaseFlow::phaseVolumeFraction::key() };
-
-    FieldIdentifiers fieldsToBeSync;
-    fieldsToBeSync.addElementFields( fields, regionNames );
-
-    CommunicationTools::getInstance().synchronizeFields( fieldsToBeSync, mesh, domain.getNeighbors(), true );
-  } );
-}
-
-
-void ImmiscibleMultiphaseFlow::updateVolumeConstraint( ElementSubRegionBase & subRegion ) const
-{
-  GEOS_MARK_FUNCTION;
-
-  arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolumeFraction = subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-
-  forAll< parallelDevicePolicy<> >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const ei )
-  {
-    phaseVolumeFraction[ei][1] = 1.0 - phaseVolumeFraction[ei][0];
-  } );
-}
-
-
-void ImmiscibleMultiphaseFlow::resetStateToBeginningOfStep( DomainPartition & domain )
-{
-  GEOS_MARK_FUNCTION;
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions< CellElementSubRegion,
-                                                SurfaceElementSubRegion >( regionNames,
-                                                                           [&]( localIndex const,
-                                                                                auto & subRegion )
-    {
-      arrayView1d< real64 > const & pres =
-        subRegion.template getField< fields::flow::pressure >();
-      arrayView1d< real64 const > const & pres_n =
-        subRegion.template getField< fields::flow::pressure_n >();
-      pres.setValues< parallelDevicePolicy<> >( pres_n );
-
-      // after the update, save the new saturation
-      arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac_n =
-        subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction_n >();
-
-      arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolFrac =
-        subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-      phaseVolFrac.setValues< parallelDevicePolicy<> >( phaseVolFrac_n );
-
-      arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const & phaseMass_n =
-        subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseMass_n >();
-
-      arrayView2d< real64, immiscibleFlow::USD_PHASE > const & phaseMass =
-        subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseMass >();
-      phaseMass.setValues< parallelDevicePolicy<> >( phaseMass_n );
-
-      if( m_isThermal )
-      {
-        arrayView1d< real64 > const & temp =
-          subRegion.template getField< fields::flow::temperature >();
-        arrayView1d< real64 const > const & temp_n =
-          subRegion.template getField< fields::flow::temperature_n >();
-        temp.setValues< parallelDevicePolicy<> >( temp_n );
-      }
-
-      // update porosity, permeability
-      updatePorosityAndPermeability( subRegion );
-      // update all fluid properties
-      updateFluidState( subRegion );
-    } );
-  } );
-}
-
-void ImmiscibleMultiphaseFlow::implicitStepComplete( real64 const & time,
-                                                     real64 const & dt,
-                                                     DomainPartition & domain )
-{
-  // Step 1: save the converged aquifer state
-  // note: we have to save the aquifer state **before** updating the pressure,
-  // otherwise the aquifer flux is saved with the wrong pressure time level
-  saveAquiferConvergedState( time, dt, domain );
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions( regionNames,
-                                                [&]( localIndex const,
-                                                     ElementSubRegionBase & subRegion )
-    {
-      // Step 3: save the converged solid state
-      string const & solidName = subRegion.getReference< string >( viewKeyStruct::solidNamesString() );
-      CoupledSolidBase const & porousMaterial = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
-      if( m_keepVariablesConstantDuringInitStep )
-      {
-        porousMaterial.ignoreConvergedState(); // newPorosity <- porosity_n
-      }
-      else
-      {
-        porousMaterial.saveConvergedState(); // porosity_n <- porosity
-      }
-
-      // Step 4: save converged state for the relperm model to handle hysteresis
-      arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
-        subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-      string const & relPermName = subRegion.getReference< string >( viewKeyStruct::relPermNamesString() );
-      RelativePermeabilityBase const & relPermMaterial =
-        getConstitutiveModel< RelativePermeabilityBase >( subRegion, relPermName );
-      relPermMaterial.saveConvergedPhaseVolFractionState( phaseVolFrac );
-
-      // Step 5: if capillary pressure is supported, send the converged porosity and permeability to the capillary pressure model
-      // note: this is needed when the capillary pressure depends on porosity and permeability (Leverett J-function for instance)
-      if( m_hasCapPressure )
-      {
+   {
+     mesh.getElemManager().forElementSubRegions< CellElementSubRegion,
+                                                 SurfaceElementSubRegion >( regionNames,
+                                                                            [&]( localIndex const,
+                                                                                 auto & subRegion )
+     {
+       arrayView1d< real64 > const & pres =
+         subRegion.template getField< fields::flow::pressure >();
+       arrayView1d< real64 const > const & pres_n =
+         subRegion.template getField< fields::flow::pressure_n >();
+       pres.setValues< parallelDevicePolicy<> >( pres_n );
+ 
+       // after the update, save the new saturation
+       arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac_n =
+         subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction_n >();
+ 
+       arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolFrac =
+         subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+       phaseVolFrac.setValues< parallelDevicePolicy<> >( phaseVolFrac_n );
+ 
+       arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const & phaseMass_n =
+         subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseMass_n >();
+ 
+       arrayView2d< real64, immiscibleFlow::USD_PHASE > const & phaseMass =
+         subRegion.template getField< fields::immiscibleMultiphaseFlow::phaseMass >();
+       phaseMass.setValues< parallelDevicePolicy<> >( phaseMass_n );
+ 
+       if( m_isThermal )
+       {
+         arrayView1d< real64 > const & temp =
+           subRegion.template getField< fields::flow::temperature >();
+         arrayView1d< real64 const > const & temp_n =
+           subRegion.template getField< fields::flow::temperature_n >();
+         temp.setValues< parallelDevicePolicy<> >( temp_n );
+       }
+ 
+       // update porosity, permeability
+       updatePorosityAndPermeability( subRegion );
+       // update all fluid properties
+       updateFluidState( subRegion );
+     } );
+   } );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::implicitStepComplete( real64 const & time,
+                                                      real64 const & dt,
+                                                      DomainPartition & domain )
+ {
+   // Step 1: save the converged aquifer state
+   // note: we have to save the aquifer state **before** updating the pressure,
+   // otherwise the aquifer flux is saved with the wrong pressure time level
+   saveAquiferConvergedState( time, dt, domain );
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions( regionNames,
+                                                 [&]( localIndex const,
+                                                      ElementSubRegionBase & subRegion )
+     {
+       // Step 3: save the converged solid state
+       string const & solidName = subRegion.getReference< string >( viewKeyStruct::solidNamesString() );
+       CoupledSolidBase const & porousMaterial = getConstitutiveModel< CoupledSolidBase >( subRegion, solidName );
+       if( m_keepVariablesConstantDuringInitStep )
+       {
+         porousMaterial.ignoreConvergedState(); // newPorosity <- porosity_n
+       }
+       else
+       {
+         porousMaterial.saveConvergedState(); // porosity_n <- porosity
+       }
+ 
+       // Step 4: save converged state for the relperm model to handle hysteresis
+       arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
+         subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+       string const & relPermName = subRegion.getReference< string >( viewKeyStruct::relPermNamesString() );
+       RelativePermeabilityBase const & relPermMaterial =
+         getConstitutiveModel< RelativePermeabilityBase >( subRegion, relPermName );
+       relPermMaterial.saveConvergedPhaseVolFractionState( phaseVolFrac );
+ 
+       // Step 5: if capillary pressure is supported, send the converged porosity and permeability to the capillary pressure model
+       // note: this is needed when the capillary pressure depends on porosity and permeability (Leverett J-function for instance)
+       if( m_hasCapPressure )
+       {
         arrayView2d< real64 const > const porosity = porousMaterial.getPorosity();
 
         string const & permName = subRegion.getReference< string >( viewKeyStruct::permeabilityNamesString() );
@@ -1284,127 +1552,128 @@ void ImmiscibleMultiphaseFlow::implicitStepComplete( real64 const & time,
         CapillaryPressureBase const & capPressureMaterial =
           getConstitutiveModel< CapillaryPressureBase >( subRegion, capPressName );
         capPressureMaterial.saveConvergedRockState( porosity, permeability );
-      }
-    } );
-  } );
-
-}
-
-void ImmiscibleMultiphaseFlow::saveConvergedState( ElementSubRegionBase & subRegion ) const
-{
-  FlowSolverBase::saveConvergedState( subRegion );
-
-  arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
-    subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-  arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolFrac_n =
-    subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction_n >();
-  phaseVolFrac_n.setValues< parallelDevicePolicy<> >( phaseVolFrac );
-
-  arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseMass =
-    subRegion.getField< fields::immiscibleMultiphaseFlow::phaseMass >();
-  arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseMass_n =
-    subRegion.getField< fields::immiscibleMultiphaseFlow::phaseMass_n >();
-  phaseMass_n.setValues< parallelDevicePolicy<> >( phaseMass );
-
-}
-
-void ImmiscibleMultiphaseFlow::updateState( DomainPartition & domain )
-{
-  GEOS_MARK_FUNCTION;
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions< CellElementSubRegion,
-                                                SurfaceElementSubRegion >( regionNames, [&]( localIndex const,
-                                                                                             auto & subRegion )
-    {
-      // update porosity, permeability, and solid internal energy
-      updatePorosityAndPermeability( subRegion );
-      // update all fluid properties
-      updateVolumeConstraint( subRegion );
-      updateFluidState( subRegion );
-    } );
-  } );
-}
-
-real64 ImmiscibleMultiphaseFlow::setNextDtBasedOnStateChange( real64 const & currentDt,
-                                                              DomainPartition & domain )
-{
-  if( m_targetRelativePresChange >= 1.0 &&
-      m_targetPhaseVolFracChange >= 1.0 )
-  {
-    return LvArray::NumericLimits< real64 >::max;
-  }
-
-  real64 maxRelativePresChange = 0.0;
-  real64 maxAbsolutePhaseVolFracChange = 0.0;
-
-  integer const numPhase = m_numPhases;
-
-  forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
-                                                               MeshLevel & mesh,
-                                                               string_array const & regionNames )
-  {
-    mesh.getElemManager().forElementSubRegions( regionNames,
-                                                [&]( localIndex const,
-                                                     ElementSubRegionBase & subRegion )
-    {
-      arrayView1d< integer const > const ghostRank = subRegion.ghostRank();
-
-      arrayView1d< real64 const > const pres = subRegion.getField< fields::flow::pressure >();
-      arrayView1d< real64 const > const pres_n = subRegion.getField< fields::flow::pressure_n >();
-      arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
-        subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
-      arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolFrac_n =
-        subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction_n >();
-
-      RAJA::ReduceMax< parallelDeviceReduce, real64 > subRegionMaxPresChange( 0.0 );
-      RAJA::ReduceMax< parallelDeviceReduce, real64 > subRegionMaxPhaseVolFracChange( 0.0 );
-
-      forAll< parallelDevicePolicy<> >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const ei )
-      {
-        if( ghostRank[ei] < 0 )
-        {
-          // switch from relative to absolute when values less than 1
-          subRegionMaxPresChange.max( LvArray::math::abs( pres[ei] - pres_n[ei] ) / LvArray::math::max( LvArray::math::abs( pres_n[ei] ), 1.0 ) );
-          for( integer ip = 0; ip < numPhase; ++ip )
-          {
-            subRegionMaxPhaseVolFracChange.max( LvArray::math::abs( phaseVolFrac[ei][ip] - phaseVolFrac_n[ei][ip] ) );
-          }
-        }
-      } );
-
-      maxRelativePresChange = LvArray::math::max( maxRelativePresChange, subRegionMaxPresChange.get() );
-      maxAbsolutePhaseVolFracChange = LvArray::math::max( maxAbsolutePhaseVolFracChange, subRegionMaxPhaseVolFracChange.get() );
-
-    } );
-  } );
-
-  maxRelativePresChange = MpiWrapper::max( maxRelativePresChange );
-  maxAbsolutePhaseVolFracChange = MpiWrapper::max( maxAbsolutePhaseVolFracChange );
-
-  GEOS_LOG_LEVEL_RANK_0( logInfo::TimeStep, GEOS_FMT( "{}: max relative pressure change during time step = {} %",
-                                                      getName(), GEOS_FMT( "{:.{}f}", 100*maxRelativePresChange, 3 ) ) );
-  GEOS_LOG_LEVEL_RANK_0( logInfo::TimeStep, GEOS_FMT( "{}: max absolute phase volume fraction change during time step = {}",
-                                                      getName(), GEOS_FMT( "{:.{}f}", maxAbsolutePhaseVolFracChange, 3 ) ) );
-
-  real64 const eps = LvArray::NumericLimits< real64 >::epsilon;
-
-  real64 const nextDtPressure = currentDt * ( 1.0 + m_solutionChangeScalingFactor ) * m_targetRelativePresChange
-                                / std::max( eps, maxRelativePresChange + m_solutionChangeScalingFactor * m_targetRelativePresChange );
-  if( m_nonlinearSolverParameters.getLogLevel() > 0 )
-    GEOS_LOG_RANK_0( GEOS_FMT( "{}: next time step based on pressure change = {}", getName(), nextDtPressure ));
-  real64 const nextDtPhaseVolFrac = currentDt * ( 1.0 + m_solutionChangeScalingFactor ) * m_targetPhaseVolFracChange
-                                    / std::max( eps, maxAbsolutePhaseVolFracChange + m_solutionChangeScalingFactor * m_targetPhaseVolFracChange );
-  if( m_nonlinearSolverParameters.getLogLevel() > 0 )
-    GEOS_LOG_RANK_0( GEOS_FMT( "{}: next time step based on phase volume fraction change = {}", getName(), nextDtPhaseVolFrac ));
-
-  return std::min( nextDtPressure, nextDtPhaseVolFrac );
-
-}
-
-REGISTER_CATALOG_ENTRY( PhysicsSolverBase, ImmiscibleMultiphaseFlow, string const &, Group * const )
-
-} // namespace geos
+        capPressureMaterial.saveConvergedPhaseVolFractionState( phaseVolFrac );
+       }
+     } );
+   } );
+ }
+ 
+ void ImmiscibleMultiphaseFlow::saveConvergedState( ElementSubRegionBase & subRegion ) const
+ {
+   FlowSolverBase::saveConvergedState( subRegion );
+ 
+   arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
+     subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+   arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolFrac_n =
+     subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction_n >();
+   phaseVolFrac_n.setValues< parallelDevicePolicy<> >( phaseVolFrac );
+ 
+   arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseMass =
+     subRegion.getField< fields::immiscibleMultiphaseFlow::phaseMass >();
+   arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseMass_n =
+     subRegion.getField< fields::immiscibleMultiphaseFlow::phaseMass_n >();
+   phaseMass_n.setValues< parallelDevicePolicy<> >( phaseMass );
+ 
+ }
+ 
+ void ImmiscibleMultiphaseFlow::updateState( DomainPartition & domain )
+ {
+   GEOS_MARK_FUNCTION;
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions< CellElementSubRegion,
+                                                 SurfaceElementSubRegion >( regionNames, [&]( localIndex const,
+                                                                                              auto & subRegion )
+     {
+       // update porosity, permeability, and solid internal energy
+       updatePorosityAndPermeability( subRegion );
+       // update all fluid properties
+       updateVolumeConstraint( subRegion );
+       updateFluidState( subRegion );
+     } );
+   } );
+ }
+ 
+ real64 ImmiscibleMultiphaseFlow::setNextDtBasedOnStateChange( real64 const & currentDt,
+                                                               DomainPartition & domain )
+ {
+   if( m_targetRelativePresChange >= 1.0 &&
+       m_targetPhaseVolFracChange >= 1.0 )
+   {
+     return LvArray::NumericLimits< real64 >::max;
+   }
+ 
+   real64 maxRelativePresChange = 0.0;
+   real64 maxAbsolutePhaseVolFracChange = 0.0;
+ 
+   integer const numPhase = m_numPhases;
+ 
+   forDiscretizationOnMeshTargets( domain.getMeshBodies(), [&]( string const &,
+                                                                MeshLevel & mesh,
+                                                                string_array const & regionNames )
+   {
+     mesh.getElemManager().forElementSubRegions( regionNames,
+                                                 [&]( localIndex const,
+                                                      ElementSubRegionBase & subRegion )
+     {
+       arrayView1d< integer const > const ghostRank = subRegion.ghostRank();
+ 
+       arrayView1d< real64 const > const pres = subRegion.getField< fields::flow::pressure >();
+       arrayView1d< real64 const > const pres_n = subRegion.getField< fields::flow::pressure_n >();
+       arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const phaseVolFrac =
+         subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction >();
+       arrayView2d< real64, immiscibleFlow::USD_PHASE > const phaseVolFrac_n =
+         subRegion.getField< fields::immiscibleMultiphaseFlow::phaseVolumeFraction_n >();
+ 
+       RAJA::ReduceMax< parallelDeviceReduce, real64 > subRegionMaxPresChange( 0.0 );
+       RAJA::ReduceMax< parallelDeviceReduce, real64 > subRegionMaxPhaseVolFracChange( 0.0 );
+ 
+       forAll< parallelDevicePolicy<> >( subRegion.size(), [=] GEOS_HOST_DEVICE ( localIndex const ei )
+       {
+         if( ghostRank[ei] < 0 )
+         {
+           // switch from relative to absolute when values less than 1
+           subRegionMaxPresChange.max( LvArray::math::abs( pres[ei] - pres_n[ei] ) / LvArray::math::max( LvArray::math::abs( pres_n[ei] ), 1.0 ) );
+           for( integer ip = 0; ip < numPhase; ++ip )
+           {
+             subRegionMaxPhaseVolFracChange.max( LvArray::math::abs( phaseVolFrac[ei][ip] - phaseVolFrac_n[ei][ip] ) );
+           }
+         }
+       } );
+ 
+       maxRelativePresChange = LvArray::math::max( maxRelativePresChange, subRegionMaxPresChange.get() );
+       maxAbsolutePhaseVolFracChange = LvArray::math::max( maxAbsolutePhaseVolFracChange, subRegionMaxPhaseVolFracChange.get() );
+ 
+     } );
+   } );
+ 
+   maxRelativePresChange = MpiWrapper::max( maxRelativePresChange );
+   maxAbsolutePhaseVolFracChange = MpiWrapper::max( maxAbsolutePhaseVolFracChange );
+ 
+   GEOS_LOG_LEVEL_RANK_0( logInfo::TimeStep, GEOS_FMT( "{}: max relative pressure change during time step = {} %",
+                                                       getName(), GEOS_FMT( "{:.{}f}", 100*maxRelativePresChange, 3 ) ) );
+   GEOS_LOG_LEVEL_RANK_0( logInfo::TimeStep, GEOS_FMT( "{}: max absolute phase volume fraction change during time step = {}",
+                                                       getName(), GEOS_FMT( "{:.{}f}", maxAbsolutePhaseVolFracChange, 3 ) ) );
+ 
+   real64 const eps = LvArray::NumericLimits< real64 >::epsilon;
+ 
+   real64 const nextDtPressure = currentDt * ( 1.0 + m_solutionChangeScalingFactor ) * m_targetRelativePresChange
+                                 / std::max( eps, maxRelativePresChange + m_solutionChangeScalingFactor * m_targetRelativePresChange );
+   if( m_nonlinearSolverParameters.getLogLevel() > 0 )
+     GEOS_LOG_RANK_0( GEOS_FMT( "{}: next time step based on pressure change = {}", getName(), nextDtPressure ));
+   real64 const nextDtPhaseVolFrac = currentDt * ( 1.0 + m_solutionChangeScalingFactor ) * m_targetPhaseVolFracChange
+                                     / std::max( eps, maxAbsolutePhaseVolFracChange + m_solutionChangeScalingFactor * m_targetPhaseVolFracChange );
+   if( m_nonlinearSolverParameters.getLogLevel() > 0 )
+     GEOS_LOG_RANK_0( GEOS_FMT( "{}: next time step based on phase volume fraction change = {}", getName(), nextDtPhaseVolFrac ));
+ 
+   return std::min( nextDtPressure, nextDtPhaseVolFrac );
+ 
+ }
+ 
+ REGISTER_CATALOG_ENTRY( PhysicsSolverBase, ImmiscibleMultiphaseFlow, string const &, Group * const )
+ 
+ } // namespace geos
+ 
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp b/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp
index 7526130316c..b3769837600 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp
+++ b/src/coreComponents/physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlow.hpp
@@ -27,6 +27,12 @@
 namespace geos
 {
 
+
+namespace constitutive
+{
+class ConstitutiveBase;
+} // namespace constitutive
+
 //START_SPHINX_INCLUDE_00
 /**
  * @class ImmiscibleMultiphaseFlow
@@ -160,12 +166,11 @@ class ImmiscibleMultiphaseFlow : public FlowSolverBase
    * @param matrix the system matrix
    * @param rhs the system right-hand side vector
    */
-  virtual void
-  assembleFluxTerms( real64 const dt,
-                     DomainPartition const & domain,
-                     DofManager const & dofManager,
-                     CRSMatrixView< real64, globalIndex const > const & localMatrix,
-                     arrayView1d< real64 > const & localRhs ) const;
+  void assembleFluxTerms( real64 const dt,
+                          DomainPartition & domain,
+                          DofManager const & dofManager,
+                          CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                          arrayView1d< real64 > const & localRhs ) const;
 
   /**
    * @brief Function to perform the Application of Dirichlet type BC's
@@ -215,6 +220,10 @@ class ImmiscibleMultiphaseFlow : public FlowSolverBase
   struct viewKeyStruct : public FlowSolverBase::viewKeyStruct
   {
     // inputs
+    static constexpr char const * capPressureNamesString() { return "capPressureNames"; }
+    static constexpr char const * relPermNamesString() { return "relPermNames"; }
+    static constexpr char const * elemDofFieldString() { return "elemDofField"; }
+    static constexpr char const * interfaceFaceSetNamesString() { return "interfaceFaceSetNames"; }
 
     // density averaging scheme
     static constexpr char const * gravityDensitySchemeString()    { return "gravityDensityScheme"; }
@@ -228,9 +237,9 @@ class ImmiscibleMultiphaseFlow : public FlowSolverBase
     static constexpr char const * maxRelativePresChangeString() { return "maxRelativePressureChange"; }
     static constexpr char const * useTotalMassEquationString() { return "useTotalMassEquation"; }
 
-    static constexpr char const * capPressureNamesString() { return "capillary_pressure"; }
-    static constexpr char const * relPermNamesString() { return "relative_permeability"; }
-    static constexpr char const * elemDofFieldString() { return "elemDofField"; }
+//    static constexpr char const * capPressureNamesString() { return "capillary_pressure"; }
+//    static constexpr char const * relPermNamesString() { return "relative_permeability"; }
+//    static constexpr char const * elemDofFieldString() { return "elemDofField"; }
   };
 
 
@@ -300,6 +309,15 @@ class ImmiscibleMultiphaseFlow : public FlowSolverBase
   /// damping factor for solution change targets
   real64 m_solutionChangeScalingFactor;
 
+  string_array m_interfaceFaceSetNames;
+
+  stdVector< std::array< std::tuple< constitutive::RelativePermeabilityBase *,
+                                     constitutive::CapillaryPressureBase *,
+                                     constitutive::TwoPhaseImmiscibleFluid * >, 2 > >  m_interfaceConstitutivePairs;
+
+  unordered_map< localIndex, localIndex >  m_interfaceRegionByConnector;
+  unordered_map< localIndex, localIndex >  m_connectorIndicesByInterfaceRegion;
+
 
 private:
 
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/CapillaryPressureUpdateKernel.hpp b/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/CapillaryPressureUpdateKernel.hpp
new file mode 100644
index 00000000000..2a02f536ea9
--- /dev/null
+++ b/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/CapillaryPressureUpdateKernel.hpp
@@ -0,0 +1,73 @@
+/*
+ * ------------------------------------------------------------------------------------------------------------
+ * SPDX-License-Identifier: LGPL-2.1-only
+ *
+ * Copyright (c) 2016-2024 Lawrence Livermore National Security LLC
+ * Copyright (c) 2018-2024 TotalEnergies
+ * Copyright (c) 2018-2024 The Board of Trustees of the Leland Stanford Junior University
+ * Copyright (c) 2023-2024 Chevron
+ * Copyright (c) 2019-     GEOS/GEOSX Contributors
+ * All rights reserved
+ *
+ * See top level LICENSE, COPYRIGHT, CONTRIBUTORS, NOTICE, and ACKNOWLEDGEMENTS files for details.
+ * ------------------------------------------------------------------------------------------------------------
+ */
+
+/**
+ * @file CapillaryPressureUpdateKernel.hpp
+ */
+
+#ifndef GEOS_PHYSICSSOLVERS_FLUIDFLOW_IMMISCIBLEMULTIPHASE_CAPILLARYPRESSUREUPDATEKERNEL_HPP
+#define GEOS_PHYSICSSOLVERS_FLUIDFLOW_IMMISCIBLEMULTIPHASE_CAPILLARYPRESSUREUPDATEKERNEL_HPP
+
+#include "common/DataTypes.hpp"
+#include "common/GEOS_RAJA_Interface.hpp"
+
+namespace geos
+{
+
+namespace immiscibleMultiphaseKernels
+{
+
+/******************************** CapillaryPressureUpdateKernel ********************************/
+
+struct CapillaryPressureUpdateKernel
+{
+  template< typename POLICY, typename CAPPRES_WRAPPER >
+  static void
+  launch( localIndex const size,
+          CAPPRES_WRAPPER const & capPresWrapper,
+          arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const & phaseVolFrac )
+  {
+    forAll< POLICY >( size, [=] GEOS_HOST_DEVICE ( localIndex const k )
+    {
+      for( localIndex q = 0; q < capPresWrapper.numGauss(); ++q )
+      {
+        capPresWrapper.update( k, q, phaseVolFrac[k] );
+      }
+    } );
+  }
+
+  template< typename POLICY, typename CAPPRES_WRAPPER >
+  static void
+  launch( SortedArrayView< localIndex const > const & targetSet,
+          CAPPRES_WRAPPER const & capPresWrapper,
+          arrayView2d< real64 const, immiscibleFlow::USD_PHASE > const & phaseVolFrac )
+  {
+    forAll< POLICY >( targetSet.size(), [=] GEOS_HOST_DEVICE ( localIndex const a )
+    {
+      localIndex const k = targetSet[a];
+      for( localIndex q = 0; q < capPresWrapper.numGauss(); ++q )
+      {
+        capPresWrapper.update( k, q, phaseVolFrac[k] );
+      }
+    } );
+  }
+};
+
+} // namespace immiscibleMultiphaseKernels
+
+} // namespace geos
+
+
+#endif //GEOS_PHYSICSSOLVERS_FLUIDFLOW_IMMISCIBLEMULTIPHASE_CAPILLARYPRESSUREUPDATEKERNEL_HPP
diff --git a/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp b/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp
index ebb78332b43..0881a8b07ee 100644
--- a/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp
+++ b/src/coreComponents/physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/ImmiscibleMultiphaseKernels.hpp
@@ -17,39 +17,2201 @@
  * @file ImmiscibleMultiphaseKernels.hpp
  */
 
+
 #ifndef GEOS_PHYSICSSOLVERS_FLUIDFLOW_MULTIPHASEKERNELS_HPP
 #define GEOS_PHYSICSSOLVERS_FLUIDFLOW_MULTIPHASEKERNELS_HPP
 
-#include "codingUtilities/Utilities.hpp"
-#include "common/DataLayouts.hpp"
-#include "common/DataTypes.hpp"
-#include "common/GEOS_RAJA_Interface.hpp"
+
+ #include "codingUtilities/Utilities.hpp"
+ #include "common/DataLayouts.hpp"
+ #include "common/DataTypes.hpp"
+ #include "common/GEOS_RAJA_Interface.hpp"
+ #include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
+ #include "constitutive/solid/CoupledSolidBase.hpp"
+ #include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluidFields.hpp"
+ #include "constitutive/capillaryPressure/CapillaryPressureFields.hpp"
+ #include "constitutive/capillaryPressure/CapillaryPressureBase.hpp"
+ #include "constitutive/capillaryPressure/JFunctionCapillaryPressure.hpp"
+ #include "constitutive/capillaryPressure/TableCapillaryPressure.hpp"
+ #include "constitutive/capillaryPressure/TableCapillaryPressureHysteresis.hpp"
+ #include "constitutive/permeability/PermeabilityBase.hpp"
+ #include "constitutive/permeability/PermeabilityFields.hpp"
+ #include "constitutive/relativePermeability/RelativePermeabilityBase.hpp"
+ #include "constitutive/relativePermeability/RelativePermeabilityFields.hpp"
+ #include "constitutive/ConstitutiveManager.hpp"
+#include "constitutive/capillaryPressure/CapillaryPressureSelector.hpp"
+#include "constitutive/relativePermeability/RelativePermeabilitySelector.hpp"
+
+#include "constitutive/ConstitutivePassThru.hpp"
 #include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluid.hpp"
-#include "constitutive/solid/CoupledSolidBase.hpp"
-#include "constitutive/fluid/twophaseimmisciblefluid/TwoPhaseImmiscibleFluidFields.hpp"
-#include "constitutive/capillaryPressure/CapillaryPressureFields.hpp"
-#include "constitutive/capillaryPressure/CapillaryPressureBase.hpp"
-#include "constitutive/permeability/PermeabilityBase.hpp"
-#include "constitutive/permeability/PermeabilityFields.hpp"
-#include "constitutive/relativePermeability/RelativePermeabilityBase.hpp"
-#include "constitutive/relativePermeability/RelativePermeabilityFields.hpp"
-#include "fieldSpecification/AquiferBoundaryCondition.hpp"
-#include "finiteVolume/BoundaryStencil.hpp"
-#include "finiteVolume/FluxApproximationBase.hpp"
-#include "linearAlgebra/interfaces/InterfaceTypes.hpp"
-#include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
-#include "physicsSolvers/fluidFlow/FlowSolverBaseFields.hpp"
-#include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlowFields.hpp"
-#include "physicsSolvers/fluidFlow/CompositionalMultiphaseUtilities.hpp"
-#include "physicsSolvers/fluidFlow/StencilAccessors.hpp"
-#include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/KernelLaunchSelectors.hpp"
+
+
+ #include "fieldSpecification/AquiferBoundaryCondition.hpp"
+ #include "finiteVolume/BoundaryStencil.hpp"
+ #include "finiteVolume/CellElementStencilTPFA.hpp"
+ #include "finiteVolume/FluxApproximationBase.hpp"
+ #include "linearAlgebra/interfaces/InterfaceTypes.hpp"
+ #include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
+ #include "physicsSolvers/fluidFlow/FlowSolverBaseFields.hpp"
+ #include "physicsSolvers/fluidFlow/ImmiscibleMultiphaseFlowFields.hpp"
+ #include "physicsSolvers/fluidFlow/CompositionalMultiphaseUtilities.hpp"
+ #include "physicsSolvers/fluidFlow/StencilAccessors.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/compositional/RelativePermeabilityUpdateKernel.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/compositional/CapillaryPressureUpdateKernel.hpp"
+ #include "physicsSolvers/PhysicsSolverBaseKernels.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/KernelLaunchSelectors.hpp"
+ #include "physicsSolvers/fluidFlow/kernels/immiscibleMultiphase/KernelLaunchSelectors.hpp"
+
 
 namespace geos
 {
 namespace immiscibleMultiphaseKernels
 {
+
 using namespace constitutive;
 
+GEOS_HOST_DEVICE
+inline
+constexpr bool ENABLE_LOCAL_SOLVER_DEBUG = false;
+
+static void local_solver( real64 uT, stdVector< real64 > saturations, stdVector< real64 > pressures, stdVector< real64 > JFMultipliers, stdVector< real64 > trappedSats1,
+                          stdVector< real64 > trappedSats2, stdVector< fields::cappres::ModeIndexType> modes, stdVector< real64 > transHat, stdVector< real64 > dTransHat_dP, stdVector< real64 > gravCoefHat, stdVector< real64 > gravCoef,
+                          stdVector< real64 >  cellCenterDuT, stdVector< real64 > cellCenterDens, stdVector< real64 > cellCenterDens_dP,
+                          std::vector< RelativePermeabilityBase * > relPerms, std::vector< CapillaryPressureBase * > capPressures,
+                          std::vector< TwoPhaseImmiscibleFluid * > fluids, std::vector< real64 > &phi, std::vector< real64 > &grad_phi_P, std::vector< real64 > &grad_phi_S, bool &converged,
+                          stdVector< real64 > const & phaseMaxHistVolFrac1, stdVector< real64 > const & phaseMinHistVolFrac1,
+                          stdVector< real64 > const & phaseMaxHistVolFrac2, stdVector< real64 > const & phaseMinHistVolFrac2,
+                          real64 & warmStartPc )
+{
+
+  // getting wrappers:
+
+  constitutive::constitutiveUpdatePassThru( *capPressures[0], [&] ( auto & castedCapPres1 )
+  {
+    auto capPresWrapper1 = castedCapPres1.createKernelWrapper();
+
+
+    constitutive::constitutiveUpdatePassThru( *capPressures[1], [&] ( auto & castedCapPres2 )
+    {
+      auto capPresWrapper2 = castedCapPres2.createKernelWrapper();
+
+
+      constitutive::constitutiveUpdatePassThru( *relPerms[0], [&] ( auto & castedRelPerm1 )
+      {
+        auto relPermWrapper1 = castedRelPerm1.createKernelWrapper();
+
+
+        constitutive::constitutiveUpdatePassThru( *relPerms[1], [&] ( auto & castedRelPerm2 )
+        {
+          auto relPermWrapper2 = castedRelPerm2.createKernelWrapper();
+
+          auto fluidWrapper1 = fluids[0]->createKernelWrapper();
+          auto fluidWrapper2 = fluids[1]->createKernelWrapper();
+
+
+          std::ofstream outFile( "iterations2.csv" );
+
+
+          // Write data to the file
+          outFile << "Jacobian";
+          outFile << ",";
+          outFile << "residual";
+          outFile << ",";
+          outFile << "Fw_alpha";
+          outFile << ",";
+          outFile << "Fw_beta";
+          outFile << ",";
+          outFile << "Pc_int";
+          outFile << ",";
+          outFile << "Pc_int1";
+          outFile << ",";
+          outFile << "Pc_int2";
+          outFile << ",";
+          outFile << "Fn_alpha";
+          outFile << ",";
+          outFile << "Fn_beta";
+          outFile << ",";
+          outFile << "Vw_alpha";
+          outFile << ",";
+          outFile << "Vn_alpha";
+          outFile << ",";
+          outFile << "Vw_beta";
+          outFile << ",";
+          outFile << "Vn_beta";
+          outFile << ",";
+          outFile << "Gw_alpha";
+          outFile << ",";
+          outFile << "Gn_alpha";
+          outFile << ",";
+          outFile << "Gw_beta";
+          outFile << ",";
+          outFile << "Gn_beta";
+          outFile << ",";
+          outFile << "Cw_alpha";
+          outFile << ",";
+          outFile << "Cn_alpha";
+          outFile << ",";
+          outFile << "Cw_beta";
+          outFile << ",";
+          outFile << "Cn_beta";
+          outFile << ",";
+          outFile << "transHats0";
+          outFile << ",";
+          outFile << "transHats1";
+          outFile << ",";
+          outFile << "gravCoefHats";
+          outFile << ",";
+          outFile << "gravCoef0";
+          outFile << ",";
+          outFile << "gravCoef1";
+          outFile << ",";
+          outFile << "uT";
+          outFile << ",";
+          outFile << "duT_dP0";
+          outFile << ",";
+          outFile << "duT_dS0";  
+          outFile << ",";
+          outFile << "duT_dP1";
+          outFile << ",";
+          outFile << "duT_dS1";                           
+          outFile << std::endl;
+
+
+
+          // nonlinear solver's parameters
+          real64 tol = 1.0e-9;
+          int max_iter = 50;
+          converged = 0;
+          bool damping = true;
+
+          // Local newton loop:
+
+          // Use of the capillary pressure kernel wrapper
+
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseVolFrac1( 1, 2 );
+          StackArray< real64, 3, 2, constitutive::cappres::LAYOUT_CAPPRES > capPres1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dPhaseVolFrac_dCapPres1( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dCapPres1_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > trappedVolFrac1( 1, 1, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > facePhaseVolFrac1( 1, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > faceTrappedVolFrac1( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::cappres::LAYOUT_CAPPRES > faceCapPres1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dfacePhaseVolFrac_dCapPres1( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dCapPres1_dfacePhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseVolFrac2( 1, 2 );
+          StackArray< real64, 3, 2, constitutive::cappres::LAYOUT_CAPPRES > capPres2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dPhaseVolFrac_dCapPres2( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dCapPres2_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > trappedVolFrac2( 1, 1, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > facePhaseVolFrac2( 1, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > faceTrappedVolFrac2( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::cappres::LAYOUT_CAPPRES > faceCapPres2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dfacePhaseVolFrac_dCapPres2( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::cappres::LAYOUT_CAPPRES_DS > dCapPres2_dfacePhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 1, 2 > JFunc1( 2 );
+          StackArray< real64, 1, 2 > JFunc2( 2 );
+
+          
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseMaxHistoricalVolFraction1( 1, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseMinHistoricalVolFraction1( 1, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseMaxHistoricalVolFraction2( 1, 2 );
+          StackArray< real64, 2, 2, immiscibleFlow::LAYOUT_PHASE > phaseMinHistoricalVolFraction2( 1, 2 );
+          StackArray< real64, 2, 2, compflow::LAYOUT_PHASE > phaseMode2PeakVolFraction1( 1, 2 );
+          StackArray< real64, 2, 2, compflow::LAYOUT_PHASE > phaseMode2PeakVolFraction2( 1, 2 );
+          phaseMode2PeakVolFraction1[0][0] = 0.0;
+          phaseMode2PeakVolFraction1[0][1] = 0.0;
+          phaseMode2PeakVolFraction2[0][0] = 0.0;
+          phaseMode2PeakVolFraction2[0][1] = 0.0;
+          arraySlice1d<real64, compflow::USD_PHASE - 1> phaseMode2PeakSlice1 = phaseMode2PeakVolFraction1[0];
+          arraySlice1d<real64, compflow::USD_PHASE - 1> phaseMode2PeakSlice2 = phaseMode2PeakVolFraction2[0];
+
+          if( phaseMaxHistVolFrac1.size() >= 2 && phaseMaxHistVolFrac1[0] >= 0.0 )
+          {
+
+            phaseMaxHistoricalVolFraction1[0][0] = phaseMaxHistVolFrac1[0];
+            phaseMaxHistoricalVolFraction1[0][1] = phaseMaxHistVolFrac1[1];
+            phaseMinHistoricalVolFraction1[0][0] = phaseMinHistVolFrac1[0];
+            phaseMinHistoricalVolFraction1[0][1] = phaseMinHistVolFrac1[1];
+          }
+          else
+          {
+
+            phaseMaxHistoricalVolFraction1[0][0] = saturations[0];
+            phaseMaxHistoricalVolFraction1[0][1] = 1.0 - saturations[0];
+            phaseMinHistoricalVolFraction1[0][0] = saturations[0];
+            phaseMinHistoricalVolFraction1[0][1] = 1.0 - saturations[0];
+          }
+          
+          if( phaseMaxHistVolFrac2.size() >= 2 && phaseMaxHistVolFrac2[0] >= 0.0 )
+          {
+
+            phaseMaxHistoricalVolFraction2[0][0] = phaseMaxHistVolFrac2[0];
+            phaseMaxHistoricalVolFraction2[0][1] = phaseMaxHistVolFrac2[1];
+            phaseMinHistoricalVolFraction2[0][0] = phaseMinHistVolFrac2[0];
+            phaseMinHistoricalVolFraction2[0][1] = phaseMinHistVolFrac2[1];
+          }
+          else
+          {
+            phaseMaxHistoricalVolFraction2[0][0] = saturations[1];
+            phaseMaxHistoricalVolFraction2[0][1] = 1.0 - saturations[1];
+            phaseMinHistoricalVolFraction2[0][0] = saturations[1];
+            phaseMinHistoricalVolFraction2[0][1] = 1.0 - saturations[1];
+          }
+
+          // compute relative permeability for both cell centers:
+
+          trappedVolFrac1[0][0][0] = trappedSats1[0];
+          trappedVolFrac1[0][0][1] = trappedSats1[1];
+
+          trappedVolFrac2[0][0][0] = trappedSats2[0];
+          trappedVolFrac2[0][0][1] = trappedSats2[1];
+
+          faceTrappedVolFrac1[0][0][0] = trappedSats1[0];
+          faceTrappedVolFrac1[0][0][1] = trappedSats1[1];
+
+          faceTrappedVolFrac2[0][0][0] = trappedSats2[0];
+          faceTrappedVolFrac2[0][0][1] = trappedSats2[1];
+
+          phaseVolFrac1[0][0] = saturations[0];
+          phaseVolFrac1[0][1] = 1.0 - saturations[0];
+
+          phaseVolFrac2[0][0] = saturations[1];
+          phaseVolFrac2[0][1] = 1.0 - saturations[1];
+
+          real64 Pc1_min = 0.0;
+          real64 Pc2_min = 0.0;
+          real64 Pc1_max = 0.0;
+          real64 Pc2_max = 0.0;
+
+          real64 density2[2]{};
+          real64 dDens_dP2[2][2]{};
+
+          density2[0] =  cellCenterDens[0];  
+          density2[1] =  cellCenterDens[1];         
+
+          dDens_dP2[0][0] = cellCenterDens_dP[0];
+          dDens_dP2[0][1] = cellCenterDens_dP[1];
+          dDens_dP2[1][0] = cellCenterDens_dP[2];
+          dDens_dP2[1][1] = cellCenterDens_dP[3];
+
+          JFunc1[0] = JFMultipliers[0];
+          JFunc2[0] = JFMultipliers[1];
+
+          using T1 = std::decay_t< decltype(castedCapPres1) >;
+          if constexpr (std::is_same_v< T1, JFunctionCapillaryPressure >) {
+            capPresWrapper1.compute( phaseVolFrac1[0],
+                                     JFunc1.toSliceConst(),
+                                     capPres1[0][0],
+                                     dCapPres1_dPhaseVolFrac[0][0] );
+
+            facePhaseVolFrac1[0][1] = 0.0;
+            facePhaseVolFrac1[0][0] = 1.0;
+            capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                     JFunc1.toSliceConst(),
+                                     faceCapPres1[0][0],
+                                     dCapPres1_dfacePhaseVolFrac[0][0] );
+            Pc1_min = faceCapPres1[0][0][0];
+            facePhaseVolFrac1[0][1] = 1.0;
+            facePhaseVolFrac1[0][0] = 0.0;
+            capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                     JFunc1.toSliceConst(),
+                                     faceCapPres1[0][0],
+                                     dCapPres1_dfacePhaseVolFrac[0][0] );
+            Pc1_max = faceCapPres1[0][0][0];
+
+          }
+          else if constexpr (std::is_same_v< T1, TableCapillaryPressureHysteresis >) {
+            auto preComputeMode0 = modes[0];
+            capPresWrapper1.compute( phaseVolFrac1[0],
+                                     phaseMaxHistoricalVolFraction1[0],
+                                     phaseMinHistoricalVolFraction1[0],
+                                     trappedVolFrac1[0][0],
+                                     capPres1[0][0],
+                                     dCapPres1_dPhaseVolFrac[0][0],
+                                     modes[0],
+                                     phaseMode2PeakSlice1 );   
+
+            if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+            std::cout << "  [BOUNDS_DEBUG] Cell0: T1=TableCapillaryPressureHysteresis"
+                      << ", preComputeMode=" << static_cast<int>(preComputeMode0)
+                      << ", postComputeMode=" << static_cast<int>(modes[0])
+                      << ", S=" << phaseVolFrac1[0][0]
+                      << ", Pc=" << capPres1[0][0][0] << std::endl;
+            }
+
+            if (modes[0] == fields::cappres::ModeIndexType::DRAINAGE || 
+                modes[0] == fields::cappres::ModeIndexType::IMBIBITION) {
+              if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell0: DRAINAGE/IMBIBITION path" << std::endl; }
+              integer const tableIdx1 = static_cast<integer>(modes[0]);
+              real64 Pc1_at_S1, dPc1_at_S1;
+              real64 Pc1_at_S0, dPc1_at_S0;
+              real64 const S_one = 1.0;
+              real64 const S_zero = 0.0;
+              capPresWrapper1.computeRawTablePc( tableIdx1, S_one, Pc1_at_S1, dPc1_at_S1 );
+              capPresWrapper1.computeRawTablePc( tableIdx1, S_zero, Pc1_at_S0, dPc1_at_S0 );
+              Pc1_min = LvArray::math::min( Pc1_at_S1, Pc1_at_S0 );
+              Pc1_max = LvArray::math::max( Pc1_at_S1, Pc1_at_S0 );
+              
+              if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell0: Pc1_min=" << Pc1_min 
+                        << " (table@S=1:" << Pc1_at_S1 << ", table@S=0:" << Pc1_at_S0 << ")" << std::endl; }
+            } else {
+              if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell0: SCANNING path, modes[0]=" << static_cast<int>(modes[0]) << std::endl; }
+              real64 const S_min_hist1 = phaseMinHistoricalVolFraction1[0][0];
+              real64 const S_max_hist1 = phaseMaxHistoricalVolFraction1[0][0];
+              
+              auto scanBoundsMode1 = modes[0];
+              
+              if (modes[0] == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION ||
+                  modes[0] == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE ||
+                  modes[0] == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                capPresWrapper1.computeScanningCurvePcRange(
+                    S_min_hist1, S_max_hist1, modes[0], Pc1_min, Pc1_max );
+              }
+              else {
+              facePhaseVolFrac1[0][1] = 0.0;
+              facePhaseVolFrac1[0][0] = 1.0;
+                scanBoundsMode1 = modes[0];
+              capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                       phaseMaxHistoricalVolFraction1[0],
+                                       phaseMinHistoricalVolFraction1[0],
+                                       faceTrappedVolFrac1[0][0],
+                                       faceCapPres1[0][0],
+                                       dCapPres1_dfacePhaseVolFrac[0][0],
+                                         scanBoundsMode1,
+                                       phaseMode2PeakSlice1 );    
+              Pc1_min = faceCapPres1[0][0][0];
+              
+              facePhaseVolFrac1[0][1] = 1.0;
+              facePhaseVolFrac1[0][0] = 0.0;
+                scanBoundsMode1 = modes[0];
+              capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                       phaseMaxHistoricalVolFraction1[0],
+                                       phaseMinHistoricalVolFraction1[0],
+                                       faceTrappedVolFrac1[0][0],
+                                       faceCapPres1[0][0],
+                                       dCapPres1_dfacePhaseVolFrac[0][0],
+                                         scanBoundsMode1,
+                                       phaseMode2PeakSlice1 );      
+              Pc1_max = faceCapPres1[0][0][0];
+              }
+            }
+          }
+          else
+          {
+            if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell0: GENERIC (non-hysteresis) path" << std::endl; }
+            capPresWrapper1.compute( phaseVolFrac1[0],
+                                     capPres1[0][0],
+                                     dCapPres1_dPhaseVolFrac[0][0] );
+
+            facePhaseVolFrac1[0][1] = 0.0;
+            facePhaseVolFrac1[0][0] = 1.0;
+            capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                     faceCapPres1[0][0],
+                                     dCapPres1_dfacePhaseVolFrac[0][0] );
+            Pc1_min = faceCapPres1[0][0][0];
+            facePhaseVolFrac1[0][1] = 1.0;
+            facePhaseVolFrac1[0][0] = 0.0;
+            capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                     faceCapPres1[0][0],
+                                     dCapPres1_dfacePhaseVolFrac[0][0] );
+            Pc1_max = faceCapPres1[0][0][0];
+            if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell0 GENERIC: Pc1_min=" << Pc1_min << ", Pc1_max=" << Pc1_max << std::endl; }
+          }
+
+          using T2 = std::decay_t< decltype(castedCapPres2) >;
+          if constexpr (std::is_same_v< T2, JFunctionCapillaryPressure >) {
+            // evaluating cell-center Pc:
+
+            capPresWrapper2.compute( phaseVolFrac2[0],
+                                     JFunc2.toSliceConst(),
+                                     capPres2[0][0],
+                                     dCapPres2_dPhaseVolFrac[0][0] );
+
+// finding endpoints:
+
+            facePhaseVolFrac2[0][1] = 0.0;
+            facePhaseVolFrac2[0][0] = 1.0;
+            capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                     JFunc2.toSliceConst(),
+                                     faceCapPres2[0][0],
+                                     dCapPres2_dfacePhaseVolFrac[0][0] );
+            Pc2_min = faceCapPres2[0][0][0];
+            facePhaseVolFrac2[0][1] = 1.0;
+            facePhaseVolFrac2[0][0] = 0.0;
+            capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                     JFunc2.toSliceConst(),
+                                     faceCapPres2[0][0],
+                                     dCapPres2_dfacePhaseVolFrac[0][0] );
+            Pc2_max = faceCapPres2[0][0][0];
+
+          }
+          else if constexpr (std::is_same_v< T2, TableCapillaryPressureHysteresis >) {
+            auto preComputeMode1 = modes[1];
+            capPresWrapper2.compute( phaseVolFrac2[0],
+                                     phaseMaxHistoricalVolFraction2[0],
+                                     phaseMinHistoricalVolFraction2[0],
+                                     trappedVolFrac2[0][0],
+                                     capPres2[0][0],
+                                     dCapPres2_dPhaseVolFrac[0][0],
+                                     modes[1],
+                                     phaseMode2PeakSlice2 );                         
+
+            if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+            std::cout << "  [BOUNDS_DEBUG] Cell1: T2=TableCapillaryPressureHysteresis"
+                      << ", preComputeMode=" << static_cast<int>(preComputeMode1)
+                      << ", postComputeMode=" << static_cast<int>(modes[1])
+                      << ", S=" << phaseVolFrac2[0][0]
+                      << ", Pc=" << capPres2[0][0][0] << std::endl;
+            }
+
+            if (modes[1] == fields::cappres::ModeIndexType::DRAINAGE || 
+                modes[1] == fields::cappres::ModeIndexType::IMBIBITION) {
+              if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell1: DRAINAGE/IMBIBITION path" << std::endl; }
+              integer const tableIdx2 = static_cast<integer>(modes[1]);
+              real64 Pc2_at_S1, dPc2_at_S1;
+              real64 Pc2_at_S0, dPc2_at_S0;
+              real64 const S_one_2 = 1.0;
+              real64 const S_zero_2 = 0.0;
+              capPresWrapper2.computeRawTablePc( tableIdx2, S_one_2, Pc2_at_S1, dPc2_at_S1 );
+              capPresWrapper2.computeRawTablePc( tableIdx2, S_zero_2, Pc2_at_S0, dPc2_at_S0 );
+              Pc2_min = LvArray::math::min( Pc2_at_S1, Pc2_at_S0 );
+              Pc2_max = LvArray::math::max( Pc2_at_S1, Pc2_at_S0 );
+              
+              if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell1: Pc2_min=" << Pc2_min 
+                        << " (table@S=1:" << Pc2_at_S1 << ", table@S=0:" << Pc2_at_S0 << ")" << std::endl; }
+            } else {
+              if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell1: SCANNING path, modes[1]=" << static_cast<int>(modes[1]) << std::endl; }
+              real64 const S_min_hist2 = phaseMinHistoricalVolFraction2[0][0];
+              real64 const S_max_hist2 = phaseMaxHistoricalVolFraction2[0][0];
+              auto scanBoundsMode2 = modes[1];
+              
+              if (modes[1] == fields::cappres::ModeIndexType::DRAINAGE_TO_IMBIBITION ||
+                  modes[1] == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE ||
+                  modes[1] == fields::cappres::ModeIndexType::IMBIBITION_TO_DRAINAGE_FROM_SCANNING) {
+                capPresWrapper2.computeScanningCurvePcRange(
+                    S_min_hist2, S_max_hist2, modes[1], Pc2_min, Pc2_max );
+              }
+              else {
+              facePhaseVolFrac2[0][1] = 0.0;
+              facePhaseVolFrac2[0][0] = 1.0;
+                scanBoundsMode2 = modes[1];
+              capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                       phaseMaxHistoricalVolFraction2[0],
+                                       phaseMinHistoricalVolFraction2[0],
+                                       faceTrappedVolFrac2[0][0],
+                                       faceCapPres2[0][0],
+                                       dCapPres2_dfacePhaseVolFrac[0][0],
+                                         scanBoundsMode2,
+                                       phaseMode2PeakSlice2 );  
+              Pc2_min = faceCapPres2[0][0][0];
+              
+              facePhaseVolFrac2[0][1] = 1.0;
+              facePhaseVolFrac2[0][0] = 0.0;
+                scanBoundsMode2 = modes[1];
+              capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                       phaseMaxHistoricalVolFraction2[0],
+                                       phaseMinHistoricalVolFraction2[0],
+                                       faceTrappedVolFrac2[0][0],
+                                       faceCapPres2[0][0],
+                                       dCapPres2_dfacePhaseVolFrac[0][0],
+                                         scanBoundsMode2,
+                                       phaseMode2PeakSlice2 );      
+              Pc2_max = faceCapPres2[0][0][0];
+              }
+            }
+          }
+          else
+          {
+            if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell1: GENERIC (non-hysteresis) path" << std::endl; }
+            // evaluating cell-center Pc:
+
+            capPresWrapper2.compute( phaseVolFrac2[0],
+                                     capPres2[0][0],
+                                     dCapPres2_dPhaseVolFrac[0][0] );
+
+// finding endpoints:
+
+            facePhaseVolFrac2[0][1] = 0.0;
+            facePhaseVolFrac2[0][0] = 1.0;
+            capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                     faceCapPres2[0][0],
+                                     dCapPres2_dfacePhaseVolFrac[0][0] );
+            Pc2_min = faceCapPres2[0][0][0];
+            facePhaseVolFrac2[0][1] = 1.0;
+            facePhaseVolFrac2[0][0] = 0.0;
+            capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                     faceCapPres2[0][0],
+                                     dCapPres2_dfacePhaseVolFrac[0][0] );
+            Pc2_max = faceCapPres2[0][0][0];
+            if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) { std::cout << "  [BOUNDS_DEBUG] Cell1 GENERIC: Pc2_min=" << Pc2_min << ", Pc2_max=" << Pc2_max << std::endl; }
+          }
+
+          if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+          std::cout << "  [BOUNDS_DEBUG] FINAL: modes[0]=" << static_cast<int>(modes[0]) 
+                    << ", modes[1]=" << static_cast<int>(modes[1])
+                    << ", Pc1_min=" << Pc1_min << ", Pc1_max=" << Pc1_max 
+                    << ", Pc2_min=" << Pc2_min << ", Pc2_max=" << Pc2_max << std::endl;
+          }
+
+          // Use of the relative permeability kernel wrapper
+
+
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > faceRelPerm1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::relperm::LAYOUT_RELPERM_DS > dfacePhaseRelPerm1_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > relPerm1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::relperm::LAYOUT_RELPERM_DS > dPhaseRelPerm1_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > faceRelPerm2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::relperm::LAYOUT_RELPERM_DS > dfacePhaseRelPerm2_dPhaseVolFrac( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::relperm::LAYOUT_RELPERM > relPerm2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::relperm::LAYOUT_RELPERM_DS > dPhaseRelPerm2_dPhaseVolFrac( 1, 1, 2, 2 );
+
+
+          using T5 = std::decay_t< decltype(castedRelPerm1) >;
+          if constexpr (std::is_same_v< T5, constitutive::TableRelativePermeabilityHysteresis >) {
+            relPermWrapper1.compute( phaseVolFrac1[0],
+                                     phaseMaxHistoricalVolFraction1[0],
+                                     phaseMinHistoricalVolFraction1[0],
+                                     trappedVolFrac1[0][0],
+                                     relPerm1[0][0],
+                                     dPhaseRelPerm1_dPhaseVolFrac[0][0] );
+
+          }
+          else
+          {
+
+            relPermWrapper1.compute( phaseVolFrac1[0],
+                                     trappedVolFrac1[0][0],
+                                     relPerm1[0][0],
+                                     dPhaseRelPerm1_dPhaseVolFrac[0][0] );
+          }
+
+          using T6 = std::decay_t< decltype(castedRelPerm2) >;
+          if constexpr (std::is_same_v< T6, constitutive::TableRelativePermeabilityHysteresis >) {
+            relPermWrapper2.compute( phaseVolFrac2[0],
+                                     phaseMaxHistoricalVolFraction2[0],
+                                     phaseMinHistoricalVolFraction2[0],
+                                     trappedVolFrac2[0][0],
+                                     relPerm2[0][0],
+                                     dPhaseRelPerm2_dPhaseVolFrac[0][0] );
+
+          }
+          else
+          {
+
+            relPermWrapper2.compute( phaseVolFrac2[0],
+                                     trappedVolFrac2[0][0],
+                                     relPerm2[0][0],
+                                     dPhaseRelPerm2_dPhaseVolFrac[0][0] );
+          }
+
+
+          // Use of the fluid model kernel wrapper
+          StackArray< real64, 3, 2, constitutive::multifluid::LAYOUT_PHASE > phaseDensity1( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::multifluid::LAYOUT_PHASE > phaseViscosity1( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::multifluid::LAYOUT_PHASE_DC > dPhaseDens1_dP( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::multifluid::LAYOUT_PHASE_DC > dPhaseVisc1_dP( 1, 1, 2, 2 );
+          StackArray< real64, 3, 2, constitutive::multifluid::LAYOUT_PHASE > phaseDensity2( 1, 1, 2 );
+          StackArray< real64, 3, 2, constitutive::multifluid::LAYOUT_PHASE > phaseViscosity2( 1, 1, 2 );
+          StackArray< real64, 4, 4, constitutive::multifluid::LAYOUT_PHASE_DC > dPhaseDens2_dP( 1, 1, 2, 2 );
+          StackArray< real64, 4, 4, constitutive::multifluid::LAYOUT_PHASE_DC > dPhaseVisc2_dP( 1, 1, 2, 2 );
+
+          // Declare the MultiFluidVar (PhaseProp) type
+          TwoPhaseImmiscibleFluid::PhaseProp phaseDensity_temp1;
+          TwoPhaseImmiscibleFluid::PhaseProp phaseViscosity_temp1;
+          phaseDensity_temp1.value.resize( 1, 1, 2 ); // or whatever sizes you need
+          phaseDensity_temp1.derivs.resize( 1, 1, 2, 2 ); // make sure all dims > 0
+          phaseViscosity_temp1.value.resize( 1, 1, 2 ); // or whatever sizes you need
+          phaseViscosity_temp1.derivs.resize( 1, 1, 2, 2 ); // make sure all dims > 0
+
+          auto phaseDensitySlice0 = TwoPhaseImmiscibleFluid::PhaseProp::SliceType(
+            phaseDensity_temp1.value[0][0], phaseDensity_temp1.derivs[0][0] );
+          auto phaseViscositySlice0 = TwoPhaseImmiscibleFluid::PhaseProp::SliceType(
+            phaseViscosity_temp1.value[0][0], phaseViscosity_temp1.derivs[0][0] );
+          fluidWrapper1.compute( pressures[0], phaseDensitySlice0, phaseViscositySlice0 );
+
+          // Temporary:
+          phaseDensity1[0][0][0] = phaseDensitySlice0.value[0];
+          phaseDensity1[0][0][1] = phaseDensitySlice0.value[1];
+          dPhaseDens1_dP[0][0][0][0] = phaseDensitySlice0.derivs[0][0];
+          dPhaseDens1_dP[0][0][0][1] = 0;
+          dPhaseDens1_dP[0][0][1][0] = phaseDensitySlice0.derivs[1][0];
+          dPhaseDens1_dP[0][0][1][1] = 0;
+
+          phaseViscosity1[0][0][0] = phaseViscositySlice0.value[0];
+          phaseViscosity1[0][0][1] = phaseViscositySlice0.value[1];
+          dPhaseVisc1_dP[0][0][0][0] = phaseViscositySlice0.derivs[0][0];
+          dPhaseVisc1_dP[0][0][0][1] = 0;
+          dPhaseVisc1_dP[0][0][1][0] = phaseViscositySlice0.derivs[1][0];
+          dPhaseVisc1_dP[0][0][1][1] = 0;
+
+          auto phaseDensitySlice1 = TwoPhaseImmiscibleFluid::PhaseProp::SliceType(
+            phaseDensity_temp1.value[0][0], phaseDensity_temp1.derivs[0][0] );
+          auto phaseViscositySlice1 = TwoPhaseImmiscibleFluid::PhaseProp::SliceType(
+            phaseViscosity_temp1.value[0][0], phaseViscosity_temp1.derivs[0][0] );
+          fluidWrapper2.compute( pressures[1], phaseDensitySlice1, phaseViscositySlice1 );
+
+
+          phaseDensity2[0][0][0] = phaseDensitySlice1.value[0];
+          phaseDensity2[0][0][1] = phaseDensitySlice1.value[1];
+          dPhaseDens2_dP[0][0][0][0] = phaseDensitySlice1.derivs[0][0];
+          dPhaseDens2_dP[0][0][0][1] = 0;
+          dPhaseDens2_dP[0][0][1][0] = phaseDensitySlice1.derivs[1][0];
+          dPhaseDens2_dP[0][0][1][1] = 0;
+
+          phaseViscosity2[0][0][0] = phaseViscositySlice1.value[0];
+          phaseViscosity2[0][0][1] = phaseViscositySlice1.value[1];
+          dPhaseVisc2_dP[0][0][0][0] = phaseViscositySlice1.derivs[0][0];
+          dPhaseVisc2_dP[0][0][0][1] = 0;
+          dPhaseVisc2_dP[0][0][1][0] = phaseViscositySlice1.derivs[1][0];
+          dPhaseVisc2_dP[0][0][1][1] = 0;
+
+          // clear working arrays
+          real64 halfFluxVal[2][2]{};
+          real64 dhalfFlux1_dP[2][2]{};
+          real64 dhalfFlux1_dS[2][2]{};
+          real64 dhalfFlux2_dP[2][2]{};
+          real64 dhalfFlux2_dS[2][2]{};
+          real64 dhalfFlux_duT[2][2]{};
+          real64 dhalfFlux_dpc[2][2]{};
+
+          //new
+        real64 fluxVal[2]{};
+        real64 dFlux_dP[2][2]{};
+        real64 dFlux_dS[2][2]{};
+
+        real64 duT_dP[2]{};
+        real64 duT_dS[2]{};
+
+        duT_dP[0] = cellCenterDuT[0];
+        duT_dP[1] = cellCenterDuT[1];
+
+        duT_dS[0] = cellCenterDuT[2];
+        duT_dS[1] = cellCenterDuT[3];
+
+          // initial guess:
+
+          real64 const Pc1 = capPres1[0][0][0];
+          real64 const Pc2 = capPres2[0][0][0];
+
+          real64 Pc_union_min = fmin( Pc1_min, Pc2_min );
+          real64 Pc_union_max = fmax( Pc1_max, Pc2_max );
+
+          real64 Pc_min_all = fmax( Pc1_min, Pc2_min );
+          real64 Pc_max_all = fmin( Pc1_max, Pc2_max );
+          bool rangesOverlap = Pc_min_all < Pc_max_all;
+
+          real64 Pc_bracket_lo = Pc_union_min;
+          real64 Pc_bracket_hi = Pc_union_max;
+          real64 res_bracket_lo = 0.0;
+          real64 res_bracket_hi = 0.0;
+          bool bracket_lo_set = false;
+          bool bracket_hi_set = false;
+
+          constexpr bool ENABLE_WARM_START = true;
+          real64 Pc_int;
+          bool usedWarmStart = false;
+          if( ENABLE_WARM_START && warmStartPc > 0.0 )
+          {
+            Pc_int = warmStartPc;
+            usedWarmStart = true;
+            }
+            else
+            {
+            Pc_int = rangesOverlap ? ( Pc_min_all + Pc_max_all ) / 2.0
+                                   : LvArray::math::max( Pc1, Pc2 );
+          }
+          Pc_int = fmin( Pc_union_max, fmax( Pc_int, Pc_union_min ) );
+
+          real64 Pc_int_iterate = Pc_int;
+
+          int iter = 0;
+          int div = 0;
+
+          int n_same_pc = 0;
+          real64 prev_Pc_evaluated = -1.0e30;
+          int stuck_probe_level = 0;
+
+          constexpr bool ENABLE_BEST_SOLUTION_FALLBACK = false;
+          constexpr real64 FALLBACK_TOL_FACTOR = 100.0;
+          real64 best_Pc = 0.0;
+          real64 best_absRes = 1.0e30;
+          bool fallback_used = false;
+
+          constexpr bool ENABLE_SWEEP_FALLBACK = true;
+          constexpr real64 SWEEP_DS = 0.005;
+          constexpr integer SWEEP_MIN_POINTS = 100;
+          constexpr real64 SWEEP_ACCEPT_TOL_FACTOR = 100.0;
+          bool sweep_active = false;
+          real64 sweep_best_Pc = 0.0;
+          real64 sweep_best_absRes = 1.0e30;
+          int sweep_newton_iter_end = 0;
+
+          real64 last_local_residual = 0.0;
+          real64 last_local_jacobian = 0.0;
+          real64 last_facePhaseVolFrac1_0 = 0.0;
+          real64 last_facePhaseVolFrac2_0 = 0.0;
+          real64 last_faceCapPres1 = 0.0;
+          real64 last_faceCapPres2 = 0.0;
+          integer last_iter = 0;
+
+          while( iter < max_iter )
+          {
+
+            Pc_int_iterate = Pc_int;
+            
+            constexpr bool ENABLE_INITIAL_SAT_DEBUG = false;
+            if constexpr (ENABLE_INITIAL_SAT_DEBUG) {
+              if (iter == 0) {
+                std::cout << "[INITIAL_SAT_DEBUG] Local solver iter=" << iter << ", Initial S1=" << phaseVolFrac1[0][0] 
+                          << ", Initial S2=" << phaseVolFrac2[0][0] << std::endl;
+                std::cout << "[INITIAL_SAT_DEBUG] Initial Pc1=" << capPres1[0][0][0] 
+                          << ", Initial Pc2=" << capPres2[0][0][0] << std::endl;
+              }
+            }
+
+            // clear working arrays
+            real64 density[2]{};
+            real64 dDens_dP[2][2]{};
+            real64 gravityCof[2]{};
+            real64 viscosity[2]{};
+            real64 dVisc_dP[2][2]{};
+
+            real64 viscous[2][2]{};
+            real64 bouyancy[2][2]{};
+            real64 capillarity[2][2]{};
+
+            real64 dV1_dS[2][2]{};
+            real64 dG1_dS[2][2]{};
+            real64 dC1_dS[2][2]{};
+            real64 dV2_dS[2][2]{};
+            real64 dG2_dS[2][2]{};
+            real64 dC2_dS[2][2]{};
+            real64 dV1_dpc[2][2]{};
+            real64 dG1_dpc[2][2]{};
+            real64 dC1_dpc[2][2]{};
+            real64 dV2_dpc[2][2]{};
+            real64 dG2_dpc[2][2]{};
+            real64 dC2_dpc[2][2]{};
+
+            real64 local_residual = 0;
+            real64 local_jacobian = 0;
+
+            {
+              bool bracketReady = bracket_lo_set && bracket_hi_set;
+              real64 clamp_lo = bracketReady ? Pc_bracket_lo : Pc_union_min;
+              real64 clamp_hi = bracketReady ? Pc_bracket_hi : Pc_union_max;
+              Pc_int = fmin( clamp_hi, fmax( Pc_int, clamp_lo ) );
+            }
+
+            faceCapPres1[0][0][0] = fmin( Pc1_max, Pc_int );
+            faceCapPres2[0][0][0] = fmin( Pc2_max, Pc_int );
+            bool const faceCapPres1_clamped = (faceCapPres1[0][0][0] < Pc_int - 1e-10);
+            bool const faceCapPres2_clamped = (faceCapPres2[0][0][0] < Pc_int - 1e-10);
+
+            JFunc1[0] = JFMultipliers[0];
+            JFunc2[0] = JFMultipliers[1];
+
+            constexpr bool ENABLE_TCH_COMPUTEINV_DEBUG = false;
+            constexpr bool ENABLE_TCH_COMPUTE_DEBUG = false;
+
+            using T3 = std::decay_t< decltype(castedCapPres1) >;
+            if constexpr (std::is_same_v< T3, JFunctionCapillaryPressure >) {
+              capPresWrapper1.computeInv( facePhaseVolFrac1[0],
+                                          JFunc1.toSliceConst(),
+                                          faceCapPres1[0][0],
+                                          dfacePhaseVolFrac_dCapPres1[0][0] );
+              facePhaseVolFrac1[0][0] = fmin( 1.0, fmax( facePhaseVolFrac1[0][0], 0.0 ));
+              facePhaseVolFrac1[0][1] = fmin( 1.0, fmax( facePhaseVolFrac1[0][1], 0.0 ));
+              //get derivatives:
+              capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                       JFunc1.toSliceConst(),
+                                       faceCapPres1[0][0],
+                                       dCapPres1_dfacePhaseVolFrac[0][0] );
+
+            }
+            else if constexpr (std::is_same_v< T3, TableCapillaryPressureHysteresis >) {
+              if constexpr (ENABLE_TCH_COMPUTEINV_DEBUG) {
+                if (iter < 5 || iter % 10 == 0 || iter >= max_iter - 5) {
+                  std::cout << "[TCH_COMPUTEINV_DEBUG] Cell1, iter=" << iter << std::endl;
+                  std::cout << "  BEFORE computeInv: Pc=" << faceCapPres1[0][0][0] 
+                            << ", S=" << facePhaseVolFrac1[0][0] 
+                            << ", mode=" << modes[0] << std::endl;
+                  std::cout << "  phaseMaxHistoricalVolFraction1[0][0]=" << phaseMaxHistoricalVolFraction1[0][0] 
+                            << ", phaseMinHistoricalVolFraction1[0][0]=" << phaseMinHistoricalVolFraction1[0][0] << std::endl;
+                }
+              }
+              
+              auto tempMode0 = modes[0];
+              capPresWrapper1.computeInv( facePhaseVolFrac1[0],
+                phaseMaxHistoricalVolFraction1[0],
+                phaseMinHistoricalVolFraction1[0],
+                phaseMode2PeakSlice1,
+                faceTrappedVolFrac1[0][0],
+                faceCapPres1[0][0],
+                dfacePhaseVolFrac_dCapPres1[0][0],
+                tempMode0 );   
+              real64 dS_dPc_after_computeInv_TCH = dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+              facePhaseVolFrac1[0][0] = fmin( 1.0, fmax( facePhaseVolFrac1[0][0], 0.0 ));
+              facePhaseVolFrac1[0][1] = fmin( 1.0, fmax( facePhaseVolFrac1[0][1], 0.0 ));
+              
+              if constexpr (ENABLE_TCH_COMPUTEINV_DEBUG) {
+                if (iter < 5 || iter % 10 == 0 || iter >= max_iter - 5) {
+                  std::cout << "  AFTER computeInv: Pc=" << faceCapPres1[0][0][0] 
+                            << ", S=" << facePhaseVolFrac1[0][0] 
+                            << ", dS_dPc=" << dS_dPc_after_computeInv_TCH << std::endl;
+                }
+              }
+              
+              real64 Pc_before_compute_TCH = faceCapPres1[0][0][0];
+              if( modes[0] == fields::cappres::ModeIndexType::DRAINAGE ||
+                  modes[0] == fields::cappres::ModeIndexType::IMBIBITION )
+              {
+                real64 rawPc = 0.0, rawDPcDS = 0.0;
+                capPresWrapper1.computeRawTablePc( static_cast< integer >( modes[0] ),
+                                                   facePhaseVolFrac1[0][0],
+                                                   rawPc, rawDPcDS );
+                faceCapPres1[0][0][0] = rawPc;
+                dCapPres1_dfacePhaseVolFrac[0][0][0][0] = rawDPcDS;
+              }
+              else
+              {
+                auto tempComputeMode0 = modes[0];
+              capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                       phaseMaxHistoricalVolFraction1[0],
+                                       phaseMinHistoricalVolFraction1[0],
+                                       faceTrappedVolFrac1[0][0],
+                                       faceCapPres1[0][0],
+                                       dCapPres1_dfacePhaseVolFrac[0][0],
+                                         tempComputeMode0,
+                                       phaseMode2PeakSlice1 );
+              }
+              real64 dPc_dS_after_compute_TCH = dCapPres1_dfacePhaseVolFrac[0][0][0][0];
+              
+              if constexpr (ENABLE_TCH_COMPUTE_DEBUG) {
+                if (iter < 5 || iter % 10 == 0 || iter >= max_iter - 5) {
+                  std::cout << "[TCH_COMPUTE_DEBUG] Cell1, iter=" << iter << std::endl;
+                  std::cout << "  BEFORE compute: Pc=" << Pc_before_compute_TCH 
+                            << ", S=" << facePhaseVolFrac1[0][0] << std::endl;
+                  std::cout << "  AFTER compute: Pc=" << faceCapPres1[0][0][0] 
+                            << ", dPc_dS=" << dPc_dS_after_compute_TCH << std::endl;
+                  std::cout << "  Pc change=" << (faceCapPres1[0][0][0] - Pc_before_compute_TCH) << std::endl;
+                  real64 product = dS_dPc_after_computeInv_TCH * dPc_dS_after_compute_TCH;
+                  std::cout << "  dS_dPc * dPc_dS = " << product 
+                            << " (should be ~1.0, error=" << std::abs(product - 1.0) << ")" << std::endl;
+                }
+              }
+
+            }
+            else
+            {
+              capPresWrapper1.computeInv( facePhaseVolFrac1[0],
+                                       faceCapPres1[0][0],
+                                       dfacePhaseVolFrac_dCapPres1[0][0] );
+              real64 dS_dPc_after_computeInv_TCP = dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+              facePhaseVolFrac1[0][0] = fmin( 1.0, fmax( facePhaseVolFrac1[0][0], 0.0 ));
+              facePhaseVolFrac1[0][1] = fmin( 1.0, fmax( facePhaseVolFrac1[0][1], 0.0 ));
+              //get derivatives:
+              real64 Pc_before_compute_TCP = faceCapPres1[0][0][0];
+              real64 dPc_dS_before_TCP = dCapPres1_dfacePhaseVolFrac[0][0][0][0];
+              capPresWrapper1.compute( facePhaseVolFrac1[0],
+                                       faceCapPres1[0][0],
+                                       dCapPres1_dfacePhaseVolFrac[0][0] );
+              real64 dPc_dS_after_compute_TCP = dCapPres1_dfacePhaseVolFrac[0][0][0][0];
+              constexpr bool ENABLE_COMPUTE_DEBUG = false;
+              if constexpr (ENABLE_COMPUTE_DEBUG) {
+                std::cout << "[COMPUTE_DEBUG_TCP] After computeInv(): dS_dPc=" << dS_dPc_after_computeInv_TCP 
+                          << ", S=" << facePhaseVolFrac1[0][0] << ", Pc=" << faceCapPres1[0][0][0] << std::endl;
+                std::cout << "[COMPUTE_DEBUG_TCP] After compute(): Pc_before=" << Pc_before_compute_TCP 
+                          << ", Pc_after=" << faceCapPres1[0][0][0] 
+                          << ", dPc_dS_before=" << dPc_dS_before_TCP
+                          << ", dPc_dS_after=" << dPc_dS_after_compute_TCP 
+                          << ", S=" << facePhaseVolFrac1[0][0] << std::endl;
+                real64 product = dS_dPc_after_computeInv_TCP * dPc_dS_after_compute_TCP;
+                std::cout << "[COMPUTE_DEBUG_TCP] dS_dPc * dPc_dS = " << product 
+                          << " (should be ~1.0, error=" << std::abs(product - 1.0) << ")" << std::endl;
+                real64 Pc_diff = faceCapPres1[0][0][0] - Pc_before_compute_TCP;
+                std::cout << "[COMPUTE_DEBUG_TCP] Pc change after compute() = " << Pc_diff 
+                          << " (should be ~0.0)" << std::endl;
+              }
+            }
+            
+            if (faceCapPres1_clamped) {
+              dfacePhaseVolFrac_dCapPres1[0][0][0][0] = 0.0;
+            }
+
+            using T4 = std::decay_t< decltype(castedCapPres2) >;
+            if constexpr (std::is_same_v< T4, JFunctionCapillaryPressure >) {
+              // evaluating cell-center Pc:
+              capPresWrapper2.computeInv( facePhaseVolFrac2[0],
+                                          JFunc2.toSliceConst(),
+                                          faceCapPres2[0][0],
+                                          dfacePhaseVolFrac_dCapPres2[0][0] );
+              facePhaseVolFrac2[0][0] = fmin( 1.0, fmax( facePhaseVolFrac2[0][0], 0.0 ));
+              facePhaseVolFrac2[0][1] = fmin( 1.0, fmax( facePhaseVolFrac2[0][1], 0.0 ));
+
+//get derivatives:
+
+              capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                       JFunc2.toSliceConst(),
+                                       faceCapPres2[0][0],
+                                       dCapPres2_dfacePhaseVolFrac[0][0] );
+
+            }
+            else if constexpr (std::is_same_v< T4, TableCapillaryPressureHysteresis >) {
+              if constexpr (ENABLE_TCH_COMPUTEINV_DEBUG) {
+                if (iter < 5 || iter % 10 == 0 || iter >= max_iter - 5) {
+                  std::cout << "[TCH_COMPUTEINV_DEBUG] Cell2, iter=" << iter << std::endl;
+                  std::cout << "  BEFORE computeInv: Pc=" << faceCapPres2[0][0][0] 
+                            << ", S=" << facePhaseVolFrac2[0][0] 
+                            << ", mode=" << modes[1] << std::endl;
+                  std::cout << "  phaseMaxHistoricalVolFraction2[0][0]=" << phaseMaxHistoricalVolFraction2[0][0] 
+                            << ", phaseMinHistoricalVolFraction2[0][0]=" << phaseMinHistoricalVolFraction2[0][0] << std::endl;
+                }
+              }
+              
+              auto tempMode1 = modes[1];
+              capPresWrapper2.computeInv( facePhaseVolFrac2[0],
+                phaseMaxHistoricalVolFraction2[0],
+                phaseMinHistoricalVolFraction2[0],
+                phaseMode2PeakSlice2,
+                faceTrappedVolFrac2[0][0],
+                faceCapPres2[0][0],
+                dfacePhaseVolFrac_dCapPres2[0][0],
+                tempMode1 );     
+              facePhaseVolFrac2[0][0] = fmin( 1.0, fmax( facePhaseVolFrac2[0][0], 0.0 ));
+              facePhaseVolFrac2[0][1] = fmin( 1.0, fmax( facePhaseVolFrac2[0][1], 0.0 ));
+              real64 dS_dPc_after_computeInv_TCH2 = dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+              
+              if constexpr (ENABLE_TCH_COMPUTEINV_DEBUG) {
+                if (iter < 5 || iter % 10 == 0 || iter >= max_iter - 5) {
+                  std::cout << "  AFTER computeInv: Pc=" << faceCapPres2[0][0][0] 
+                            << ", S=" << facePhaseVolFrac2[0][0] 
+                            << ", dS_dPc=" << dS_dPc_after_computeInv_TCH2 << std::endl;
+                }
+              }
+              
+              real64 Pc_before_compute_TCH2 = faceCapPres2[0][0][0];
+
+              if( modes[1] == fields::cappres::ModeIndexType::DRAINAGE ||
+                  modes[1] == fields::cappres::ModeIndexType::IMBIBITION )
+              {
+                real64 rawPc2 = 0.0, rawDPcDS2 = 0.0;
+                capPresWrapper2.computeRawTablePc( static_cast< integer >( modes[1] ),
+                                                   facePhaseVolFrac2[0][0],
+                                                   rawPc2, rawDPcDS2 );
+                faceCapPres2[0][0][0] = rawPc2;
+                dCapPres2_dfacePhaseVolFrac[0][0][0][0] = rawDPcDS2;
+              }
+              else
+              {
+                auto tempComputeMode1 = modes[1];
+              capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                       phaseMaxHistoricalVolFraction2[0],
+                                       phaseMinHistoricalVolFraction2[0],
+                                       faceTrappedVolFrac2[0][0],
+                                       faceCapPres2[0][0],
+                                       dCapPres2_dfacePhaseVolFrac[0][0],
+                                         tempComputeMode1,
+                                       phaseMode2PeakSlice2 );
+              }
+              
+              if constexpr (ENABLE_TCH_COMPUTE_DEBUG) {
+                if (iter < 5 || iter % 10 == 0 || iter >= max_iter - 5) {
+                  std::cout << "[TCH_COMPUTE_DEBUG] Cell2, iter=" << iter << std::endl;
+                  std::cout << "  BEFORE compute: Pc=" << Pc_before_compute_TCH2 
+                            << ", S=" << facePhaseVolFrac2[0][0] << std::endl;
+                  std::cout << "  AFTER compute: Pc=" << faceCapPres2[0][0][0] 
+                            << ", dPc_dS=" << dCapPres2_dfacePhaseVolFrac[0][0][0] << std::endl;
+                  std::cout << "  Pc change=" << (faceCapPres2[0][0][0] - Pc_before_compute_TCH2) << std::endl;
+                  real64 dPc_dS_after_compute_TCH2 = dCapPres2_dfacePhaseVolFrac[0][0][0][0];
+                  real64 product = dS_dPc_after_computeInv_TCH2 * dPc_dS_after_compute_TCH2;
+                  std::cout << "  dS_dPc * dPc_dS = " << product 
+                            << " (should be ~1.0, error=" << std::abs(product - 1.0) << ")" << std::endl;
+                }
+              }
+
+            }
+            else
+            {
+              // evaluating cell-center Pc:
+              capPresWrapper2.computeInv( facePhaseVolFrac2[0],
+                                       faceCapPres2[0][0],
+                                       dfacePhaseVolFrac_dCapPres2[0][0] );
+              facePhaseVolFrac2[0][0] = fmin( 1.0, fmax( facePhaseVolFrac2[0][0], 0.0 ));
+              facePhaseVolFrac2[0][1] = fmin( 1.0, fmax( facePhaseVolFrac2[0][1], 0.0 ));
+
+//get derivatives:
+
+              real64 Pc_before_compute_TCP2 = faceCapPres2[0][0][0];
+              capPresWrapper2.compute( facePhaseVolFrac2[0],
+                                       faceCapPres2[0][0],
+                                       dCapPres2_dfacePhaseVolFrac[0][0] );
+              constexpr bool ENABLE_COMPUTE_DEBUG = false;
+              if constexpr (ENABLE_COMPUTE_DEBUG) {
+                std::cout << "[COMPUTE_DEBUG_TCP] After compute() cell2: Pc_before=" << Pc_before_compute_TCP2 
+                          << ", Pc_after=" << faceCapPres2[0][0][0] 
+                          << ", dPc_dS=" << dCapPres2_dfacePhaseVolFrac[0][0][0] 
+                          << ", S=" << facePhaseVolFrac2[0][0] << std::endl;
+              }
+            }
+            
+            if (faceCapPres2_clamped) {
+              dfacePhaseVolFrac_dCapPres2[0][0][0][0] = 0.0;
+            }
+            
+            // compute relative permeability for both faces:
+
+            using T7 = std::decay_t< decltype(castedRelPerm1) >;
+            if constexpr (std::is_same_v< T7, constitutive::TableRelativePermeabilityHysteresis >) {
+
+              relPermWrapper1.compute( facePhaseVolFrac1[0],
+                                       phaseMaxHistoricalVolFraction1[0],
+                                       phaseMinHistoricalVolFraction1[0],
+                                       faceTrappedVolFrac1[0][0],
+                                       faceRelPerm1[0][0],
+                                       dfacePhaseRelPerm1_dPhaseVolFrac[0][0] );
+
+            }
+            else
+            {
+
+              relPermWrapper1.compute( facePhaseVolFrac1[0],
+                                       faceTrappedVolFrac1[0][0],
+                                       faceRelPerm1[0][0],
+                                       dfacePhaseRelPerm1_dPhaseVolFrac[0][0] );
+            }
+            
+            constexpr bool ENABLE_RELPERM_DEBUG = false;
+            if constexpr (ENABLE_RELPERM_DEBUG) {
+              if (iter == 0) {
+                std::cout << "[RELPERM_DEBUG] After relPerm1 compute: S1_face=" << facePhaseVolFrac1[0][0] 
+                          << ", faceRelPerm1[0][0][0]=" << faceRelPerm1[0][0][0] 
+                          << ", faceRelPerm1[0][0][1]=" << faceRelPerm1[0][0][1] << std::endl;
+                std::cout << "[RELPERM_DEBUG] dfacePhaseRelPerm1_dPhaseVolFrac[0][0][0][0]=" 
+                          << dfacePhaseRelPerm1_dPhaseVolFrac[0][0][0][0] 
+                          << ", dfacePhaseRelPerm1_dPhaseVolFrac[0][0][1][1]=" 
+                          << dfacePhaseRelPerm1_dPhaseVolFrac[0][0][1][1] << std::endl;
+              }
+            }
+
+            using T8 = std::decay_t< decltype(castedRelPerm2) >;
+            if constexpr (std::is_same_v< T8, constitutive::TableRelativePermeabilityHysteresis >) {
+
+              relPermWrapper2.compute( facePhaseVolFrac2[0],
+                                       phaseMaxHistoricalVolFraction2[0],
+                                       phaseMinHistoricalVolFraction2[0],
+                                       faceTrappedVolFrac2[0][0],
+                                       faceRelPerm2[0][0],
+                                       dfacePhaseRelPerm2_dPhaseVolFrac[0][0] );
+
+            }
+            else
+            {
+
+              relPermWrapper2.compute( facePhaseVolFrac2[0],
+                                       faceTrappedVolFrac2[0][0],
+                                       faceRelPerm2[0][0],
+                                       dfacePhaseRelPerm2_dPhaseVolFrac[0][0] );
+            }
+            
+            if constexpr (ENABLE_RELPERM_DEBUG) {
+              if (iter == 0) {
+                std::cout << "[RELPERM_DEBUG] After relPerm2 compute: S2_face=" << facePhaseVolFrac2[0][0] 
+                          << ", faceRelPerm2[0][0][0]=" << faceRelPerm2[0][0][0] 
+                          << ", faceRelPerm2[0][0][1]=" << faceRelPerm2[0][0][1] << std::endl;
+                std::cout << "[RELPERM_DEBUG] dfacePhaseRelPerm2_dPhaseVolFrac[0][0][0][0]=" 
+                          << dfacePhaseRelPerm2_dPhaseVolFrac[0][0][0][0] 
+                          << ", dfacePhaseRelPerm2_dPhaseVolFrac[0][0][1][1]=" 
+                          << dfacePhaseRelPerm2_dPhaseVolFrac[0][0][1][1] << std::endl;
+              }
+            }
+
+
+            bool check = false;
+            bool k_up_0_w = 1;
+            bool k_up_1_w = 1;
+            bool k_up_0_n = 1;
+            bool k_up_1_n = 1;
+
+            if( uT < 0.0 )
+            {
+              k_up_0_w = 0;
+              k_up_1_w = 0;
+              k_up_0_n = 0;
+              k_up_1_n = 0;
+            }
+
+            if( std::fabs( uT ) < 1e-20 )
+            {
+              k_up_0_w = 1;
+              k_up_1_w = 1;
+              k_up_0_n = 0;
+              k_up_1_n = 0;
+            }
+
+
+            localIndex k_up_0[2] = {static_cast< localIndex >(!k_up_0_w), static_cast< localIndex >(!k_up_0_n)};
+            localIndex k_up_1[2] = {static_cast< localIndex >(k_up_1_w), static_cast< localIndex >(k_up_1_n)};
+            bool k_up_0_check[2] = {false, false};
+            bool k_up_1_check[2] = {false, false};
+
+            while( !check )
+            {
+              k_up_0_check[0] = false;
+              k_up_0_check[1] = false;
+              k_up_1_check[0] = false;
+              k_up_1_check[1] = false;
+              for( integer ix = 0; ix < 2; ++ix ) // for loop over each half flux
+              {
+
+                // clear working arrays for each half flux:
+                real64 densMean[2]{};
+                real64 dDensMean_dP[2][2]{};
+
+                real64 presGrad[2]{};
+                real64 dPresGrad_dP[2][2]{};
+
+                real64 gravHead[2]{};
+                real64 dGravHead_dP[2][2]{};
+
+                real64 capGrad[2]{};
+                // real64 capPresIC[2][2]{};
+                // real64 jFMultiplier[2][2]{};
+                real64 dCapGrad_dP[2][2]{};
+                real64 dCapGrad_dS[2][2]{};
+
+                real64 mobility[2]{};
+                real64 dMob_dP[2][2]{};
+                real64 dMob_dS[2][2]{};
+
+                real64 total_mobility = 0;
+                gravityCof[0] = 0;
+                gravityCof[1] = 0;
+
+                for( integer ip = 0; ip < 2; ++ip ) // loop over phases
+                {
+                  // calculate quantities on primary connected cells
+                  if( ix == 0 )
+                  {
+                    density[ip]  = phaseDensity1[0][0][ip];
+                    dDens_dP[ip][ix] = dPhaseDens1_dP[0][0][ip][ip];
+
+                    viscosity[ip]  = phaseViscosity1[0][0][ip];
+                    dVisc_dP[ip][ix] = dPhaseVisc1_dP[0][0][ip][ip];
+                  }
+                  else
+                  {
+                    density[ip]  = phaseDensity2[0][0][ip];
+                    dDens_dP[ip][ix] = dPhaseDens2_dP[0][0][ip][ip];
+
+                    viscosity[ip]  = phaseViscosity2[0][0][ip];
+                    dVisc_dP[ip][ix] = dPhaseVisc2_dP[0][0][ip][ip];
+                  }
+
+                  densMean[ip] = density[ip];
+                  dDensMean_dP[ip][0] = dDens_dP[ip][ix];
+                  dDensMean_dP[ip][1] = dDens_dP[ip][ix];
+
+                  //***** calculation of flux *****
+
+                  // compute potential difference
+                  real64 potScale = 0.0;
+                  real64 dPresGrad_dTrans = 0.0;
+                  real64 dGravHead_dTrans = 0.0;
+                  real64 dCapGrad_dTrans = 0.0;
+                  constexpr int signPotDiff[2] = {1, -1};
+                  constexpr int signTix[2] = {1, -1};
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+
+                    real64 const pressure = pressures[ix];
+                    presGrad[ip] += signTix[ke] * transHat[ix] * pressure;
+                    dPresGrad_dTrans += signPotDiff[ke] * pressure;
+                    dPresGrad_dP[ip][ke] = signTix[ke] * transHat[ix];
+
+                    real64 gravD = 0.0;
+
+                    if( ke == 0 )
+                    {
+                      gravD += signTix[ke] * transHat[ix] * gravCoef[ix];
+                    }
+                    else
+                    {
+                      gravD += signTix[ke] * transHat[ix] * gravCoefHat[ix];
+                    }
+
+                    real64 pot = signTix[ke] * transHat[ix] * pressure - densMean[ip] * gravD;
+
+                    gravHead[ip] += densMean[ip] * gravD;
+                    gravityCof[ip] += gravD;
+
+                    dGravHead_dTrans += signPotDiff[ke] * densMean[ip] * gravCoefHat[ix];
+
+                    for( integer i = 0; i < 2; ++i )
+                    {
+                      dGravHead_dP[ip][i] += dDensMean_dP[ip][i] * gravD;
+                    }
+
+                    real64 capPres = capPres1[0][0][ip];
+
+                    if( ke == 1 && ix == 0 )
+                    {
+                      capPres = faceCapPres1[0][0][ip];
+                    }
+                    else if( ke == 1 && ix == 1 )
+                    {
+                      capPres = faceCapPres2[0][0][ip];
+                    }
+                    else if( ke == 0 && ix == 1 )
+                    {
+
+                      capPres = capPres2[0][0][ip];
+                    }
+
+                    dCapGrad_dTrans -= signPotDiff[ke] * capPres;
+                    pot -= signTix[ke] * transHat[ix] * capPres;
+
+                    capGrad[ip] -= signTix[ke] * transHat[ix] * capPres;
+
+                    potScale = fmax( potScale, fabs( pot ) );
+                  }
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+                    dPresGrad_dP[ip][ke] += signTix[ke] * dTransHat_dP[ix] * dPresGrad_dTrans;
+
+                    dGravHead_dP[ip][ke] += signTix[ke] * dTransHat_dP[ix] * dGravHead_dTrans;
+
+                    real64 dCapPres_dS;
+                    if( ke == 0 )
+                    {
+
+
+                      dCapPres_dS = dCapPres1_dfacePhaseVolFrac[0][0][ip][ip];
+                    }
+                    else // ke == 1
+                    {
+
+
+                      dCapPres_dS = dCapPres2_dfacePhaseVolFrac[0][0][ip][ip];
+                    }
+
+                    constexpr bool ENABLE_DCAPPRES_DS_DEBUG = false;
+                    if constexpr (ENABLE_DCAPPRES_DS_DEBUG) {
+                      if (iter == 0 && ix == 0 && ip == 0 && ke == 0) {
+                        std::cout << "[DCAPPRES_DS_DEBUG] iter=" << iter << ", ix=" << ix << ", ip=" << ip << ", ke=" << ke << std::endl;
+                        std::cout << "[DCAPPRES_DS_DEBUG] dCapPres_dS=" << dCapPres_dS << " (from cell " << (ke+1) << ")" << std::endl;
+                        std::cout << "[DCAPPRES_DS_DEBUG] dCapPres1_dfacePhaseVolFrac[0][0][0][0]=" << dCapPres1_dfacePhaseVolFrac[0][0][0][0] << std::endl;
+                        std::cout << "[DCAPPRES_DS_DEBUG] dCapPres2_dfacePhaseVolFrac[0][0][0][0]=" << dCapPres2_dfacePhaseVolFrac[0][0][0][0] << std::endl;
+                      }
+                    }
+
+                    dCapGrad_dP[ip][ke] += signTix[ke] * dTransHat_dP[ix] * dCapGrad_dTrans;
+                    dCapGrad_dS[ip][ke] -= signTix[ke] * transHat[ix] * dCapPres_dS;
+                  }
+
+                  // *** upwinding ***
+                  // compute potential gradient
+                  real64 potGrad = presGrad[ip] - gravHead[ip];
+
+                  potGrad += capGrad[ip];
+
+                  // choose upstream cell
+                  constexpr int sign[2] = {1, -1};
+
+                  constexpr bool ENABLE_UPWIND_DEBUG = false;
+                  if constexpr (ENABLE_UPWIND_DEBUG) {
+                    if (iter == 0 && ip == 0) {
+                      std::cout << "[UPWIND_DEBUG] iter=" << iter << ", ip=" << ip << ", ix=" << ix << ", k_up_0[ip]=" << k_up_0[ip] << ", k_up_1[ip]=" << k_up_1[ip] << std::endl;
+                      std::cout << "[UPWIND_DEBUG] potGrad=" << potGrad << ", capGrad[ip]=" << capGrad[ip] << std::endl;
+                      std::cout << "[UPWIND_DEBUG] dfacePhaseRelPerm1_dPhaseVolFrac[0][0][ip][ip]=" << dfacePhaseRelPerm1_dPhaseVolFrac[0][0][ip][ip] << std::endl;
+                      std::cout << "[UPWIND_DEBUG] dPhaseRelPerm1_dPhaseVolFrac[0][0][ip][ip]=" << dPhaseRelPerm1_dPhaseVolFrac[0][0][ip][ip] << std::endl;
+                    }
+                  }
+
+                  if( k_up_0[ip] == 1 && ix == 0 )
+                  {
+                    mobility[ip] = faceRelPerm1[0][0][ip] / viscosity[ip];
+                    dMob_dP[ip][k_up_0[ip]] = mobility[ip] * (-dVisc_dP[ip][ix] / viscosity[ip]);
+
+                    dMob_dS[ip][k_up_0[ip]] = sign[ip] * dfacePhaseRelPerm1_dPhaseVolFrac[0][0][ip][ip] / viscosity[ip];
+                    if constexpr (ENABLE_UPWIND_DEBUG) {
+                      if (iter == 0 && ip == 0) {
+                        std::cout << "[UPWIND_DEBUG] Branch: k_up_0[ip]==1 && ix==0" << std::endl;
+                        std::cout << "[UPWIND_DEBUG] dMob_dS[ip][k_up_0[ip]]=" << dMob_dS[ip][k_up_0[ip]] << ", ix=" << ix << std::endl;
+                      }
+                    }
+                  }
+                  else if( k_up_1[ip] == 0 && ix == 1 )
+                  {
+                    mobility[ip] = relPerm2[0][0][ip] / viscosity[ip];
+                    dMob_dP[ip][0] = mobility[ip] * (-dVisc_dP[ip][ix] / viscosity[ip]);
+                    dMob_dS[ip][0] = sign[ip] * dPhaseRelPerm2_dPhaseVolFrac[0][0][ip][ip] / viscosity[ip];
+                    if constexpr (ENABLE_UPWIND_DEBUG) {
+                      if (iter == 0 && ip == 0) {
+                        std::cout << "[UPWIND_DEBUG] Branch: k_up_1[ip]==0 && ix==1" << std::endl;
+                        std::cout << "[UPWIND_DEBUG] dMob_dS[ip][0]=" << dMob_dS[ip][0] << ", ix=" << ix << std::endl;
+                      }
+                    }
+                  }
+                  else if( k_up_1[ip] == 1 && ix == 1 )
+                  {
+                    mobility[ip] = faceRelPerm2[0][0][ip] / viscosity[ip];
+                    dMob_dP[ip][1] = mobility[ip] * (-dVisc_dP[ip][ix] / viscosity[ip]);
+                    dMob_dS[ip][1] = sign[ip] * dfacePhaseRelPerm2_dPhaseVolFrac[0][0][ip][ip] / viscosity[ip];
+                    if constexpr (ENABLE_UPWIND_DEBUG) {
+                      if (iter == 0 && ip == 0) {
+                        std::cout << "[UPWIND_DEBUG] Branch: k_up_1[ip]==1 && ix==1" << std::endl;
+                        std::cout << "[UPWIND_DEBUG] dMob_dS[ip][1]=" << dMob_dS[ip][1] << ", ix=" << ix << std::endl;
+                      }
+                    }
+                  }
+                  else
+                  {
+                    mobility[ip] = relPerm1[0][0][ip] / viscosity[ip];
+                    dMob_dP[ip][ix] = mobility[ip] * (-dVisc_dP[ip][ix] / viscosity[ip]);
+                    dMob_dS[ip][ix] = sign[ip] * dPhaseRelPerm1_dPhaseVolFrac[0][0][ip][ip] / viscosity[ip];
+                    if constexpr (ENABLE_UPWIND_DEBUG) {
+                      if (iter == 0 && ip == 0) {
+                        std::cout << "[UPWIND_DEBUG] Branch: else (default)" << std::endl;
+                        std::cout << "[UPWIND_DEBUG] dMob_dS[ip][ix]=" << dMob_dS[ip][ix] << ", ix=" << ix << std::endl;
+                      }
+                    }
+                  }
+                  real64 constexpr eps = 0.0;
+                  total_mobility += mobility[ip] + eps;
+                } // loop over phases
+
+                constexpr bool ENABLE_MOBILITY_DEBUG = false;
+                if constexpr (ENABLE_MOBILITY_DEBUG) {
+                  if (iter == 0 && ix == 0) {
+                    std::cout << "[MOBILITY_DEBUG] ix=" << ix << ", S1_face=" << facePhaseVolFrac1[0][0] 
+                              << ", S2_face=" << facePhaseVolFrac2[0][0] << std::endl;
+                    std::cout << "[MOBILITY_DEBUG] mobility[0]=" << mobility[0] << ", mobility[1]=" << mobility[1] 
+                              << ", total_mobility=" << total_mobility << std::endl;
+                    std::cout << "[MOBILITY_DEBUG] dMob_dS[0][0]=" << dMob_dS[0][0] << ", dMob_dS[0][1]=" << dMob_dS[0][1] << std::endl;
+                    std::cout << "[MOBILITY_DEBUG] dMob_dS[1][0]=" << dMob_dS[1][0] << ", dMob_dS[1][1]=" << dMob_dS[1][1] << std::endl;
+                    if (ix == 0) {
+                      std::cout << "[MOBILITY_DEBUG] faceRelPerm1[0][0][0]=" << faceRelPerm1[0][0][0] 
+                                << ", faceRelPerm1[0][0][1]=" << faceRelPerm1[0][0][1] << std::endl;
+                      std::cout << "[MOBILITY_DEBUG] dfacePhaseRelPerm1_dPhaseVolFrac[0][0][0][0]=" 
+                                << dfacePhaseRelPerm1_dPhaseVolFrac[0][0][0][0] 
+                                << ", dfacePhaseRelPerm1_dPhaseVolFrac[0][0][1][1]=" 
+                                << dfacePhaseRelPerm1_dPhaseVolFrac[0][0][1][1] << std::endl;
+                    }
+                  }
+                }
+
+                /// Three Forces Flux Contribution: 1- Viscous 2- Gravitational 3- Capillary
+                constexpr int sign[2] = {1, -1};
+                // real64 constexpr eps = 0.0;
+
+                // loop over phases
+                for( integer ip = 0; ip < 2; ++ip )
+                {
+                  // 1- Viscous: pressure gradient depends on all points in the stencil
+                  viscous[ip][ix] = mobility[ip] / total_mobility * uT;
+                  halfFluxVal[ip][ix] = viscous[ip][ix];
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+                    real64 dV_dP = sign[ip] * (dMob_dP[0][ke] * mobility[1] - dMob_dP[1][ke] * mobility[0]) / (total_mobility * total_mobility) * uT;
+                    real64 dV_dS = sign[ip] * (dMob_dS[0][ke] * mobility[1] - dMob_dS[1][ke] * mobility[0]) / (total_mobility * total_mobility) * uT;
+                    real64 dV_du = mobility[ip] / total_mobility;
+
+                    if( ix == 0 )
+                    {
+                      dV1_dS[ip][ke] = dV_dS;
+                      dhalfFlux1_dP[ip][ke] = dV_dP;
+                      dhalfFlux1_dS[ip][ke] = dV1_dS[ip][ke];
+                      dhalfFlux_duT[ip][ix] = dV_du;
+                      dV1_dpc[ip][ke] = dV1_dS[ip][ke] * dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+                      // GEOS_UNUSED_VAR( dV1_dpc[ip][ke] );
+                      GEOS_UNUSED_VAR( dhalfFlux_duT[ip][ix] );
+                      
+                      constexpr bool ENABLE_DV_DEBUG = false;
+                      if constexpr (ENABLE_DV_DEBUG) {
+                        if (iter == 0 && ip == 0 && ke == 0) {
+                          std::cout << "[DV_DEBUG] ix=" << ix << ", ip=" << ip << ", ke=" << ke 
+                                    << ", dV_dS=" << dV_dS << ", dV1_dS[ip][ke]=" << dV1_dS[ip][ke] << std::endl;
+                          std::cout << "[DV_DEBUG] dMob_dS[0][ke]=" << dMob_dS[0][ke] << ", dMob_dS[1][ke]=" << dMob_dS[1][ke] << std::endl;
+                          std::cout << "[DV_DEBUG] mobility[0]=" << mobility[0] << ", mobility[1]=" << mobility[1] << std::endl;
+                          std::cout << "[DV_DEBUG] uT=" << uT << ", total_mobility=" << total_mobility << std::endl;
+                        }
+                      }
+                    }
+                    else
+                    {
+                      dV2_dS[ip][ke] = dV_dS;
+                      dhalfFlux2_dP[ip][ke] =  dV_dP;
+                      dhalfFlux2_dS[ip][ke] =  dV2_dS[ip][ke];
+                      dhalfFlux_duT[ip][ix]= dV_du;
+                      dV2_dpc[ip][ke] = dV2_dS[ip][ke] * dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+                      // GEOS_UNUSED_VAR( dV2_dpc[ip][ke] );
+                      GEOS_UNUSED_VAR( dhalfFlux_duT[ip][ix] );
+                    }
+                  }
+
+                  // 2- Gravitational: gravitational head depends only on the two cells connected (same as mean density)
+                  bouyancy[ip][ix] = -1.0 * sign[ix] * sign[ip] * mobility[0] * mobility[1] / total_mobility * gravityCof[0] * (density[0] - density[1]);
+                  halfFluxVal[ip][ix] += bouyancy[ip][ix];
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+                    real64 dG_dP = sign[ix] * sign[ip] * (dMob_dP[0][ke] * mobility[1] * mobility[1] + dMob_dP[1][ke] * mobility[0] * mobility[0]) / (total_mobility * total_mobility) * gravityCof[0] *
+                                   (density[0] - density[1]) +
+                                   sign[ix] * (mobility[0] * mobility[1]) / total_mobility * (dDens_dP[0][ix] - dDens_dP[1][ix]);
+
+                    real64 dG_dS =  sign[ix] * sign[ip] * (dMob_dS[0][ke] * mobility[1] * mobility[1] + dMob_dS[1][ke] * mobility[0] * mobility[0]) / (total_mobility * total_mobility) *
+                                   gravityCof[0] * (density[0] - density[1]);
+
+                    if( ix == 0 )
+                    {
+                      dG1_dS[ip][ke] = dG_dS;
+                      dhalfFlux1_dP[ip][ke] -= dG_dP;
+                      dhalfFlux1_dS[ip][ke] -= dG1_dS[ip][ke];
+                      dG1_dpc[ip][ke] = dG1_dS[ip][ke] * dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+                      // GEOS_UNUSED_VAR( dG1_dpc[ip][ke] );
+                    }
+                    else
+                    {
+                      dG2_dS[ip][ke] = dG_dS;
+                      dhalfFlux2_dP[ip][ke] -= dG_dP;
+                      dhalfFlux2_dS[ip][ke] -= dG2_dS[ip][ke];
+                      dG2_dpc[ip][ke] = dG2_dS[ip][ke] * dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+                      // GEOS_UNUSED_VAR( dG2_dpc[ip][ke] );
+                    }
+                  }
+
+                  // 3- Capillary: capillary pressure contribution
+                  capillarity[ip][ix] = -1.0 * sign[ix] * sign[ip] * mobility[0] * mobility[1] / total_mobility * (capGrad[1] -capGrad[0]);
+                  halfFluxVal[ip][ix] += capillarity[ip][ix];
+
+                  for( integer ke = 0; ke < 2; ++ke )
+                  {
+                    real64 dC_dP = sign[ix] * sign[ip] * (dMob_dP[0][ke] * mobility[1] * mobility[1] + dMob_dP[1][ke] * mobility[0] * mobility[0]) / (total_mobility * total_mobility) *
+                                   (capGrad[1] -capGrad[0]) +
+                                   sign[ix] * sign[ip] * mobility[0] * mobility[1] / total_mobility * (dCapGrad_dP[1][ke] - dCapGrad_dP[0][ke]);
+
+                    real64 dC_dS_term1 = sign[ix] * sign[ip] * (dMob_dS[0][ke] * mobility[1] * mobility[1] + dMob_dS[1][ke] * mobility[0] * mobility[0]) / (total_mobility * total_mobility) *
+                                   (capGrad[1] -capGrad[0]);
+
+                    real64 dC_dS_term2 = sign[ix] * sign[ip] * (mobility[0] * mobility[1]) / total_mobility;
+
+                    real64 dC_dS_term3 = (dCapGrad_dS[1][ke] - dCapGrad_dS[0][ke]);
+
+                    if( ix == 0 )
+                    {
+                      dC1_dS[ip][ke] = dC_dS_term1 + dC_dS_term2 * dC_dS_term3;
+                      dhalfFlux1_dP[ip][ke] -= dC_dP;
+                      dhalfFlux1_dS[ip][ke] -= dC1_dS[ip][ke];
+                      if (std::fabs(facePhaseVolFrac1[0][0] - 1.0) > 1e-8){
+                        dC1_dpc[ip][ke] =  dC1_dS[ip][ke] * dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+                      } else {
+                        dC1_dpc[ip][ke] = dC_dS_term1 * dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+                      }
+                      
+                      // GEOS_UNUSED_VAR( dC1_dpc[ip][ke] );
+                    }
+                    else
+                    {
+                      dC2_dS[ip][ke] = dC_dS_term1 + dC_dS_term2 * dC_dS_term3;
+                      dhalfFlux2_dP[ip][ke] -= dC_dP;
+                      dhalfFlux2_dS[ip][ke] -= dC2_dS[ip][ke];
+                      if (std::fabs(facePhaseVolFrac2[0][0] - 1.0) > 1e-8){
+                        dC2_dpc[ip][ke] =  dC2_dS[ip][ke] * dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+                      } else {
+                        dC2_dpc[ip][ke] = dC_dS_term1 * dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+                      }
+                      // GEOS_UNUSED_VAR( dC2_dpc[ip][ke] );
+                    }
+
+                  }
+
+
+                  if( halfFluxVal[ip][0] > 0.0 )
+                  {
+                    k_up_0_check[ip] = true;
+                  }
+                  if( halfFluxVal[ip][1] > 0.0 )
+                  {
+                    k_up_1_check[ip] = true;
+                  }
+
+                } // loop over phases
+
+              } // loop over half fluxes
+
+              check = true;
+
+              bool flip0[2] = {0, 0};
+              bool flip0_k_up[2] = {0, 0};
+              bool flip1[2] = {0, 0};
+              bool flip1_k_up[2] = {0, 0};
+              // loop over phases
+              for( integer ip = 0; ip < 2; ++ip )
+              {
+                bool k_up_0_b = !static_cast< bool >(k_up_0[ip]);
+                bool k_up_1_b = static_cast< bool >(k_up_1[ip]);
+                flip0_k_up[ip] =  k_up_0_b;
+                flip1_k_up[ip] =  k_up_1_b;
+
+                if( std::fabs( uT ) < 1e-20 )
+                {
+
+                  if((std::fabs( halfFluxVal[ip][0] ) < 1e-20) && (std::fabs( halfFluxVal[ip][1] ) < 1e-20))
+                  {
+                    k_up_0_check[ip] = !k_up_0_b;
+                    k_up_1_check[ip] = !k_up_1_b;
+                  }
+                  else
+                  {
+                    k_up_0_check[ip] = k_up_0_b;
+                    k_up_1_check[ip] = k_up_1_b;
+                  }
+
+                  if( k_up_0_check[ip] != k_up_0_b )
+                  {
+                    flip0[ip] = 1;
+                    check = false;
+                  }
+
+                  if( k_up_1_check[ip] != k_up_1_b )
+                  {
+                    flip1[ip] = 1;
+                    check = false;
+                  }
+
+                }
+                else
+                {
+                  if( std::fabs( halfFluxVal[ip][0] ) < 1e-20 )
+                  {
+                    k_up_0_check[ip] = k_up_0_b;
+                  }
+
+                  if( std::fabs( halfFluxVal[ip][1] ) < 1e-20 )
+                  {
+                    k_up_1_check[ip] = k_up_1_b;
+                  }
+
+                  if( k_up_0_check[ip] != k_up_0_b )
+                  {
+                    k_up_0[ip] = static_cast< localIndex >(k_up_0_b);
+                    check = false;
+                  }
+
+                  if( k_up_1_check[ip] != k_up_1_b )
+                  {
+                    k_up_1[ip] = static_cast< localIndex >(!k_up_1_b);
+                    check = false;
+                  }
+                }
+
+              }
+
+              if( flip0[0] || flip0[1] )
+              {
+                k_up_0[0] = static_cast< localIndex >(flip0_k_up[0]);
+                k_up_0[1] = static_cast< localIndex >(flip0_k_up[1]);
+              }
+
+              if( flip1[0] || flip1[1] )
+              {
+                k_up_1[0] = static_cast< localIndex >(!flip1_k_up[0]);
+                k_up_1[1] = static_cast< localIndex >(!flip1_k_up[1]);
+              }
+
+            } // while check for BJ PPU
+
+            real64 constexpr eps2 = 1e-12;
+            // real64 constexpr eps2 = 0.0;
+            // newton update
+            dhalfFlux_dpc[0][0] = dhalfFlux1_dS[0][1]*dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+            real64 dhalfFlux_dpc00 = dV1_dpc[0][1] - dG1_dpc[0][1] - dC1_dpc[0][1];
+            dhalfFlux_dpc[0][1] = dhalfFlux2_dS[0][1]*dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+            real64 dhalfFlux_dpc01 = dV2_dpc[0][1] - dG2_dpc[0][1] - dC2_dpc[0][1];
+
+            dhalfFlux_dpc[1][0] = dhalfFlux1_dS[1][1]*dfacePhaseVolFrac_dCapPres1[0][0][0][0];
+            real64 dhalfFlux_dpc10 = dV1_dpc[1][1] - dG1_dpc[1][1] - dC1_dpc[1][1];
+            dhalfFlux_dpc[1][1] = dhalfFlux2_dS[1][1]*dfacePhaseVolFrac_dCapPres2[0][0][0][0];
+            real64 dhalfFlux_dpc11 = dV2_dpc[1][1] - dG2_dpc[1][1] - dC2_dpc[1][1];
+
+            dhalfFlux_dpc[0][0] = dhalfFlux_dpc00;
+            dhalfFlux_dpc[0][1] = dhalfFlux_dpc01;
+            dhalfFlux_dpc[1][0] = dhalfFlux_dpc10;
+            dhalfFlux_dpc[1][1] = dhalfFlux_dpc11;
+
+
+
+            real64 const denom = dhalfFlux_dpc[0][0] - dhalfFlux_dpc[0][1];
+            real64 const denomAbs = LvArray::math::abs(denom);
+            local_jacobian = (denomAbs < eps2) ? (denom >= 0.0 ? eps2 : -eps2) : denom;
+            local_residual = halfFluxVal[0][0] - halfFluxVal[0][1];
+            
+
+
+            last_local_residual = local_residual;
+            last_local_jacobian = local_jacobian;
+            last_facePhaseVolFrac1_0 = facePhaseVolFrac1[0][0];
+            last_facePhaseVolFrac2_0 = facePhaseVolFrac2[0][0];
+            last_faceCapPres1 = faceCapPres1[0][0][0];
+            last_faceCapPres2 = faceCapPres2[0][0][0];
+            last_iter = iter;
+            
+            constexpr bool ENABLE_NEWTON_ITER_DEBUG = false;
+            if constexpr (ENABLE_NEWTON_ITER_DEBUG) {
+              if (iter < 10 || iter % 10 == 0 || iter >= max_iter - 3) {
+                std::cout << "  [NI] it=" << iter 
+                          << " Pc=" << Pc_int 
+                          << " S1=" << facePhaseVolFrac1[0][0] 
+                          << " S2=" << facePhaseVolFrac2[0][0]
+                          << " Pc1f=" << faceCapPres1[0][0][0] 
+                          << " Pc2f=" << faceCapPres2[0][0][0]
+                          << " dSdPc1=" << dfacePhaseVolFrac_dCapPres1[0][0][0][0]
+                          << " dSdPc2=" << dfacePhaseVolFrac_dCapPres2[0][0][0][0]
+                          << " res=" << local_residual 
+                          << " jac=" << local_jacobian 
+                          << " dPc=" << (std::abs(local_jacobian) > 1e-30 ? local_residual/local_jacobian : 0.0)
+                          << std::endl;
+              }
+            }
+            
+            if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+              if (false) {
+                std::cout << "[LOCAL_SOLVER_DEBUG_ITER] iter=" << iter << ", Pc_int=" << Pc_int 
+                          << ", Pc1_face=" << faceCapPres1[0][0][0] << ", Pc2_face=" << faceCapPres2[0][0][0] << std::endl;
+                std::cout << "[LOCAL_SOLVER_DEBUG_ITER] S1_face=" << facePhaseVolFrac1[0][0] 
+                          << ", S2_face=" << facePhaseVolFrac2[0][0] << std::endl;
+                std::cout << "[LOCAL_SOLVER_DEBUG_ITER] halfFluxVal[0][0]=" << halfFluxVal[0][0] 
+                          << ", halfFluxVal[0][1]=" << halfFluxVal[0][1] << std::endl;
+                std::cout << "[LOCAL_SOLVER_DEBUG_ITER] dhalfFlux_dpc[0][0]=" << dhalfFlux_dpc[0][0] 
+                          << ", dhalfFlux_dpc[0][1]=" << dhalfFlux_dpc[0][1] << std::endl;
+                std::cout << "[LOCAL_SOLVER_DEBUG_ITER] local_residual=" << local_residual 
+                          << ", local_jacobian=" << local_jacobian << std::endl;
+              }
+            }
+
+            {
+              real64 absRes = std::fabs( local_residual );
+              if( absRes < best_absRes )
+              {
+                best_absRes = absRes;
+                best_Pc = Pc_int;
+              }
+            }
+
+            bool bracketEstablished = bracket_lo_set && bracket_hi_set;
+            if( !bracketEstablished )
+            {
+              if( !bracket_lo_set && !bracket_hi_set )
+              {
+                Pc_bracket_lo = Pc_int;
+                res_bracket_lo = local_residual;
+                bracket_lo_set = true;
+              }
+              else
+              {
+                if( res_bracket_lo * local_residual < 0.0 )
+                {
+                  Pc_bracket_hi = Pc_int;
+                  res_bracket_hi = local_residual;
+                  bracket_hi_set = true;
+                  if( Pc_bracket_lo > Pc_bracket_hi )
+                  {
+                    real64 tmpPc = Pc_bracket_lo;
+                    real64 tmpRes = res_bracket_lo;
+                    Pc_bracket_lo = Pc_bracket_hi;
+                    res_bracket_lo = res_bracket_hi;
+                    Pc_bracket_hi = tmpPc;
+                    res_bracket_hi = tmpRes;
+                  }
+                }
+                else
+                {
+                  Pc_bracket_lo = Pc_int;
+                  res_bracket_lo = local_residual;
+              }
+              }
+            }
+            else
+            {
+              if( local_residual * res_bracket_lo <= 0.0 )
+              {
+                Pc_bracket_hi = Pc_int;
+                res_bracket_hi = local_residual;
+              }
+              else
+              {
+                Pc_bracket_lo = Pc_int;
+                res_bracket_lo = local_residual;
+              }
+            }
+            bracketEstablished = bracket_lo_set && bracket_hi_set;
+
+            constexpr bool ENABLE_BRACKET_DEBUG = false;
+            if constexpr (ENABLE_BRACKET_DEBUG) {
+              if (iter < 5 || iter % 10 == 0) {
+                std::cout << "  [BRACKET] iter=" << iter 
+                          << " established=" << bracketEstablished
+                          << " lo=" << Pc_bracket_lo << " (res=" << res_bracket_lo << ")"
+                          << " hi=" << Pc_bracket_hi << " (res=" << res_bracket_hi << ")"
+                          << " width=" << (Pc_bracket_hi - Pc_bracket_lo) << std::endl;
+              }
+            }
+
+            real64 const convergeTol = ( ENABLE_BEST_SOLUTION_FALLBACK && fallback_used ) ? ( FALLBACK_TOL_FACTOR * tol ) : tol;
+            bool const eitherClamped = faceCapPres1_clamped || faceCapPres2_clamped;
+            bool const rejectClampedConvergence = eitherClamped && !bracketEstablished && iter < max_iter - 5;
+            if( std::fabs( local_residual ) < convergeTol && !rejectClampedConvergence )
+            {
+              converged = 1;
+              outFile << GEOS_FMT( "{:10.10e}", local_jacobian );
+              outFile << GEOS_FMT( ",{:10.10e}", local_residual );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", Pc_int_iterate );
+              outFile << GEOS_FMT( ",{:10.10e}", faceCapPres1[0][0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", faceCapPres2[0][0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", transHat[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", transHat[1] );
+              outFile << GEOS_FMT( ",{:10.10e}", gravCoefHat[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", gravCoef[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", gravCoef[1] );
+              outFile << GEOS_FMT( ",{:10.10e}", uT );
+              outFile << GEOS_FMT( ",{:10.10e}", duT_dP[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", duT_dS[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", duT_dP[1] );
+              outFile << GEOS_FMT( ",{:10.10e}", duT_dS[1] );                                          
+              outFile << std::endl;
+              break; // Converged
+            }
+
+            {
+              bool atLoBound = (std::fabs(Pc_int - Pc_union_min) < 1e-10 * (std::fabs(Pc_union_min) + 1.0));
+              bool atHiBound = (std::fabs(Pc_int - Pc_union_max) < 1e-10 * (std::fabs(Pc_union_max) + 1.0));
+              if( (atLoBound || atHiBound) && std::fabs( local_residual ) < 10.0 * tol && !rejectClampedConvergence )
+              {
+                converged = 1;
+                break;
+              }
+            }
+
+            if( iter >= max_iter - 1 )
+            {
+              if constexpr ( ENABLE_SWEEP_FALLBACK )
+              {
+                if( !sweep_active )
+                {
+                  sweep_active = true;
+                  sweep_newton_iter_end = iter;
+                  sweep_best_Pc = best_Pc;
+                  sweep_best_absRes = best_absRes;
+                  bracket_lo_set = false;
+                  bracket_hi_set = false;
+                  Pc_int = Pc_union_min;
+                  max_iter += 500;
+                  if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+                    std::cout << "[SWEEP] Activated at iter=" << iter
+                              << ", sweeping [" << Pc_union_min << ", " << Pc_union_max << "]"
+                              << ", dS=" << SWEEP_DS << std::endl;
+                  }
+                  iter++;
+                  continue;  // re-enter loop to evaluate at Pc_union_min
+                }
+                else
+                {
+                  real64 const sweepAcceptTol = SWEEP_ACCEPT_TOL_FACTOR * tol;
+                  if( sweep_best_absRes < sweepAcceptTol )
+                  {
+                    Pc_int = sweep_best_Pc;
+                    converged = 1;
+                    if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+                      std::cout << "[SWEEP] Accepted best: Pc=" << sweep_best_Pc
+                                << ", |res|=" << sweep_best_absRes
+                                << " < sweepTol=" << sweepAcceptTol << std::endl;
+                    }
+                    break;
+                  }
+                  else
+                  {
+                    if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+                      std::cout << "[SWEEP] DIVERGED: sweep_best_Pc=" << sweep_best_Pc
+                                << ", sweep_best_absRes=" << sweep_best_absRes
+                                << ", sweepAcceptTol=" << sweepAcceptTol << std::endl;
+                    }
+                    div = 1;
+              local_jacobian = 0.0;
+                    break;
+              }
+              }
+            }
+            else
+            {
+                if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+                  std::cout << "[LOCAL_SOLVER_DEBUG] DIVERGED: best_Pc=" << best_Pc
+                            << ", best_absRes=" << best_absRes
+                            << ", fallbackTol=" << FALLBACK_TOL_FACTOR * tol << std::endl;
+                }
+                div = 1;
+                local_jacobian = 0.0;
+                break;
+              }
+            }
+
+            if( sweep_active && !bracketEstablished )
+            {
+              real64 const absRes_sweep = std::fabs( local_residual );
+              if( absRes_sweep < sweep_best_absRes )
+              {
+                sweep_best_absRes = absRes_sweep;
+                sweep_best_Pc = Pc_int;
+              }
+
+              real64 const absDSdPc1 = std::fabs( dfacePhaseVolFrac_dCapPres1[0][0][0][0] );
+              real64 const absDSdPc2 = std::fabs( dfacePhaseVolFrac_dCapPres2[0][0][0][0] );
+              real64 const max_absDSdPc = fmax( absDSdPc1, absDSdPc2 );
+              real64 const dPc_max_cap = ( Pc_union_max - Pc_union_min ) / static_cast< real64 >( SWEEP_MIN_POINTS );
+              real64 dPc_step;
+              if( max_absDSdPc > 1e-20 )
+              {
+                dPc_step = SWEEP_DS / max_absDSdPc;
+              }
+              else
+              {
+                dPc_step = dPc_max_cap;
+              }
+              dPc_step = fmin( dPc_step, dPc_max_cap );
+
+              real64 const Pc_next = Pc_int + dPc_step;
+
+              if( Pc_next >= Pc_union_max )
+              {
+                Pc_int = sweep_best_Pc;
+                max_iter = iter + 2;
+                if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+                  std::cout << "[SWEEP] Completed full sweep, no sign change found."
+                            << " sweep_best_Pc=" << sweep_best_Pc
+                            << ", sweep_best_absRes=" << sweep_best_absRes << std::endl;
+                }
+              }
+              else
+              {
+                Pc_int = Pc_next;
+              }
+
+              if constexpr (ENABLE_BRACKET_DEBUG) {
+                if( (iter - sweep_newton_iter_end) % 20 == 0 || Pc_next >= Pc_union_max ) {
+                  std::cout << "  [SWEEP] Pc=" << Pc_int
+                            << ", dPc_step=" << dPc_step
+                            << ", best_Pc=" << sweep_best_Pc
+                            << ", best_absRes=" << sweep_best_absRes << std::endl;
+                }
+              }
+            }
+            else if( sweep_active && bracketEstablished )
+            {
+              if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+                std::cout << "[SWEEP] Bracket found! Switching to bisection."
+                          << " bracket=[" << Pc_bracket_lo << ", " << Pc_bracket_hi << "]" << std::endl;
+              }
+              Pc_int = ( Pc_bracket_lo + Pc_bracket_hi ) / 2.0;
+            }
+            else
+            {
+              real64 deltaPc = local_residual / local_jacobian;
+
+              if (damping) {
+                real64 max_dpc = fmax( fabs(dCapPres1_dfacePhaseVolFrac[0][0][0][0]), fabs(dCapPres2_dfacePhaseVolFrac[0][0][0][0]));
+                  real64 sign = std::copysign(1.0, deltaPc);
+                  deltaPc = fmin( fabs(deltaPc), max_dpc * 0.1 );
+                  deltaPc *= sign;
+              }
+
+              real64 Pc_newton = Pc_int - deltaPc;
+
+              bool useBisection = false;
+              if( bracketEstablished )
+              {
+                real64 brak_width = Pc_bracket_hi - Pc_bracket_lo;
+                if( Pc_newton <= Pc_bracket_lo || Pc_newton >= Pc_bracket_hi ||
+                    std::fabs(deltaPc) > 0.75 * brak_width )
+                {
+                  useBisection = true;
+                }
+              }
+
+              if( useBisection )
+              {
+                Pc_int = ( Pc_bracket_lo + Pc_bracket_hi ) / 2.0;
+              }
+              else
+              {
+                Pc_int = fmin( Pc_union_max, fmax( Pc_newton, Pc_union_min ) );
+              }
+
+              if( std::fabs( Pc_int - prev_Pc_evaluated ) < 1e-10 * std::fabs( Pc_int ) + 1e-30 )
+              {
+                n_same_pc++;
+              }
+              else
+              {
+                n_same_pc = 0;
+              }
+              prev_Pc_evaluated = Pc_int_iterate;
+
+              if( n_same_pc >= 3 && !bracketEstablished )
+              {
+                real64 Pc_probe = 0.0;
+                real64 const Pc_inner_max = fmin( Pc1_max, Pc2_max );
+                if( stuck_probe_level == 0 )
+                {
+                  Pc_probe = ( Pc1 + Pc2 ) / 2.0;
+                }
+                else if( stuck_probe_level == 1 )
+                {
+                  Pc_probe = Pc_inner_max - 1.0;
+                }
+                else if( stuck_probe_level == 2 )
+                {
+                  Pc_probe = Pc_inner_max;
+                }
+                else
+                {
+                  if( std::fabs( Pc_int - Pc_union_min ) < std::fabs( Pc_int - Pc_union_max ) )
+                    Pc_probe = Pc_union_max;
+                  else
+                    Pc_probe = Pc_union_min;
+                }
+
+                if( std::fabs( Pc_probe - Pc_int ) > 1e-10 * ( std::fabs( Pc_int ) + 1.0 ) )
+                {
+                  Pc_int = Pc_probe;
+                }
+                else
+                {
+                  stuck_probe_level++;
+                  continue;
+                }
+                stuck_probe_level++;
+                n_same_pc = 0;
+
+                if constexpr (ENABLE_BRACKET_DEBUG) {
+                  std::cout << "  [STUCK] Forced probe (level " << (stuck_probe_level - 1)
+                            << ") to Pc_int=" << Pc_int << std::endl;
+                }
+              }
+
+              if constexpr (ENABLE_BRACKET_DEBUG) {
+                if (iter < 5 || iter % 10 == 0) {
+                  char const * stepName = useBisection ? "BISECTION" : "NEWTON";
+                  std::cout << "  [STEP] " << stepName
+                            << " -> Pc_int=" << Pc_int << std::endl;
+                }
+              }
+            } // end step selection
+
+              // truncate the updated capillary pressure (extended capillary pressure condition) for reporting/plotting:
+
+              real64 faceCapPres1_plot = fmin( Pc1_max, fmax( Pc_int, Pc1_min ));
+              real64 faceCapPres2_plot = fmin( Pc2_max, fmax( Pc_int, Pc2_min ));
+              faceCapPres1_plot = fmin( Pc2_max, fmax( faceCapPres1_plot, Pc2_min ));
+              faceCapPres2_plot = fmin( Pc1_max, fmax( faceCapPres2_plot, Pc1_min ));
+              
+              // Write data to the file
+              outFile << GEOS_FMT( "{:10.10e}", local_jacobian );
+              outFile << GEOS_FMT( ",{:10.10e}", local_residual );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", Pc_int_iterate );
+              outFile << GEOS_FMT( ",{:10.10e}", faceCapPres1[0][0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", faceCapPres2[0][0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", halfFluxVal[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", viscous[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", bouyancy[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[0][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[1][0] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[0][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", capillarity[1][1] );
+              outFile << GEOS_FMT( ",{:10.10e}", transHat[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", transHat[1] );
+              outFile << GEOS_FMT( ",{:10.10e}", gravCoefHat[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", gravCoef[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", gravCoef[1] );
+              outFile << GEOS_FMT( ",{:10.10e}", uT );
+              outFile << GEOS_FMT( ",{:10.10e}", duT_dP[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", duT_dS[0] );
+              outFile << GEOS_FMT( ",{:10.10e}", duT_dP[1] );
+              outFile << GEOS_FMT( ",{:10.10e}", duT_dS[1] );  
+              outFile << std::endl;
+
+              iter++;
+            
+          } // while loop
+
+          if( converged )
+          {
+            warmStartPc = Pc_int;
+          }
+
+          if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+            const char* modeNames[] = {
+              "DRAINAGE",
+              "IMBIBITION", 
+              "DRAINAGE_TO_IMBIBITION",
+              "IMBIBITION_TO_DRAINAGE",
+              "IMBIBITION_TO_DRAINAGE_FROM_SCANNING"
+            };
+            integer mode0 = static_cast<integer>(modes[0]);
+            integer mode1 = static_cast<integer>(modes[1]);
+            const char* name0 = (mode0 >= 0 && mode0 <= 4) ? modeNames[mode0] : "UNKNOWN";
+            const char* name1 = (mode1 >= 0 && mode1 <= 4) ? modeNames[mode1] : "UNKNOWN";
+            
+            std::cout << "[LOCAL_SOLVER_DEBUG] converged=" << converged << ", iter=" << last_iter << ", div=" << div << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Modes: cell0=" << name0 << " (" << mode0 << "), cell1=" << name1 << " (" << mode1 << ")" << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Capillary Pressures: Pc1=" << Pc1 << ", Pc2=" << Pc2 << ", Pc_int=" << Pc_int << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Pc bounds: Pc1_min=" << Pc1_min << ", Pc1_max=" << Pc1_max << ", Pc2_min=" << Pc2_min << ", Pc2_max=" << Pc2_max << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Initial saturations: S1=" << saturations[0] << ", S2=" << saturations[1] << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Last face saturations: S1_face=" << last_facePhaseVolFrac1_0 << ", S2_face=" << last_facePhaseVolFrac2_0 << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Last face capillary pressures: Pc1_face=" << last_faceCapPres1 << ", Pc2_face=" << last_faceCapPres2 << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Last residual: local_residual=" << last_local_residual << ", local_jacobian=" << last_local_jacobian << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Best solution: best_Pc=" << best_Pc << ", best_absRes=" << best_absRes
+                      << ", fallbackTol=" << FALLBACK_TOL_FACTOR * tol << ", fallback_used=" << fallback_used << std::endl;
+            std::cout << "[LOCAL_SOLVER_DEBUG] Warm-start: used=" << usedWarmStart << ", warmStartPc=" << warmStartPc << std::endl;
+            if( sweep_active ) {
+              std::cout << "[LOCAL_SOLVER_DEBUG] Sweep: active, sweep_best_Pc=" << sweep_best_Pc
+                        << ", sweep_best_absRes=" << sweep_best_absRes
+                        << ", sweep_iter=" << (last_iter - sweep_newton_iter_end) << std::endl;
+            }
+          }
+
+          if( converged )
+          {
+
+            real64 constexpr eps3 = 1e-12;
+            real64 const denom_deriv = dhalfFlux_dpc[0][0] - dhalfFlux_dpc[0][1];
+            real64 const denomAbs_deriv = LvArray::math::abs(denom_deriv);
+            real64 const denom_protected = (denomAbs_deriv < eps3) ? (denom_deriv >= 0.0 ? eps3 : -eps3) : denom_deriv;
+
+            real64 const dPc_int_dS1 =(-1.0) * (dhalfFlux1_dS[0][0] +  dhalfFlux_duT[0][0] * duT_dS[0] - dhalfFlux_duT[0][1] * duT_dS[0]) / denom_protected;
+            real64 const dPc_int_dS2 =(-1.0) * (dhalfFlux_duT[0][0] * duT_dS[1] - dhalfFlux2_dS[0][0] - dhalfFlux_duT[0][1] * duT_dS[1]) / denom_protected;
+            real64 const dPc_int_du =(-1.0) * (dhalfFlux_duT[0][0]  - dhalfFlux_duT[0][1]) / denom_protected;
+
+            dFlux_dP[0][0] =  (dhalfFlux_duT[0][0] * duT_dP[0] + dhalfFlux_dpc[0][0] * dPc_int_du * duT_dP[0]) * density2[0] + halfFluxVal[0][0] * dDens_dP2[0][0];
+            dFlux_dS[0][0] = (dhalfFlux1_dS[0][0] +  dhalfFlux_duT[0][0] * duT_dS[0] + dhalfFlux_dpc[0][0] * dPc_int_dS1) * density2[0];
+
+            dFlux_dP[0][1] = (dhalfFlux_duT[0][1] * duT_dP[1] + dhalfFlux_dpc[0][1] * dPc_int_du * duT_dP[1]) * density2[0] + halfFluxVal[0][1] * dDens_dP2[0][1];
+            dFlux_dS[0][1] = (dhalfFlux2_dS[0][0] +  dhalfFlux_duT[0][1] * duT_dS[1] + dhalfFlux_dpc[0][1] * dPc_int_dS2) * density2[0];
+
+            dFlux_dP[1][0] =  (dhalfFlux_duT[1][0] * duT_dP[0] + dhalfFlux_dpc[1][0] * dPc_int_du * duT_dP[0]) * density2[1] + halfFluxVal[1][0] * dDens_dP2[1][0];
+            dFlux_dS[1][0] = (dhalfFlux1_dS[1][0] +  dhalfFlux_duT[1][0] * duT_dS[0] + dhalfFlux_dpc[1][0] * dPc_int_dS1) * density2[1];
+
+            dFlux_dP[1][1] = (dhalfFlux_duT[1][1] * duT_dP[1] + dhalfFlux_dpc[1][1] * dPc_int_du * duT_dP[1]) * density2[1] + halfFluxVal[1][1] * dDens_dP2[1][1];
+            dFlux_dS[1][1] = (dhalfFlux2_dS[1][0] +  dhalfFlux_duT[1][1] * duT_dS[1] + dhalfFlux_dpc[1][1] * dPc_int_dS2) * density2[1];
+
+            fluxVal[0] = halfFluxVal[0][0] * density2[0];
+            fluxVal[1] = halfFluxVal[1][0] * density2[1];
+
+            constexpr bool ENABLE_GLOBAL_DERIVATIVES_DEBUG = false;
+            if constexpr (ENABLE_GLOBAL_DERIVATIVES_DEBUG) {
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG] fluxVal[0]=" << fluxVal[0] << ", fluxVal[1]=" << fluxVal[1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG] dFlux_dP[0][0]=" << dFlux_dP[0][0] << ", dFlux_dP[0][1]=" << dFlux_dP[0][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG] dFlux_dP[1][0]=" << dFlux_dP[1][0] << ", dFlux_dP[1][1]=" << dFlux_dP[1][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG] dFlux_dS[0][0]=" << dFlux_dS[0][0] << ", dFlux_dS[0][1]=" << dFlux_dS[0][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG] dFlux_dS[1][0]=" << dFlux_dS[1][0] << ", dFlux_dS[1][1]=" << dFlux_dS[1][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG] Intermediate values:" << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dPc_int_dS1=" << dPc_int_dS1 << ", dPc_int_dS2=" << dPc_int_dS2 << ", dPc_int_du=" << dPc_int_du << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   halfFluxVal[0][0]=" << halfFluxVal[0][0] << ", halfFluxVal[0][1]=" << halfFluxVal[0][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   halfFluxVal[1][0]=" << halfFluxVal[1][0] << ", halfFluxVal[1][1]=" << halfFluxVal[1][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dhalfFlux_dpc[0][0]=" << dhalfFlux_dpc[0][0] << ", dhalfFlux_dpc[0][1]=" << dhalfFlux_dpc[0][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dhalfFlux_dpc[1][0]=" << dhalfFlux_dpc[1][0] << ", dhalfFlux_dpc[1][1]=" << dhalfFlux_dpc[1][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dhalfFlux1_dS[0][0]=" << dhalfFlux1_dS[0][0] << ", dhalfFlux1_dS[0][1]=" << dhalfFlux1_dS[0][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dhalfFlux1_dS[1][0]=" << dhalfFlux1_dS[1][0] << ", dhalfFlux1_dS[1][1]=" << dhalfFlux1_dS[1][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dhalfFlux2_dS[0][0]=" << dhalfFlux2_dS[0][0] << ", dhalfFlux2_dS[0][1]=" << dhalfFlux2_dS[0][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dhalfFlux2_dS[1][0]=" << dhalfFlux2_dS[1][0] << ", dhalfFlux2_dS[1][1]=" << dhalfFlux2_dS[1][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dhalfFlux_duT[0][0]=" << dhalfFlux_duT[0][0] << ", dhalfFlux_duT[0][1]=" << dhalfFlux_duT[0][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   dhalfFlux_duT[1][0]=" << dhalfFlux_duT[1][0] << ", dhalfFlux_duT[1][1]=" << dhalfFlux_duT[1][1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   duT_dS[0]=" << duT_dS[0] << ", duT_dS[1]=" << duT_dS[1] << std::endl;
+              std::cout << "[GLOBAL_DERIVATIVES_DEBUG]   density2[0]=" << density2[0] << ", density2[1]=" << density2[1] << std::endl;
+            }
+
+          } else {
+
+            if constexpr (ENABLE_LOCAL_SOLVER_DEBUG) {
+            std::cout << "**********************Diverged*******************" << std::endl;
+            
+            const char* modeNames[] = {
+              "DRAINAGE",
+              "IMBIBITION", 
+              "DRAINAGE_TO_IMBIBITION",
+              "IMBIBITION_TO_DRAINAGE",
+              "IMBIBITION_TO_DRAINAGE_FROM_SCANNING"
+            };
+            integer mode0 = static_cast<integer>(modes[0]);
+            integer mode1 = static_cast<integer>(modes[1]);
+            const char* name0 = (mode0 >= 0 && mode0 <= 4) ? modeNames[mode0] : "UNKNOWN";
+            const char* name1 = (mode1 >= 0 && mode1 <= 4) ? modeNames[mode1] : "UNKNOWN";
+            std::cout << "  [DEBUG] Modes: cell0=" << name0 << " (" << mode0 << "), cell1=" << name1 << " (" << mode1 << ")" << std::endl;
+            std::cout << "  [DEBUG] Capillary Pressures: Pc1=" << Pc1 << ", Pc2=" << Pc2 << ", Pc_int=" << Pc_int << std::endl;
+            std::cout << "  [DEBUG] Pc bounds: Pc1_min=" << Pc1_min << ", Pc1_max=" << Pc1_max << ", Pc2_min=" << Pc2_min << ", Pc2_max=" << Pc2_max << std::endl;
+            std::cout << "  [DEBUG] Initial saturations: S1=" << saturations[0] << ", S2=" << saturations[1] << std::endl;
+            std::cout << "  [DEBUG] Last iteration values: iter=" << last_iter << ", div=" << div << std::endl;
+            std::cout << "  [DEBUG] Last face saturations: S1_face=" << last_facePhaseVolFrac1_0 << ", S2_face=" << last_facePhaseVolFrac2_0 << std::endl;
+            std::cout << "  [DEBUG] Last face capillary pressures: Pc1_face=" << last_faceCapPres1 << ", Pc2_face=" << last_faceCapPres2 << std::endl;
+            std::cout << "  [DEBUG] Last residual: local_residual=" << last_local_residual << ", local_jacobian=" << last_local_jacobian << std::endl;
+            }
+
+          }
+          
+          phi[0] = fluxVal[0];
+          phi[1] = fluxVal[1];
+
+          grad_phi_P[0] = dFlux_dP[0][0];
+          grad_phi_P[1] = dFlux_dP[0][1];
+          grad_phi_P[2] = dFlux_dP[1][0];
+          grad_phi_P[3] = dFlux_dP[1][1];
+
+          grad_phi_S[0] = dFlux_dS[0][0];
+          grad_phi_S[1] = dFlux_dS[0][1];
+          grad_phi_S[2] = dFlux_dS[1][0];
+          grad_phi_S[3] = dFlux_dS[1][1];
+
+
+// Close the file after writing
+          outFile.close();
+
+        } );
+
+      } );
+
+    } );
+
+  } );
+
+
+}
 
 /******************************** FluxComputeKernelBase ********************************/
 
@@ -78,17 +2240,23 @@ class FluxComputeKernelBase
                       fields::flow::gravityCoefficient,
                       fields::immiscibleMultiphaseFlow::phaseVolumeFraction,
                       fields::immiscibleMultiphaseFlow::phaseMobility,
+                      fields::immiscibleMultiphaseFlow::phaseMass_n,
                       fields::immiscibleMultiphaseFlow::dPhaseMobility >;
 
   using MultiphaseFluidAccessors =
     StencilMaterialAccessors< constitutive::TwoPhaseImmiscibleFluid,
                               fields::twophaseimmisciblefluid::phaseDensity,
-                              fields::twophaseimmisciblefluid::dPhaseDensity >;
+                              fields::twophaseimmisciblefluid::dPhaseDensity,
+                              fields::twophaseimmisciblefluid::phaseViscosity,
+                              fields::twophaseimmisciblefluid::dPhaseViscosity >;
 
   using CapPressureAccessors =
     StencilMaterialAccessors< CapillaryPressureBase,
                               fields::cappres::phaseCapPressure,
-                              fields::cappres::dPhaseCapPressure_dPhaseVolFraction >;
+                              fields::cappres::dPhaseCapPressure_dPhaseVolFraction
+                              >;
+                              // ,fields::cappres::jFuncMultiplier >;
+
 
   using PermeabilityAccessors =
     StencilMaterialAccessors< PermeabilityBase,
@@ -135,12 +2303,16 @@ class FluxComputeKernelBase
     m_gravCoef( multiPhaseFlowAccessors.get( fields::flow::gravityCoefficient {} ) ),
     m_pres( multiPhaseFlowAccessors.get( fields::flow::pressure {} ) ),
     m_phaseVolFrac( multiPhaseFlowAccessors.get( fields::immiscibleMultiphaseFlow::phaseVolumeFraction {} ) ),
+    m_phaseMass_n( multiPhaseFlowAccessors.get( fields::immiscibleMultiphaseFlow::phaseMass_n {} ) ),
     m_mob( multiPhaseFlowAccessors.get( fields::immiscibleMultiphaseFlow::phaseMobility {} ) ),
     m_dMob( multiPhaseFlowAccessors.get( fields::immiscibleMultiphaseFlow::dPhaseMobility {} ) ),
     m_dens( fluidAccessors.get( fields::twophaseimmisciblefluid::phaseDensity {} ) ),
+    m_visc( fluidAccessors.get( fields::twophaseimmisciblefluid::phaseViscosity {} ) ),
     m_dDens_dPres( fluidAccessors.get( fields::twophaseimmisciblefluid::dPhaseDensity {} ) ),
+    m_dVisc_dPres( fluidAccessors.get( fields::twophaseimmisciblefluid::dPhaseViscosity {} ) ),
     m_phaseCapPressure( capPressureAccessors.get( fields::cappres::phaseCapPressure {} ) ),
     m_dPhaseCapPressure_dPhaseVolFrac( capPressureAccessors.get( fields::cappres::dPhaseCapPressure_dPhaseVolFraction {} ) ),
+    // m_jFuncMultiplier( capPressureAccessors.get( fields::cappres::jFuncMultiplier {} ) ),
     m_localMatrix( localMatrix ),
     m_localRhs( localRhs ),
     m_hasCapPressure ( hasCapPressure ),
@@ -174,21 +2346,26 @@ class FluxComputeKernelBase
   /// Views on pressure and phase volume fraction
   ElementViewConst< arrayView1d< real64 const > > const m_pres;
   ElementViewConst< arrayView2d< real64 const, immiscibleFlow::USD_PHASE > > const m_phaseVolFrac;
+  ElementViewConst< arrayView2d< real64 const, immiscibleFlow::USD_PHASE > > const m_phaseMass_n;
 
   /// Views on fluid mobility
   ElementViewConst< arrayView2d< real64 const, immiscibleFlow::USD_PHASE > > const m_mob;
   ElementViewConst< arrayView3d< real64 const, immiscibleFlow::USD_PHASE_DS > > const m_dMob;
 
-  /// Views on fluid density
+  /// Views on fluid density and viscosity
   ElementViewConst< arrayView3d< real64 const, constitutive::multifluid::USD_PHASE > > const m_dens;
+  ElementViewConst< arrayView3d< real64 const, constitutive::multifluid::USD_PHASE > > const m_visc;
   ElementViewConst< arrayView4d< real64 const, constitutive::multifluid::USD_PHASE_DC > > const m_dDens_dPres;
+  ElementViewConst< arrayView4d< real64 const, constitutive::multifluid::USD_PHASE_DC > > const m_dVisc_dPres;
 
   /// Views on capillary pressure
   ElementViewConst< arrayView3d< real64 const, cappres::USD_CAPPRES > > const m_phaseCapPressure;
   ElementViewConst< arrayView4d< real64 const, cappres::USD_CAPPRES_DS > > const m_dPhaseCapPressure_dPhaseVolFrac;
+  // ElementViewConst< arrayView2d< real64 const > > const m_jFuncMultiplier;
 
   // Residual and jacobian
 
+
   /// View on the local CRS matrix
   CRSMatrixView< real64, globalIndex const > const m_localMatrix;
   /// View on the local RHS
@@ -314,6 +2491,11 @@ class FluxComputeKernel : public FluxComputeKernelBase
     /// Derivatives of transmissibility with respect to pressure
     real64 dTrans_dPres[maxNumConns][2]{};
 
+    /// Transmissibility
+    real64 transmissibilityHat[maxNumConns][2]{};
+    /// Derivatives of transmissibility with respect to pressure
+    real64 dTransHat_dPres[maxNumConns][2]{};
+
     // Local degrees of freedom and local residual/jacobian
 
     /// Indices of the matrix rows/columns corresponding to the dofs in this face
@@ -372,7 +2554,7 @@ class FluxComputeKernel : public FluxComputeKernelBase
    * @param[inout] stack the stack variables
    * @param[in] NoOpFunc the function used to customize the computation of the flux
    */
-  template< typename FUNC = NoOpFunc >   // should change to multiphase
+  template< typename FUNC = NoOpFunc >    // should change to multiphase
   GEOS_HOST_DEVICE
   void computeFlux( localIndex const iconn,
                     StackVariables & stack,
@@ -437,22 +2619,22 @@ class FluxComputeKernel : public FluxComputeKernelBase
               continue;
             }
 
-            real64 const density  = m_dens[seri[ke]][sesri[ke]][sei[ke]][0][ip];                    // r = rho1 || rho2
-            real64 const dDens_dP = m_dDens_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP];  // dr/dP = dr1/dP1 || dr2/dP
+            real64 const density  = m_dens[seri[ke]][sesri[ke]][sei[ke]][0][ip];                     // r = rho1 || rho2
+            real64 const dDens_dP = m_dDens_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP];   // dr/dP = dr1/dP1 || dr2/dP
 
             // average density and derivatives
-            densMean[ip] += density;          // rho = (rho1 + rho2)
-            dDensMean_dP[ip][ke] = dDens_dP;  // drho/dP = { (dr1/dP1) , (dr2/dP2) }
+            densMean[ip] += density;           // rho = (rho1 + rho2)
+            dDensMean_dP[ip][ke] = dDens_dP;   // drho/dP = { (dr1/dP1) , (dr2/dP2) }
 
             denom++;
           }
 
           if( denom > 1 )
           {
-            densMean[ip] /= denom; // rho = (rho1 + rho2) / denom
+            densMean[ip] /= denom;  // rho = (rho1 + rho2) / denom
             for( integer ke = 0; ke < 2; ++ke )
             {
-              dDensMean_dP[ip][ke] /= denom; // drho/dP = { (dr1/dP1) / denom , (dr2/dP2) / denom }
+              dDensMean_dP[ip][ke] /= denom;  // drho/dP = { (dr1/dP1) / denom , (dr2/dP2) / denom }
             }
           }
 
@@ -471,106 +2653,114 @@ class FluxComputeKernel : public FluxComputeKernelBase
             localIndex const esr = sesri[ke];
             localIndex const ei  = sei[ke];
 
-            real64 const pressure = m_pres[er][esr][ei];      // P = P1 || P2
-            presGrad[ip] += trans[ke] * pressure;             // DPv = T (P1 - P2)
-            dPresGrad_dTrans += signPotDiff[ke] * pressure;   // dDPv/dT = (P1 - P2)
-            dPresGrad_dP[ip][ke] = trans[ke];                 // dDPv/dP = { T , -T }
+            real64 const pressure = m_pres[er][esr][ei];       // P = P1 || P2
+            presGrad[ip] += trans[ke] * pressure;              // DPv = T (P1 - P2)
+            dPresGrad_dTrans += signPotDiff[ke] * pressure;    // dDPv/dT = (P1 - P2)
+            dPresGrad_dP[ip][ke] = trans[ke];                  // dDPv/dP = { T , -T }
 
-            real64 const gravD = trans[ke] * m_gravCoef[er][esr][ei];       // D = T g z1 || -T g z2
-            real64 pot = trans[ke] * pressure - densMean[ip] * gravD; // Phi = T P1 - rho T g z1 || -T P2 + rho T g z2
+            real64 const gravD = trans[ke] * m_gravCoef[er][esr][ei];        // D = T g z1 || -T g z2
+            real64 pot = trans[ke] * pressure - densMean[ip] * gravD;  // Phi = T P1 - rho T g z1 || -T P2 + rho T g z2
 
-            gravHead[ip] += densMean[ip] * gravD;                                         // DPg = rho (T g z1 - T g z2) = T rho g (z1 - z2)
-            dGravHead_dTrans += signPotDiff[ke] * densMean[ip] * m_gravCoef[er][esr][ei]; // dDPg/dT = rho g z1 - rho g z2 = rho g (z1 - z2)
+            gravHead[ip] += densMean[ip] * gravD;                                          // DPg = rho (T g z1 - T g z2) = T rho g (z1 -
+                                                                                           // z2)
+            dGravHead_dTrans += signPotDiff[ke] * densMean[ip] * m_gravCoef[er][esr][ei];  // dDPg/dT = rho g z1 - rho g z2 = rho g (z1 -
+                                                                                           // z2)
 
             for( integer i = 0; i < 2; ++i )
             {
-              dGravHead_dP[ip][i] += dDensMean_dP[ip][i] * gravD; // dDPg/dP = {drho/dP1 * T g (z1 - z2) , drho/dP2 * T g (z1 - z2)}
+              dGravHead_dP[ip][i] += dDensMean_dP[ip][i] * gravD;  // dDPg/dP = {drho/dP1 * T g (z1 - z2) , drho/dP2 * T g (z1 - z2)}
             }
 
-            if( m_hasCapPressure )  // check sign convention
+            if( m_hasCapPressure )   // check sign convention
             {
-              real64 const capPres = m_phaseCapPressure[er][esr][ei][0][ip];  // Pc = Pc1 || Pc2
-              dCapGrad_dTrans -= signPotDiff[ke] * capPres;                   // dDPc/dT = (-Pc1 + Pc2)
-              pot -= trans[ke] * capPres;                                     // Phi = T P1 - rho T g z1 - T Pc1 || -T P2 + rho T g z2 + T
-                                                                              // Pc2
-              capGrad[ip] -= trans[ke] * capPres;                             // DPc = T (-Pc1 + Pc2)
+              real64 const capPres = m_phaseCapPressure[er][esr][ei][0][ip];   // Pc = Pc1 || Pc2
+              dCapGrad_dTrans -= signPotDiff[ke] * capPres;                    // dDPc/dT = (-Pc1 + Pc2)
+              pot -= trans[ke] * capPres;                                      // Phi = T P1 - rho T g z1 - T Pc1 || -T P2 + rho T g z2 + T
+                                                                               // Pc2
+              capGrad[ip] -= trans[ke] * capPres;                              // DPc = T (-Pc1 + Pc2)
             }
 
-            potScale = fmax( potScale, fabs( pot ) ); // maxPhi = Phi1 > Phi2 ? Phi1 : Phi2
+            potScale = fmax( potScale, fabs( pot ) );  // maxPhi = Phi1 > Phi2 ? Phi1 : Phi2
           }
 
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dPresGrad_dP[ip][ke] += dTrans_dP[ke] * dPresGrad_dTrans;   // dDPv/dP = { T + dT/dP1 * (P1 - P2) , -T + dT/dP2 * (P1 - P2)}
-            dGravHead_dP[ip][ke] += dTrans_dP[ke] * dGravHead_dTrans;   // dDPg/dP = { drho/dP1 * T g (z1 - z2) + dT/dP1 * rho g (z1 - z2) ,
-                                                                        //             drho/dP2 * T g (z1 - z2) + dT/dP2 * rho g (z1 - z2) }
+            dPresGrad_dP[ip][ke] += dTrans_dP[ke] * dPresGrad_dTrans;    // dDPv/dP = { T + dT/dP1 * (P1 - P2) , -T + dT/dP2 * (P1 - P2)}
+            dGravHead_dP[ip][ke] += dTrans_dP[ke] * dGravHead_dTrans;    // dDPg/dP = { drho/dP1 * T g (z1 - z2) + dT/dP1 * rho g (z1 - z2)
+                                                                         // ,
+                                                                         //             drho/dP2 * T g (z1 - z2) + dT/dP2 * rho g (z1 - z2)
+                                                                         // }
             if( m_hasCapPressure )
             {
-              real64 const dCapPres_dS = m_dPhaseCapPressure_dPhaseVolFrac[seri[ke]][sesri[ke]][sei[ke]][0][ip][ip]; // dPc/dS = dPc1/dS1 ||
-                                                                                                                     // dPc2/dS2
-              dCapGrad_dP[ip][ke] += dTrans_dP[ke] * dCapGrad_dTrans;                                                // dDPc/dP = { dT/dP1 *
-                                                                                                                     // (-Pc1 + Pc2) ,
-                                                                                                                     //             dT/dP2 *
-                                                                                                                     // (-Pc1 + Pc2) }
-              dCapGrad_dS[ip][ke] -= trans[ke] * dCapPres_dS;                                                        // dDPc/dS = { -T *
-                                                                                                                     // dPc1/dS1 , T *
-                                                                                                                     // dPc2/dS2 }
+              real64 const dCapPres_dS = m_dPhaseCapPressure_dPhaseVolFrac[seri[ke]][sesri[ke]][sei[ke]][0][ip][ip];  // dPc/dS = dPc1/dS1
+                                                                                                                      // ||
+                                                                                                                      // dPc2/dS2
+              dCapGrad_dP[ip][ke] += dTrans_dP[ke] * dCapGrad_dTrans;                                                 // dDPc/dP = { dT/dP1
+                                                                                                                      // *
+                                                                                                                      // (-Pc1 + Pc2) ,
+                                                                                                                      //             dT/dP2
+                                                                                                                      // *
+                                                                                                                      // (-Pc1 + Pc2) }
+              dCapGrad_dS[ip][ke] -= trans[ke] * dCapPres_dS;                                                         // dDPc/dS = { -T *
+                                                                                                                      // dPc1/dS1 , T *
+                                                                                                                      // dPc2/dS2 }
             }
           }
 
           // *** upwinding ***
 
           // compute potential gradient
-          real64 potGrad = presGrad[ip] - gravHead[ip]; // DPhi = T (P1 - P2) - T rho g (z1 - z2)
+          real64 potGrad = presGrad[ip] - gravHead[ip];  // DPhi = T (P1 - P2) - T rho g (z1 - z2)
           if( m_hasCapPressure )
           {
-            potGrad += capGrad[ip]; // DPhi = T (P1 - P2) - T rho g (z1 - z2) + T (-Pc1 + Pc2)
+            potGrad += capGrad[ip];  // DPhi = T (P1 - P2) - T rho g (z1 - z2) + T (-Pc1 + Pc2)
           }
 
           // compute upwinding tolerance
           real64 constexpr upwRelTol = 1e-8;
-          real64 const upwAbsTol = fmax( potScale * upwRelTol, LvArray::NumericLimits< real64 >::epsilon ); // abstol = maxPhi * tol > eps ?
-                                                                                                            // maxPhi * tol : eps
+          real64 const upwAbsTol = fmax( potScale * upwRelTol, LvArray::NumericLimits< real64 >::epsilon );  // abstol = maxPhi * tol > eps
+                                                                                                             // ?
+                                                                                                             // maxPhi * tol : eps
 
           // decide mobility coefficients - smooth variation in [-upwAbsTol; upwAbsTol]
-          real64 const alpha = ( potGrad + upwAbsTol ) / ( 2 * upwAbsTol );   // alpha = (DPhi + abstol) / abstol / 2
+          real64 const alpha = ( potGrad + upwAbsTol ) / ( 2 * upwAbsTol );    // alpha = (DPhi + abstol) / abstol / 2
 
           // choose upstream cell
-          if( alpha <= 0.0 || alpha >= 1.0 )  // no smoothing needed
+          if( alpha <= 0.0 || alpha >= 1.0 )   // no smoothing needed
           {
-            localIndex const k_up = 1 - localIndex( fmax( fmin( alpha, 1.0 ), 0.0 ) ); // 1 upwind -> k_up = 0 || 2 upwind -> k_up = 1
+            localIndex const k_up = 1 - localIndex( fmax( fmin( alpha, 1.0 ), 0.0 ) );  // 1 upwind -> k_up = 0 || 2 upwind -> k_up = 1
 
-            mobility[ip] = m_mob[seri[k_up]][sesri[k_up]][sei[k_up]][ip];                     // M = Mupstream
-            dMob_dP[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dP];    // dM/dP = {dM/dP1 , 0} OR {0 , dM/dP2}
-            dMob_dS[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dS];    // dM/dS = {dM/dS1 , 0} OR {0 , dM/dS2}
+            mobility[ip] = m_mob[seri[k_up]][sesri[k_up]][sei[k_up]][ip];                      // M = Mupstream
+            dMob_dP[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dP];     // dM/dP = {dM/dP1 , 0} OR {0 , dM/dP2}
+            dMob_dS[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dS];     // dM/dS = {dM/dS1 , 0} OR {0 , dM/dS2}
           }
-          else  // perform smoothing
+          else   // perform smoothing
           {
             real64 const mobWeights[2] = { alpha, 1.0 - alpha };
             for( integer ke = 0; ke < 2; ++ke )
             {
-              mobility[ip] += mobWeights[ke] * m_mob[seri[ke]][sesri[ke]][sei[ke]][ip];               // M = alpha * M1 + (1 - alpha) * M2
-              dMob_dP[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dP]; // dM/dP = {alpha * dM1/dP1 , (1 -
-                                                                                                      // alpha) * dM2/dP2}
-              dMob_dS[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dS]; // dM/dP = {alpha * dM1/dS1 , (1 -
-                                                                                                      // alpha) * dM2/dS2}
+              mobility[ip] += mobWeights[ke] * m_mob[seri[ke]][sesri[ke]][sei[ke]][ip];                // M = alpha * M1 + (1 - alpha) * M2
+              dMob_dP[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dP];  // dM/dP = {alpha * dM1/dP1 , (1 -
+                                                                                                       // alpha) * dM2/dP2}
+              dMob_dS[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dS];  // dM/dP = {alpha * dM1/dS1 , (1 -
+                                                                                                       // alpha) * dM2/dS2}
             }
           }
 
           // pressure gradient depends on all points in the stencil
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dFlux_dP[ip][ke] += dPresGrad_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) ,
-                                                      //          -T + dT/dP2 * (P1 - P2) }
+            dFlux_dP[ip][ke] += dPresGrad_dP[ip][ke];  // dF/dP = { T + dT/dP1 * (P1 - P2) ,
+                                                       //          -T + dT/dP2 * (P1 - P2) }
           }
 
           // gravitational head depends only on the two cells connected (same as mean density)
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dFlux_dP[ip][ke] -= dGravHead_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
-                                                      // z2) ,
-                                                      //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
-                                                      // z2) }
+            dFlux_dP[ip][ke] -= dGravHead_dP[ip][ke];  // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
+                                                       // z2) ,
+                                                       //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
+                                                       // z2) }
           }
 
           // capillary pressure contribution
@@ -578,38 +2768,38 @@ class FluxComputeKernel : public FluxComputeKernelBase
           {
             for( integer ke = 0; ke < 2; ++ke )
             {
-              dFlux_dP[ip][ke] += dCapGrad_dP[ip][ke];  // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1
-                                                        // - z2) + dT/dP1 * (-Pc1 + Pc2) ,
-                                                        //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1
-                                                        // - z2) + dT/dP2 * (-Pc1 + Pc2) }
+              dFlux_dP[ip][ke] += dCapGrad_dP[ip][ke];   // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1
+                                                         // - z2) + dT/dP1 * (-Pc1 + Pc2) ,
+                                                         //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1
+                                                         // - z2) + dT/dP2 * (-Pc1 + Pc2) }
 
-              dFlux_dS[ip][ke] += dCapGrad_dS[ip][ke];  // dF/dS = { T * -dPc/dS1 , T * dPc/dS2 }
+              dFlux_dS[ip][ke] += dCapGrad_dS[ip][ke];   // dF/dS = { T * -dPc/dS1 , T * dPc/dS2 }
             }
           }
 
           // compute the flux and derivatives using upstream cell mobility
-          fluxVal[ip] = mobility[ip] * potGrad; // F = M * DPhi
+          fluxVal[ip] = mobility[ip] * potGrad;  // F = M * DPhi
 
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dFlux_dP[ip][ke] *= mobility[ip];   // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
-                                                // z2) + dT/dP1 * (-Pc1 + Pc2)] ,
-                                                //           M [-T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
-                                                // z2) + dT/dP2 * (-Pc1 + Pc2)] }
+            dFlux_dP[ip][ke] *= mobility[ip];    // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
+                                                 // z2) + dT/dP1 * (-Pc1 + Pc2)] ,
+                                                 //           M [-T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
+                                                 // z2) + dT/dP2 * (-Pc1 + Pc2)] }
 
-            dFlux_dS[ip][ke] *= mobility[ip];   // dF/dS = { M [T * -dPc/dS1] , M [T * dPc/dS2] }
+            dFlux_dS[ip][ke] *= mobility[ip];    // dF/dS = { M [T * -dPc/dS1] , M [T * dPc/dS2] }
           }
 
           // add contribution from upstream cell mobility derivatives
           for( integer ke = 0; ke < 2; ++ke )
           {
-            dFlux_dP[ip][ke] += dMob_dP[ip][ke] * potGrad;  // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho1/dP * T g (z1 - z2) - dT/dP1 *
-                                                            // rho g (z1 - z2) + dT/dP1 * (-Pc1 + Pc2)] + dM/dP1 * DPhi ,
-                                                            //           M [-T + dT/dP2 * (P1 - P2) - drho2/dP * T g (z1 - z2) - dT/dP2 *
-                                                            // rho g (z1 - z2) + dT/dP2 * (-Pc1 + Pc2)] + dM/dP2 * DPhi }
+            dFlux_dP[ip][ke] += dMob_dP[ip][ke] * potGrad;   // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho1/dP * T g (z1 - z2) - dT/dP1 *
+                                                             // rho g (z1 - z2) + dT/dP1 * (-Pc1 + Pc2)] + dM/dP1 * DPhi ,
+                                                             //           M [-T + dT/dP2 * (P1 - P2) - drho2/dP * T g (z1 - z2) - dT/dP2 *
+                                                             // rho g (z1 - z2) + dT/dP2 * (-Pc1 + Pc2)] + dM/dP2 * DPhi }
 
-            dFlux_dS[ip][ke] += dMob_dS[ip][ke] * potGrad;  // dF/dS = { M [T * -dPc/dS1] + dM/dS1 * DPhi , M [T * dPc/dS2] + dM/dS2 * DPhi
-                                                            // }
+            dFlux_dS[ip][ke] += dMob_dS[ip][ke] * potGrad;   // dF/dS = { M [T * -dPc/dS1] + dM/dS1 * DPhi , M [T * dPc/dS2] + dM/dS2 * DPhi
+                                                             // }
           }
 
           // populate local flux vector and derivatives
@@ -630,14 +2820,14 @@ class FluxComputeKernel : public FluxComputeKernelBase
           }
 
           // Customize the kernel with this lambda
-          kernelOp( k, seri, sesri, sei, connectionIndex, alpha, mobility, potGrad, fluxVal, dFlux_dP, dFlux_dS );  // Not sure what this
-                                                                                                                    // does
+          kernelOp( k, seri, sesri, sei, connectionIndex, alpha, mobility, potGrad, fluxVal, dFlux_dP, dFlux_dS );   // Not sure what this
+                                                                                                                     // does
 
-        } // loop over phases
+        }  // loop over phases
 
         connectionIndex++;
       }
-    } // loop over connection elements
+    }  // loop over connection elements
   }
 
   /**
@@ -645,7 +2835,7 @@ class FluxComputeKernel : public FluxComputeKernelBase
    * @param[in] iconn the connection index
    * @param[inout] stack the stack variables
    */
-  template< typename FUNC = NoOpFunc >                                  // should change to multiphase
+  template< typename FUNC = NoOpFunc >                                   // should change to multiphase
   GEOS_HOST_DEVICE
   void complete( localIndex const iconn,
                  StackVariables & stack,
@@ -732,46 +2922,777 @@ class FluxComputeKernel : public FluxComputeKernelBase
 };
 
 
-/****************************************** */
-
 /**
- * @class FluxComputeKernelFactory
+ * @class FaceBasedAssemblyInterfaceConditionKernel
+ * @tparam NUM_DOF number of degrees of freedom
+ * @tparam STENCILWRAPPER the type of the stencil wrapper
+ * @tparam CAPPRESWRAPPER the type of the capillary pressure wrapper
+ * @tparam RELPERMWRAPPER the type of the realtive permeability wrapper
+ * @brief Define the interface for the assembly kernel in charge of flux terms
  */
-class FluxComputeKernelFactory
+// template< integer NUM_EQN, integer NUM_DOF, typename STENCILWRAPPER, typename CAPPRESWRAPPER, typename RELPERMWRAPPER >
+template< integer NUM_EQN, integer NUM_DOF, typename STENCILWRAPPER >
+class FluxComputeInterfaceConditionKernel : public FluxComputeKernel< NUM_EQN, NUM_DOF, STENCILWRAPPER >
 {
 public:
 
+  using AbstractBase = FluxComputeKernelBase;
+  using DofNumberAccessor = AbstractBase::DofNumberAccessor;
+  using ImmiscibleMultiphaseFlowAccessors = AbstractBase::ImmiscibleMultiphaseFlowAccessors;
+  using MultiphaseFluidAccessors = AbstractBase::MultiphaseFluidAccessors;
+  using CapPressureAccessors = AbstractBase::CapPressureAccessors;
+  using PermeabilityAccessors = AbstractBase::PermeabilityAccessors;
+
+  using Base = FluxComputeKernel< NUM_EQN, NUM_DOF, STENCILWRAPPER >;
+  using Deriv = typename Base::Deriv;
+  using StackVariables = typename Base::StackVariables;
+  using Base::numEqn;
+  using Base::numDof;
+  using Base::m_stencilWrapper;
+  using Base::m_dofNumber;
+  using Base::m_rankOffset;
+  using Base::m_localMatrix;
+  using Base::m_localRhs;
+  using Base::m_numPhases;
+  using Base::m_permeability;
+  using Base::m_dPerm_dPres;
+  using Base::m_phaseVolFrac;
+  using Base::m_phaseMass_n;
+  using Base::m_phaseCapPressure;
+  // using Base::m_jFuncMultiplier;
+  using Base::m_dPhaseCapPressure_dPhaseVolFrac;
+  using Base::m_dens;
+  using Base::m_dDens_dPres;
+  using Base::m_visc;
+  using Base::m_dVisc_dPres;
+  using Base::m_dMob;
+  using Base::m_mob;
+  using Base::m_gravCoef;
+  using Base::m_ghostRank;
+  using Base::m_dt;
+  using Base::m_hasCapPressure;
+  using Base::m_useTotalMassEquation;
+  using Base::m_checkPhasePresenceInGravity;
+  using Base::m_seri;
+  using Base::m_sesri;
+  using Base::m_sei;
+  using Base::m_pres;
+
   /**
-   * @brief Create a new kernel and launch
-   * @tparam POLICY the policy used in the RAJA kernel
-   * @tparam STENCILWRAPPER the type of the stencil wrapper
+   * @brief Constructor for the kernel interface
+   * @param[in] numPhases number of fluid phases
    * @param[in] rankOffset the offset of my MPI rank
-   * @param[in] dofKey string to get the element degrees of freedom numbers
-   * @param[in] solverName name of the solver (to name accessors)
-   * @param[in] elemManager reference to the element region manager
    * @param[in] stencilWrapper reference to the stencil wrapper
+   * @param[in] capPressureWrapper reference to the capillary pressure wrapper
+   * @param[in] dofNumberAccessor
+   * @param[in] multiPhaseFlowAccessors
+   * @param[in] fluidAccessors
+   * @param[in] capPressureAccessors
+   * @param[in] permeabilityAccessors
    * @param[in] dt time step size
    * @param[inout] localMatrix the local CRS matrix
    * @param[inout] localRhs the local right-hand side vector
+   * @param[in] hasCapPressure flags for capillary pressure
+   * @param[in] useTotalMassEquation flags for using total velocity formulation
    */
-  template< typename POLICY, typename STENCILWRAPPER >
-  static void
-  createAndLaunch( integer const numPhases,
-                   globalIndex const rankOffset,
-                   string const & dofKey,
-                   integer const hasCapPressure,
-                   integer const useTotalMassEquation,
-                   integer const checkPhasePresenceInGravity,
-                   string const & solverName,
-                   ElementRegionManager const & elemManager,
-                   STENCILWRAPPER const & stencilWrapper,
-                   real64 const & dt,
-                   CRSMatrixView< real64, globalIndex const > const & localMatrix,
-                   arrayView1d< real64 > const & localRhs )
+  FluxComputeInterfaceConditionKernel( integer const numPhases,
+                                       globalIndex const rankOffset,
+                                       STENCILWRAPPER const & stencilWrapper,
+                                      //  CAPPRESWRAPPER const & capPressureWrapper,
+                                      //  RELPERMWRAPPER const & relPermWrapper,
+                                       DofNumberAccessor const & dofNumberAccessor,
+                                       ImmiscibleMultiphaseFlowAccessors const & multiPhaseFlowAccessors,
+                                       MultiphaseFluidAccessors const & fluidAccessors,
+                                       CapPressureAccessors const & capPressureAccessors,
+                                       PermeabilityAccessors const & permeabilityAccessors,
+                                       real64 const & dt,
+                                       CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                                       arrayView1d< real64 > const & localRhs,
+                                       integer const hasCapPressure,
+                                       integer const useTotalMassEquation,
+                                       integer const checkPhasePresenceInGravity,
+                                       string_array const & interfaceFaceSetNames,
+                                       stdVector< std::array< std::tuple< constitutive::RelativePermeabilityBase *,
+                                                                          constitutive::CapillaryPressureBase *,
+                                                                          constitutive::TwoPhaseImmiscibleFluid * >, 2 > > const & interfaceConstitutivePairs,
+                                       unordered_map< localIndex, localIndex > const & interfaceRegionByConnector,
+                                      //  std::tuple< constitutive::RelativePermeabilityBase *,
+                                      //              constitutive::CapillaryPressureBase *,
+                                      //              constitutive::TwoPhaseImmiscibleFluid * > const & interfaceConstitutivePairs_temp,
+                                       localIndex const GEOS_UNUSED_PARAM( domainSize ) )
+    : Base( numPhases,
+            rankOffset,
+            stencilWrapper,
+            dofNumberAccessor,
+            multiPhaseFlowAccessors,
+            fluidAccessors,
+            capPressureAccessors,
+            permeabilityAccessors,
+            dt,
+            localMatrix,
+            localRhs,
+            hasCapPressure,
+            useTotalMassEquation,
+            checkPhasePresenceInGravity ),
+    // m_capPressureWrapper( capPressureWrapper ),
+    // m_relPermWrapper( relPermWrapper ),
+    m_interfaceFaceSetNames( interfaceFaceSetNames ),
+    m_interfaceConstitutivePairs( interfaceConstitutivePairs ),
+    m_interfaceRegionByConnector( interfaceRegionByConnector )
+    // ,
+    // m_interfaceConstitutivePairs_temp( interfaceConstitutivePairs_temp )
   {
-    integer constexpr NUM_EQN = 2;
-    integer constexpr NUM_DOF = 2;
-
+    localIndex const numConn = stencilWrapper.size();
+    if( static_cast< localIndex >( m_convergedPcInt.size() ) < numConn )
+    {
+      m_convergedPcInt.resize( numConn, -1.0 );
+    }
+  }
+
+  /**
+   * @brief Compute the local flux contributions to the residual and Jacobian
+   * @tparam FUNC the type of the function that can be used to customize the computation of the flux
+   * @param[in] iconn the connection index
+   * @param[inout] stack the stack variables
+   * @param[in] NoOpFunc the function used to customize the computation of the flux
+   */
+
+  template< typename FUNC = NoOpFunc >    // should change to multiphase
+  GEOS_HOST_DEVICE
+  void computeFlux( localIndex const iconn,
+                    StackVariables & stack,
+                    FUNC && kernelOp = NoOpFunc{} ) const
+  {
+
+     bool connectorHasInterfaceConditionQ = false;
+     bool anyInterfaceConditionsQ = not m_interfaceConstitutivePairs.empty();
+     if (anyInterfaceConditionsQ) {
+         connectorHasInterfaceConditionQ =
+             m_interfaceRegionByConnector.find(iconn) != m_interfaceRegionByConnector.end();
+     }
+
+
+
+    //  if (connectorHasInterfaceConditionQ){
+    //    // Improved transmission conditions
+    //    int ammar_code = 0;
+    //  }else{
+    //    // Regular contribution
+    //    int standard_code = 0;
+    //  }
+
+    m_stencilWrapper.computeWeights( iconn,
+                                     m_permeability,
+                                     m_dPerm_dPres,
+                                     stack.transmissibility,
+                                     stack.dTrans_dPres );
+
+    localIndex k[2];
+    localIndex connectionIndex = 0;
+
+    // one-sided transmissibility
+    m_stencilWrapper.computeHalfWeights( iconn,
+                                         m_permeability,
+                                         m_dPerm_dPres,
+                                         stack.transmissibilityHat,
+                                         stack.dTransHat_dPres );
+
+
+
+    for( k[0] = 0; k[0] < stack.numFluxElems; ++k[0] )
+    {
+      for( k[1] = k[0] + 1; k[1] < stack.numFluxElems; ++k[1] )
+      {
+        // clear working arrays
+        real64 densMean[numEqn]{};
+        real64 dDensMean_dP[numEqn][2]{};
+
+        real64 presGrad[numEqn]{};
+        real64 dPresGrad_dP[numEqn][2]{};
+
+        real64 gravHead[numEqn]{};
+        real64 dGravHead_dP[numEqn][2]{};
+
+        real64 capGrad[numEqn]{};
+        // real64 capPresIC[numEqn][2]{};
+        // real64 jFMultiplier[numEqn][2]{};
+        real64 dCapGrad_dP[numEqn][2]{};
+        real64 dCapGrad_dS[numEqn][2]{};
+
+        real64 fluxVal[numEqn]{};
+        real64 dFlux_dP[numEqn][2]{};
+        real64 dFlux_dS[numEqn][2]{};
+
+        real64 mobility[numEqn]{};
+        real64 dMob_dP[numEqn][2]{};
+        real64 dMob_dS[numEqn][2]{};
+
+        real64 density2[numEqn]{};
+        real64 dDens_dP2[numEqn][2]{};
+        real64 viscosity[numEqn]{};
+        real64 dVisc_dP[numEqn][2]{};
+        real64 gravCoef2[numEqn]{};
+        real64 gravCoefHat[numEqn]{};
+
+        real64 uT = 0;
+        // real64 total_mobility = 0;
+        real64 duT_dP[numEqn]{};
+        real64 duT_dS[numEqn]{};
+
+        real64 potGrad_ip[numEqn]{};
+        real64 alpha_ip[numEqn]{};
+
+        real64 const trans[2] = { stack.transmissibility[connectionIndex][0], stack.transmissibility[connectionIndex][1] };
+        real64 const dTrans_dP[2] = { stack.dTrans_dPres[connectionIndex][0], stack.dTrans_dPres[connectionIndex][1] };
+
+        real64 const transHat[2] = { stack.transmissibilityHat[connectionIndex][0], stack.transmissibilityHat[connectionIndex][1] * -1.0};
+        real64 const dTransHat_dP[2] = { stack.dTransHat_dPres[connectionIndex][0], stack.dTransHat_dPres[connectionIndex][1] * -1.0};
+
+        // cell indices
+        localIndex const seri[2]  = {m_seri( iconn, k[0] ), m_seri( iconn, k[1] )};
+        localIndex const sesri[2] = {m_sesri( iconn, k[0] ), m_sesri( iconn, k[1] )};
+        localIndex const sei[2]   = {m_sei( iconn, k[0] ), m_sei( iconn, k[1] )};
+
+        stdVector< real64 > saturations = {m_phaseVolFrac[seri[0]][sesri[0]][sei[0]][0], m_phaseVolFrac[seri[1]][sesri[1]][sei[1]][0] };
+        stdVector< real64 > pressures = {m_pres[seri[0]][sesri[0]][sei[0]], m_pres[seri[1]][sesri[1]][sei[1]] };
+        // bool isJfunction = 0;
+
+        // loop over phases
+        for( integer ip = 0; ip < m_numPhases; ++ip )
+        {
+          // calculate quantities on primary connected cells
+          integer denom = 0;
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            // density
+            bool const phaseExists = (m_phaseVolFrac[seri[ke]][sesri[ke]][sei[ke]][ip] > 0);
+            if( m_checkPhasePresenceInGravity && !phaseExists )
+            {
+              continue;
+            }
+
+            real64 const density  = m_dens[seri[ke]][sesri[ke]][sei[ke]][0][ip];         // r = rho1 || rho2
+            real64 const dDens_dP = m_dDens_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP]; // dr/dP = dr1/dP1 || dr2/dP
+            // average density and derivatives
+            densMean[ip] += density; // rho = (rho1 + rho2)
+            dDensMean_dP[ip][ke] = dDens_dP; // drho/dP = { (dr1/dP1) , (dr2/dP2) }
+            denom++;
+          }
+
+          if( denom > 1 )
+          {
+            densMean[ip] /= denom; // rho = (rho1 + rho2) / denom
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              dDensMean_dP[ip][ke] /= denom; // drho/dP = { (dr1/dP1) / denom , (dr2/dP2) / denom }
+            }
+          }
+
+          //***** calculation of flux *****
+
+          // compute potential difference
+          real64 potScale = 0.0;
+          real64 dPresGrad_dTrans = 0.0;
+          real64 dGravHead_dTrans = 0.0;
+          real64 dCapGrad_dTrans = 0.0;
+          gravCoefHat[0] = 0;
+          gravCoefHat[1] = 0;
+          constexpr int signPotDiff[2] = {1, -1};
+
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            localIndex const er  = seri[ke];
+            localIndex const esr = sesri[ke];
+            localIndex const ei  = sei[ke];
+
+            real64 const pressure = m_pres[er][esr][ei]; // P = P1 || P2
+            presGrad[ip] += trans[ke] * pressure;  // DPv = T (P1 - P2)
+            dPresGrad_dTrans += signPotDiff[ke] * pressure; // dDPv/dT = (P1 - P2)
+            dPresGrad_dP[ip][ke] = trans[ke];      // dDPv/dP = { T , -T }
+
+            real64 const gravD = trans[ke] * m_gravCoef[er][esr][ei]; // D = T g z1 || -T g z2
+            real64 pot = trans[ke] * pressure - densMean[ip] * gravD; // Phi = T P1 - rho T g z1 || -T P2 + rho T g z2
+            gravCoefHat[0] += m_gravCoef[er][esr][ei] * 0.5;
+            gravCoefHat[1] += m_gravCoef[er][esr][ei] * 0.5;
+
+            gravCoef2[ke] = m_gravCoef[er][esr][ei];
+
+            gravHead[ip] += densMean[ip] * gravD;                              // DPg = rho (T g z1 - T g z2) = T rho g (z1 - z2)
+            dGravHead_dTrans += signPotDiff[ke] * densMean[ip] * m_gravCoef[er][esr][ei]; // dDPg/dT = rho g z1 - rho g z2 = rho g (z1 - z2)
+
+            for( integer i = 0; i < 2; ++i )
+            {
+              dGravHead_dP[ip][i] += dDensMean_dP[ip][i] * gravD; // dDPg/dP = {drho/dP1 * T g (z1 - z2) , drho/dP2 * T g (z1 - z2)}
+            }
+
+            if( m_hasCapPressure ) // check sign convention
+            {
+              real64 const capPres = m_phaseCapPressure[er][esr][ei][0][ip]; // Pc = Pc1 || Pc2
+              // jFMultiplier[ip][ke] = m_jFuncMultiplier[er][esr][ei][0];
+
+              // capPresIC[ip][ke] = capPres;
+              dCapGrad_dTrans -= signPotDiff[ke] * capPres;      // dDPc/dT = (-Pc1 + Pc2)
+              pot -= trans[ke] * capPres;                        // Phi = T P1 - rho T g z1 - T Pc1 || -T P2 + rho T g z2 + T
+              // Pc2
+              capGrad[ip] -= trans[ke] * capPres;                // DPc = T (-Pc1 + Pc2)
+            }
+
+            potScale = fmax( potScale, fabs( pot ) ); // maxPhi = Phi1 > Phi2 ? Phi1 : Phi2
+          }
+
+
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            dPresGrad_dP[ip][ke] += dTrans_dP[ke] * dPresGrad_dTrans; // dDPv/dP = { T + dT/dP1 * (P1 - P2) , -T + dT/dP2 * (P1 - P2)}
+            dGravHead_dP[ip][ke] += dTrans_dP[ke] * dGravHead_dTrans; // dDPg/dP = { drho/dP1 * T g (z1 - z2) + dT/dP1 * rho g (z1 - z2) ,
+            //             drho/dP2 * T g (z1 - z2) + dT/dP2 * rho g (z1 - z2) }
+            if( m_hasCapPressure )
+            {
+              real64 const dCapPres_dS = m_dPhaseCapPressure_dPhaseVolFrac[seri[ke]][sesri[ke]][sei[ke]][0][ip][ip]; // dPc/dS = dPc1/dS1 ||
+              // dPc2/dS2
+              dCapGrad_dP[ip][ke] += dTrans_dP[ke] * dCapGrad_dTrans;                                   // dDPc/dP = { dT/dP1 *
+              // (-Pc1 + Pc2) ,
+              //             dT/dP2 *
+              // (-Pc1 + Pc2) }
+              dCapGrad_dS[ip][ke] -= trans[ke] * dCapPres_dS;                                           // dDPc/dS = { -T *
+              // dPc1/dS1 , T *
+              // dPc2/dS2 }
+            }
+          }
+
+          // *** upwinding ***
+          // compute potential gradient
+          real64 potGrad = presGrad[ip] - gravHead[ip]; // DPhi = T (P1 - P2) - T rho g (z1 - z2)
+          if( m_hasCapPressure )
+          {
+            potGrad += capGrad[ip]; // DPhi = T (P1 - P2) - T rho g (z1 - z2) + T (-Pc1 + Pc2)
+          }
+
+          // compute upwinding tolerance
+          real64 constexpr upwRelTol = 1e-8;
+          real64 const upwAbsTol = fmax( potScale * upwRelTol, LvArray::NumericLimits< real64 >::epsilon ); // abstol = maxPhi * tol > eps ?
+          // maxPhi * tol : eps
+
+          // decide mobility coefficients - smooth variation in [-upwAbsTol; upwAbsTol]
+          real64 alpha = ( potGrad + upwAbsTol ) / ( 2 * upwAbsTol ); // alpha = (DPhi + abstol) / abstol / 2
+
+          // choose upstream cell
+          if( alpha <= 0.0 || alpha >= 1.0 ) // no smoothing needed
+          {
+            localIndex const k_up = 1 - localIndex( fmax( fmin( alpha, 1.0 ), 0.0 ) ); // 1 upwind -> k_up = 0 || 2 upwind -> k_up = 1
+
+            mobility[ip] = m_mob[seri[k_up]][sesri[k_up]][sei[k_up]][ip];          // M = Mupstream
+            density2[ip] = m_dens[seri[k_up]][sesri[k_up]][sei[k_up]][0][ip];         // r = rho1 || rho2
+            dDens_dP2[ip][k_up] = m_dDens_dPres[seri[k_up]][sesri[k_up]][sei[k_up]][0][ip][Deriv::dP]; // dr/dP = dr1/dP1 || dr2/dP
+            viscosity[ip]  = m_visc[seri[k_up]][sesri[k_up]][sei[k_up]][0][ip];
+            dVisc_dP[ip][k_up] = m_dVisc_dPres[seri[k_up]][sesri[k_up]][sei[k_up]][0][ip][Deriv::dP];
+            dMob_dP[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dP]; // dM/dP = {dM/dP1 , 0} OR {0 , dM/dP2}
+            dMob_dS[ip][k_up] = m_dMob[seri[k_up]][sesri[k_up]][sei[k_up]][ip][Deriv::dS]; // dM/dS = {dM/dS1 , 0} OR {0 , dM/dS2}
+          }
+          else // perform smoothing
+          {
+            real64 const mobWeights[2] = { alpha, 1.0 - alpha };
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              mobility[ip] += mobWeights[ke] * m_mob[seri[ke]][sesri[ke]][sei[ke]][ip];  // M = alpha * M1 + (1 - alpha) * M2
+              density2[ip] += mobWeights[ke] * m_dens[seri[ke]][sesri[ke]][sei[ke]][0][ip];       // r = rho1 || rho2
+              dDens_dP2[ip][ke] = mobWeights[ke] * m_dDens_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP]; // dr/dP = dr1/dP1 ||
+              // dr2/dP
+              viscosity[ip]  = m_visc[seri[ke]][sesri[ke]][sei[ke]][0][ip];
+              dVisc_dP[ip][ke] = m_dVisc_dPres[seri[ke]][sesri[ke]][sei[ke]][0][ip][Deriv::dP];
+              dMob_dP[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dP]; // dM/dP = {alpha * dM1/dP1 , (1 -
+              // alpha) * dM2/dP2}
+              dMob_dS[ip][ke] = mobWeights[ke] * m_dMob[seri[ke]][sesri[ke]][sei[ke]][ip][Deriv::dS]; // dM/dP = {alpha * dM1/dS1 , (1 -
+              // alpha) * dM2/dS2}
+            }
+          }
+
+          // pressure gradient depends on all points in the stencil
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            dFlux_dP[ip][ke] += dPresGrad_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) ,
+            //          -T + dT/dP2 * (P1 - P2) }
+          }
+
+          // gravitational head depends only on the two cells connected (same as mean density)
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            dFlux_dP[ip][ke] -= dGravHead_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
+            // z2) ,
+            //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
+            // z2) }
+          }
+
+          // capillary pressure contribution
+          if( m_hasCapPressure )
+          {
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              dFlux_dP[ip][ke] += dCapGrad_dP[ip][ke]; // dF/dP = { T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1
+              // - z2) + dT/dP1 * (-Pc1 + Pc2) ,
+              //          -T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1
+              // - z2) + dT/dP2 * (-Pc1 + Pc2) }
+
+              dFlux_dS[ip][ke] += dCapGrad_dS[ip][ke]; // dF/dS = { T * -dPc/dS1 , T * dPc/dS2 }
+            }
+          }
+
+          // compute the flux and derivatives using upstream cell mobility
+          fluxVal[ip] = mobility[ip] * potGrad; // F = M * DPhi
+
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            dFlux_dP[ip][ke] *= mobility[ip]; // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho/dP1 * T g (z1 - z2) - dT/dP1 * rho g (z1 -
+            // z2) + dT/dP1 * (-Pc1 + Pc2)] ,
+            //           M [-T + dT/dP2 * (P1 - P2) - drho/dP2 * T g (z1 - z2) - dT/dP2 * rho g (z1 -
+            // z2) + dT/dP2 * (-Pc1 + Pc2)] }
+
+            dFlux_dS[ip][ke] *= mobility[ip]; // dF/dS = { M [T * -dPc/dS1] , M [T * dPc/dS2] }
+          }
+
+          // add contribution from upstream cell mobility derivatives
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+
+            real64 dMob_dP2 = mobility[ip] / density2[ip] * (-dVisc_dP[ip][ke] / viscosity[ip]);
+
+            duT_dP[ke] += dFlux_dP[ip][ke] / density2[ip] + dMob_dP2 * potGrad;
+
+            dFlux_dP[ip][ke] += dMob_dP[ip][ke] * potGrad; // dF/dP = { M [ T + dT/dP1 * (P1 - P2) - drho1/dP * T g (z1 - z2) - dT/dP1 *
+            // rho g (z1 - z2) + dT/dP1 * (-Pc1 + Pc2)] + dM/dP1 * DPhi ,
+            //           M [-T + dT/dP2 * (P1 - P2) - drho2/dP * T g (z1 - z2) - dT/dP2 *
+            // rho g (z1 - z2) + dT/dP2 * (-Pc1 + Pc2)] + dM/dP2 * DPhi }
+            dFlux_dS[ip][ke] += dMob_dS[ip][ke] * potGrad; // dF/dS = { M [T * -dPc/dS1] + dM/dS1 * DPhi , M [T * dPc/dS2] + dM/dS2 * DPhi
+            // }
+          }
+
+
+          uT += fluxVal[ip] / density2[ip];
+
+          // add contribution from upstream cell mobility derivatives
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+//  duT_dP[ke] += dFlux_dP[ip][ke] - fluxVal[ip] * dDens_dP2[ip][ke] / density2[ip];
+//  // duT_dP[ke] += dFlux_dP[ip][ke];
+
+//  duT_dP[ke]  /= density2[ip];
+
+            duT_dS[ke] += dFlux_dS[ip][ke] / density2[ip];
+            // duT_dS[ke] += dFlux_dS[ip][ke];
+
+          }
+
+          potGrad_ip[ip] = potGrad;
+          alpha_ip[ip] = alpha;
+
+        } // loop over phases
+
+
+        // this determines whether the local solver is needed becuase of heterogeneous capillary pressure regions
+        // bool notOnInterface = std::fabs( jFMultiplier[0][0] - jFMultiplier[0][1] ) < 1  && std::fabs( jFMultiplier[1][0] - jFMultiplier[1][1] ) < 1;
+       bool notOnInterface = !connectorHasInterfaceConditionQ;
+        if( notOnInterface )
+        {
+          for( integer ip = 0; ip < 2; ++ip )
+          {
+            // populate local flux vector and derivatives
+            stack.localFlux[k[0]*numEqn + ip] += m_dt * fluxVal[ip];
+            stack.localFlux[k[1]*numEqn + ip] -= m_dt * fluxVal[ip];
+
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              // pressure
+              localIndex const localDofIndexPres = k[ke] * numDof;
+              stack.localFluxJacobian[k[0]*numEqn + ip][localDofIndexPres] += m_dt * dFlux_dP[ip][ke];
+              stack.localFluxJacobian[k[1]*numEqn + ip][localDofIndexPres] -= m_dt * dFlux_dP[ip][ke];
+
+              // saturation
+              localIndex const localDofIndexSat = k[ke] * numDof + 1;
+              stack.localFluxJacobian[k[0]*numEqn + ip][localDofIndexSat] += m_dt * dFlux_dS[ip][ke];
+              stack.localFluxJacobian[k[1]*numEqn + ip][localDofIndexSat] -= m_dt * dFlux_dS[ip][ke];
+            }
+
+            // Customize the kernel with this lambda
+            kernelOp( k, seri, sesri, sei, connectionIndex, alpha_ip[ip], mobility, potGrad_ip[ip], fluxVal, dFlux_dP, dFlux_dS );
+
+          }
+        }
+        else
+        {
+
+
+          bool converged = 0;
+
+
+          // clear working arrays
+          real64 halfFluxVal[numEqn][2]{};
+          // real64 dhalfFlux1_dP[numEqn][2]{};
+          // real64 dhalfFlux1_dS[numEqn][2]{};
+          // real64 dhalfFlux2_dP[numEqn][2]{};
+          // real64 dhalfFlux2_dS[numEqn][2]{};
+          // real64 dhalfFlux_duT[numEqn][2]{};
+          // real64 dhalfFlux_dpc[numEqn][2]{};
+
+
+          // stdVector< real64 > JFMultipliers = {jFMultiplier[0][0], jFMultiplier[0][1]};
+          stdVector< real64 > JFMultipliers = {0.0, 0.0};
+          // trappedSats will be extracted from models below and passed to local_solver
+          stdVector< real64 > trappedSats1 = {0.0, 0.0};
+          stdVector< real64 > trappedSats2 = {0.0, 0.0};
+          stdVector< fields::cappres::ModeIndexType> modes = {static_cast<fields::cappres::ModeIndexType>(0), static_cast<fields::cappres::ModeIndexType>(0)};
+          stdVector< real64 > transHats = {transHat[0], transHat[1]};
+          stdVector< real64 > dTransHats_dP = {dTransHat_dP[0], dTransHat_dP[1]};
+          stdVector< real64 > gravCoefHats = {gravCoefHat[0], gravCoefHat[1]};
+          stdVector< real64 > gravCoefs = {gravCoef2[0], gravCoef2[1]};
+          stdVector< real64 > cellCenterDuTdS = {duT_dP[0], duT_dP[1], duT_dS[0], duT_dS[1]};
+          stdVector< real64 > cellCenterDens = {density2[0], density2[1]};
+          stdVector< real64 > cellCenterDens_dP = {dDens_dP2[0][0], dDens_dP2[0][1], dDens_dP2[1][0], dDens_dP2[1][1]};
+          // std::vector< RelativePermeabilityBase * > relPerms = {std::get< 0 >( m_interfaceConstitutivePairs_temp ), std::get< 0 >( m_interfaceConstitutivePairs_temp )};
+          // std::vector< CapillaryPressureBase * > capPressures = {std::get< 1 >( m_interfaceConstitutivePairs_temp ), std::get< 1 >( m_interfaceConstitutivePairs_temp )};
+          // std::vector< TwoPhaseImmiscibleFluid * > fluids = {std::get< 2 >( m_interfaceConstitutivePairs_temp ), std::get< 2 >( m_interfaceConstitutivePairs_temp )};
+
+          // auto const & pairArray = m_interfaceConstitutivePairs[0];
+          localIndex const surfaceRegionIndex = m_interfaceRegionByConnector.at(iconn);
+auto const & pairArray = m_interfaceConstitutivePairs[surfaceRegionIndex];
+
+std::vector< constitutive::RelativePermeabilityBase * > relPerms = {
+  std::get<0>( pairArray[0] ),
+  std::get<0>( pairArray[1] )
+};
+
+std::vector< constitutive::CapillaryPressureBase * > capPressures = {
+  std::get<1>( pairArray[0] ),
+  std::get<1>( pairArray[1] )
+};
+
+std::vector< constitutive::TwoPhaseImmiscibleFluid * > fluids = {
+  std::get<2>( pairArray[0] ),
+  std::get<2>( pairArray[1] )
+};
+
+          // Extract historical volume fractions, trapped saturations, and mode from TableCapillaryPressureHysteresis models
+          // Initialize with sentinel values to indicate they haven't been set
+          // Use -1.0 as a sentinel value (invalid for saturations which are 0-1)
+          stdVector< real64 > phaseMaxHistoricalVolFraction1 = {-1.0, -1.0};
+          stdVector< real64 > phaseMinHistoricalVolFraction1 = {-1.0, -1.0};
+          stdVector< real64 > phaseMaxHistoricalVolFraction2 = {-1.0, -1.0};
+          stdVector< real64 > phaseMinHistoricalVolFraction2 = {-1.0, -1.0};
+          
+          // Trapped saturations are available in all capillary pressure models (via base class),
+          // but we only extract them when using hysteresis models since they're most meaningful there
+          // Initialize with sentinel values to indicate they haven't been set
+          stdVector< real64 > trappedSats1_extracted = {-1.0, -1.0};
+          stdVector< real64 > trappedSats2_extracted = {-1.0, -1.0};
+          
+          for( integer ke = 0; ke < 2; ++ke )
+          {
+            constitutive::TableCapillaryPressureHysteresis * capPresHyst = 
+              dynamic_cast<constitutive::TableCapillaryPressureHysteresis *>(capPressures[ke]);
+            
+            if( capPresHyst != nullptr )
+            {
+              // Get the mode for this cell
+              auto const & modeArray = capPresHyst->getField< fields::cappres::mode >().reference();
+              if( sei[ke] < static_cast<localIndex>(modeArray.size()) )
+              {
+                modes[ke] = static_cast<fields::cappres::ModeIndexType>(modeArray[sei[ke]]);
+              }
+              
+              // Get historical volume fractions for this cell
+              auto const & maxHistArray = capPresHyst->getField< fields::cappres::phaseMaxHistoricalVolFraction >().reference();
+              auto const & minHistArray = capPresHyst->getField< fields::cappres::phaseMinHistoricalVolFraction >().reference();
+              
+              if( sei[ke] < static_cast<localIndex>(maxHistArray.size(0)) && m_numPhases > 0 )
+              {
+                for( integer ip = 0; ip < m_numPhases; ++ip )
+                {
+                  if( ke == 0 )
+                  {
+                    phaseMaxHistoricalVolFraction1[ip] = maxHistArray[sei[ke]][ip];
+                    phaseMinHistoricalVolFraction1[ip] = minHistArray[sei[ke]][ip];
+                  }
+                  else
+                  {
+                    phaseMaxHistoricalVolFraction2[ip] = maxHistArray[sei[ke]][ip];
+                    phaseMinHistoricalVolFraction2[ip] = minHistArray[sei[ke]][ip];
+                  }
+                }
+              }
+              
+              // Get trapped volume fractions for this cell
+              // Note: phaseTrappedVolFraction is available in all capillary pressure models (via base class)
+              auto const & trappedArray = capPresHyst->getField< fields::cappres::phaseTrappedVolFraction >().reference();
+              
+              if( sei[ke] < static_cast<localIndex>(trappedArray.size(0)) && m_numPhases > 0 )
+              {
+                for( integer ip = 0; ip < m_numPhases; ++ip )
+                {
+                  if( ke == 0 )
+                  {
+                    trappedSats1_extracted[ip] = trappedArray[sei[ke]][0][ip]; // [element][subregion][phase]
+                  }
+                  else
+                  {
+                    trappedSats2_extracted[ip] = trappedArray[sei[ke]][0][ip];
+                  }
+                }
+              }
+            }
+            else
+            {
+              // For non-hysteresis models, we can still try to get trapped saturations if available
+              // but they're typically not meaningful for non-hysteresis models
+              // We'll extract them anyway in case they were set (e.g., for consistency)
+              auto const & trappedArray = capPressures[ke]->getField< fields::cappres::phaseTrappedVolFraction >().reference();
+              
+              if( sei[ke] < static_cast<localIndex>(trappedArray.size(0)) && m_numPhases > 0 )
+              {
+                for( integer ip = 0; ip < m_numPhases; ++ip )
+                {
+                  if( ke == 0 )
+                  {
+                    trappedSats1_extracted[ip] = trappedArray[sei[ke]][0][ip];
+                  }
+                  else
+                  {
+                    trappedSats2_extracted[ip] = trappedArray[sei[ke]][0][ip];
+                  }
+                }
+              }
+            }
+          }
+
+          stdVector< real64 > phi = {halfFluxVal[0][0], halfFluxVal[0][1]};
+          stdVector< real64 > grad_phi_P = {0.0, 0.0, 0.0, 0.0};
+          stdVector< real64 > grad_phi_S = {0.0, 0.0, 0.0, 0.0};
+
+
+          // Use extracted trapped saturations if available, otherwise use defaults
+          if( trappedSats1_extracted[0] >= 0.0 )
+          {
+            trappedSats1 = trappedSats1_extracted;
+          }
+          if( trappedSats2_extracted[0] >= 0.0 )
+          {
+            trappedSats2 = trappedSats2_extracted;
+          }
+          
+          real64 warmStartPc = ( iconn < static_cast< localIndex >( m_convergedPcInt.size() ) )
+                               ? m_convergedPcInt[iconn] : -1.0;
+          
+          local_solver( uT, saturations, pressures, JFMultipliers, trappedSats1, trappedSats2, modes, transHats, dTransHats_dP, gravCoefHats, gravCoefs, 
+            cellCenterDuTdS, cellCenterDens, cellCenterDens_dP, relPerms, capPressures, fluids, phi, grad_phi_P, grad_phi_S, converged,
+            phaseMaxHistoricalVolFraction1, phaseMinHistoricalVolFraction1, phaseMaxHistoricalVolFraction2, phaseMinHistoricalVolFraction2,
+            warmStartPc );
+
+          if( iconn < static_cast< localIndex >( m_convergedPcInt.size() ) )
+          {
+            m_convergedPcInt[iconn] = warmStartPc;
+          }
+          
+
+             fluxVal[0] = phi[0];
+             fluxVal[1] = phi[1];
+             dFlux_dP[0][0] = grad_phi_P[0];
+             dFlux_dP[0][1] = grad_phi_P[1];
+             dFlux_dP[1][0] = grad_phi_P[2];
+             dFlux_dP[1][1] = grad_phi_P[3];
+             dFlux_dS[0][0] = grad_phi_S[0];
+             dFlux_dS[0][1] = grad_phi_S[1];
+             dFlux_dS[1][0] = grad_phi_S[2];
+             dFlux_dS[1][1] = grad_phi_S[3];
+
+          // Global residual and jacobian update:
+          for( integer ip = 0; ip < m_numPhases; ++ip )
+          {
+            // populate local flux vector and derivatives
+            stack.localFlux[k[0]*numEqn + ip] += m_dt * fluxVal[ip];
+            stack.localFlux[k[1]*numEqn + ip] -= m_dt * fluxVal[ip];
+
+            for( integer ke = 0; ke < 2; ++ke )
+            {
+              // pressure
+              localIndex const localDofIndexPres = k[ke] * numDof;
+              stack.localFluxJacobian[k[0]*numEqn + ip][localDofIndexPres] += m_dt * dFlux_dP[ip][ke];
+              stack.localFluxJacobian[k[1]*numEqn + ip][localDofIndexPres] -= m_dt * dFlux_dP[ip][ke];
+
+              // saturation
+              localIndex const localDofIndexSat = k[ke] * numDof + 1;
+              stack.localFluxJacobian[k[0]*numEqn + ip][localDofIndexSat] += m_dt * dFlux_dS[ip][ke];
+              stack.localFluxJacobian[k[1]*numEqn + ip][localDofIndexSat] -= m_dt * dFlux_dS[ip][ke];
+            }
+
+            // Customize the kernel with this lambda
+            kernelOp( k, seri, sesri, sei, connectionIndex, alpha_ip[ip], mobility, potGrad_ip[ip], fluxVal, dFlux_dP, dFlux_dS );
+
+          } // loop over phases
+        } // end of else for interface conditions
+
+        connectionIndex++;
+      }
+    } // loop over connection elements
+  }
+
+protected:
+
+  /// Reference to the capillary pressure wrapper
+  // CAPPRESWRAPPER const m_capPressureWrapper;
+  // RELPERMWRAPPER const m_relPermWrapper;
+  string_array const m_interfaceFaceSetNames;
+  stdVector< std::array< std::tuple< constitutive::RelativePermeabilityBase *,
+                                     constitutive::CapillaryPressureBase *,
+                                     constitutive::TwoPhaseImmiscibleFluid * >, 2 > >  const m_interfaceConstitutivePairs;
+  unordered_map< localIndex, localIndex > const m_interfaceRegionByConnector;
+  // std::tuple< constitutive::RelativePermeabilityBase *,
+  //             constitutive::CapillaryPressureBase *,
+  //             constitutive::TwoPhaseImmiscibleFluid * > const m_interfaceConstitutivePairs_temp;
+
+  inline static std::vector< real64 > m_convergedPcInt;
+
+};
+
+
+
+/****************************************** */
+
+/**
+ * @class FluxComputeKernelFactory
+ */
+class FluxComputeKernelFactory
+{
+public:
+
+  /**
+   * @brief Create a new kernel and launch
+   * @tparam POLICY the policy used in the RAJA kernel
+   * @tparam STENCILWRAPPER the type of the stencil wrapper
+   * @param[in] rankOffset the offset of my MPI rank
+   * @param[in] dofKey string to get the element degrees of freedom numbers
+   * @param[in] solverName name of the solver (to name accessors)
+   * @param[in] elemManager reference to the element region manager
+   * @param[in] stencilWrapper reference to the stencil wrapper
+   * @param[in] dt time step size
+   * @param[inout] localMatrix the local CRS matrix
+   * @param[inout] localRhs the local right-hand side vector
+   */
+  template< typename POLICY, typename STENCILWRAPPER >
+  static void
+  createAndLaunch( integer const numPhases,
+                   globalIndex const rankOffset,
+                   string const & dofKey,
+                   integer const hasCapPressure,
+                   integer const useTotalMassEquation,
+                   integer const checkPhasePresenceInGravity,
+                   string const & solverName,
+                   ElementRegionManager const & elemManager,
+                   STENCILWRAPPER const & stencilWrapper,
+                   real64 const & dt,
+                   CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                   arrayView1d< real64 > const & localRhs )
+  {
+    integer constexpr NUM_EQN = 2;
+    integer constexpr NUM_DOF = 2;
+
     ElementRegionManager::ElementViewAccessor< arrayView1d< globalIndex const > > dofNumberAccessor =
       elemManager.constructArrayViewAccessor< globalIndex, 1 >( dofKey );
     dofNumberAccessor.setName( solverName + "/accessors/" + dofKey );
@@ -788,6 +3709,73 @@ class FluxComputeKernelFactory
                        checkPhasePresenceInGravity );
     kernelType::template launch< POLICY >( stencilWrapper.size(), kernel );
   }
+
+  /**
+   * @brief Create a new kernel and launch
+   * @tparam POLICY the policy used in the RAJA kernel
+   * @tparam STENCILWRAPPER the type of the stencil wrapper
+   * @tparam CAPPRESWRAPPER the type of the capillary pressure wrapper
+   * @param[in] rankOffset the offset of my MPI rank
+   * @param[in] dofKey string to get the element degrees of freedom numbers
+   * @param[in] solverName name of the solver (to name accessors)
+   * @param[in] elemManager reference to the element region manager
+   * @param[in] stencilWrapper reference to the stencil wrapper
+   * @param[in] capPresWrapper reference to the capillary pressure wrapper
+   * @param[in] dt time step size
+   * @param[inout] localMatrix the local CRS matrix
+   * @param[inout] localRhs the local right-hand side vector
+   */
+  // template< typename POLICY, typename STENCILWRAPPER, typename CAPPRESWRAPPER, typename RELPERMWRAPPER >
+  template< typename POLICY, typename STENCILWRAPPER >
+  static void
+  createAndLaunch( integer const numPhases,
+                   globalIndex const rankOffset,
+                   string const & dofKey,
+                   integer const hasCapPressure,
+                   integer const useTotalMassEquation,
+                   integer const checkPhasePresenceInGravity,
+                   string const & solverName,
+                   ElementRegionManager const & elemManager,
+                   STENCILWRAPPER const & stencilWrapper,
+                  //  CAPPRESWRAPPER const & capPresWrapper,
+                  //  RELPERMWRAPPER const & relPermWrapper,
+                   string_array const & interfaceFaceSetNames,
+                   stdVector< std::array< std::tuple< constitutive::RelativePermeabilityBase *,
+                                                      constitutive::CapillaryPressureBase *,
+                                                      constitutive::TwoPhaseImmiscibleFluid * >, 2 > > const & interfaceConstitutivePairs,
+                   unordered_map< localIndex, localIndex > const & interfaceRegionByConnector,
+                  //  std::tuple< constitutive::RelativePermeabilityBase *,
+                  //              constitutive::CapillaryPressureBase *,
+                  //              constitutive::TwoPhaseImmiscibleFluid * > const & interfaceConstitutivePairs_temp,
+                   ElementSubRegionBase const & subRegion,
+                   real64 const & dt,
+                   CRSMatrixView< real64, globalIndex const > const & localMatrix,
+                   arrayView1d< real64 > const & localRhs )
+  {
+    integer constexpr NUM_EQN = 2;
+    integer constexpr NUM_DOF = 2;
+    localIndex const domainSize = subRegion.size();
+    ElementRegionManager::ElementViewAccessor< arrayView1d< globalIndex const > > dofNumberAccessor =
+      elemManager.constructArrayViewAccessor< globalIndex, 1 >( dofKey );
+    dofNumberAccessor.setName( solverName + "/accessors/" + dofKey );
+
+    // using kernelType = FluxComputeInterfaceConditionKernel< NUM_EQN, NUM_DOF, STENCILWRAPPER, CAPPRESWRAPPER, RELPERMWRAPPER >;
+        using kernelType = FluxComputeInterfaceConditionKernel< NUM_EQN, NUM_DOF, STENCILWRAPPER >;
+    typename kernelType::ImmiscibleMultiphaseFlowAccessors flowAccessors( elemManager, solverName );
+    typename kernelType::MultiphaseFluidAccessors fluidAccessors( elemManager, solverName );
+    typename kernelType::CapPressureAccessors capPressureAccessors( elemManager, solverName );
+    typename kernelType::PermeabilityAccessors permAccessors( elemManager, solverName );
+
+    // kernelType kernel( numPhases, rankOffset, stencilWrapper, capPresWrapper, relPermWrapper, dofNumberAccessor,
+    //                    flowAccessors, fluidAccessors, capPressureAccessors, permAccessors,
+    //                    dt, localMatrix, localRhs, hasCapPressure, useTotalMassEquation,
+    //                    checkPhasePresenceInGravity, interfaceFaceSetNames, interfaceConstitutivePairs, interfaceRegionByConnector, interfaceConstitutivePairs_temp, domainSize );
+    kernelType kernel( numPhases, rankOffset, stencilWrapper, dofNumberAccessor,
+                       flowAccessors, fluidAccessors, capPressureAccessors, permAccessors,
+                       dt, localMatrix, localRhs, hasCapPressure, useTotalMassEquation,
+                       checkPhasePresenceInGravity, interfaceFaceSetNames, interfaceConstitutivePairs, interfaceRegionByConnector, domainSize );
+    kernelType::template launch< POLICY >( stencilWrapper.size(), kernel );
+  }
 };
 
 
@@ -795,7 +3783,7 @@ class FluxComputeKernelFactory
 
 enum class KernelFlags
 {
-  TotalMassEquation = 1 << 0, // 1
+  TotalMassEquation = 1 << 0,  // 1
 
   /// Add more flags like that if needed:
   // Flag2 = 1 << 1, // 2
@@ -1421,7 +4409,7 @@ class ResidualNormKernelFactory
     {
       ResidualNormKernel::launchLinf< POLICY >( subRegion.size(), kernel, residualNorm );
     }
-    else // L2 norm
+    else  // L2 norm
     {
       ResidualNormKernel::launchL2< POLICY >( subRegion.size(), kernel, residualNorm, residualNormalizer );
     }
@@ -1431,9 +4419,9 @@ class ResidualNormKernelFactory
 
 
 
-} // namespace immiscible multiphasekernels
+}  // namespace immiscible multiphasekernels
 
 
-} // namespace geos
+}  // namespace geos
 
-#endif //GEOS_PHYSICSSOLVERS_FLUIDFLOW_MULTIPHASEKERNELS_HPP
+ #endif //GEOS_PHYSICSSOLVERS_FLUIDFLOW_MULTIPHASEKERNELS_HPP
diff --git a/src/coreComponents/schema/schema.xsd.other b/src/coreComponents/schema/schema.xsd.other
index e77cc9d197a..a3def28f6b5 100644
--- a/src/coreComponents/schema/schema.xsd.other
+++ b/src/coreComponents/schema/schema.xsd.other
@@ -3267,6 +3267,10 @@ A field can represent a physical variable. (pressure, temperature, global compos
 		<xsd:attribute name="waterOilMaxRelPerm" type="real64" />
 	</xsd:complexType>
 	<xsd:complexType name="TableRelativePermeabilityHysteresisType">
+		<!--KilloughModel => (no description available)-->
+		<xsd:attribute name="KilloughModel" type="geosx_constitutive_KilloughHysteresis" />
+		<!--KilloughWrappers => (no description available)-->
+		<xsd:attribute name="KilloughWrappers" type="geosx_constitutive_KilloughHysteresis_KernelKilloughHysteresisBase" />
 		<!--dPhaseRelPerm_dPhaseVolFraction => Derivative of phase relative permeability with respect to phase volume fraction-->
 		<xsd:attribute name="dPhaseRelPerm_dPhaseVolFraction" type="real64_array4d" />
 		<!--drainageRelPermWrappers => (no description available)-->
@@ -3276,7 +3280,11 @@ A field can represent a physical variable. (pressure, temperature, global compos
 		<!--landParameter => (no description available)-->
 		<xsd:attribute name="landParameter" type="real64_array" />
 		<!--nonWettingCurve => (no description available)-->
+<<<<<<< HEAD
 		<xsd:attribute name="nonWettingCurve" type="geos_constitutive_KilloughHysteresis_HysteresisCurve" />
+=======
+		<xsd:attribute name="nonWettingCurve" type="geosx_constitutive_KilloughHysteresis_HysteresisCurve" />
+>>>>>>> Killough-PC_copy
 		<!--phaseHasHysteresis => (no description available)-->
 		<xsd:attribute name="phaseHasHysteresis" type="integer_array" />
 		<!--phaseMaxHistoricalVolFraction => Phase max historical phase volume fraction-->
diff --git a/src/docs/doxygen/GeosxConfig.hpp b/src/docs/doxygen/GeosxConfig.hpp
index 21b976a0d4c..a28bf2ae4ce 100644
--- a/src/docs/doxygen/GeosxConfig.hpp
+++ b/src/docs/doxygen/GeosxConfig.hpp
@@ -144,7 +144,7 @@
 #define adiak_VERSION ..
 
 /// Version information for caliper
-#define caliper_VERSION 2.8.0
+#define caliper_VERSION 2.4.0
 
 /// Version information for Metis
 #define metis_VERSION 5.1.0