small bugfixes

Author: ScSteffen

_tutorials/compressible_flow/Unsteady_NACA0012.md

@@ -75,7 +75,7 @@ for the physical time iterator by `TIME_ITER`. The option `TIME_DOMAIN=YES` acti
 The numerical method to solve the inner (fictional time) ODE is given by the option `TIME_DISCRE_FLOW`.
 
 ```
-% ----------UNSTEADY SIMULATION ---------------%
+% -------------UNSTEADY SIMULATION ----------------%
 %
 TIME_DOMAIN = YES
 %
@@ -140,7 +140,7 @@ The solver will stop, if the average over a certain number of elements (set with
 The windowed time-averaged Cauchy criterion can be activated by setting `WINDOW_CAUCHY_CRIT = YES` (default is `NO`).
 
 ```
-% ------------------ Coefficient-based Windowed Time Convergence Criteria -----------------------%
+% --- Coefficient-based Windowed Time Convergence Criteria ----%
 %
 % Activate the windowed cauchy criterion
 WINDOW_CAUCHY_CRIT = YES

_tutorials/design_features/Unsteady_Shape_Opt_NACA0012.md

@@ -89,8 +89,8 @@ Figure (2): Instantaneous drag and drag sensitivity shown. The time frame to ave
 Using the midpoint rule for above integral, we arrive at the following constrained optimization problem
 
 $$ \min_{\sigma} \frac{1}{M} \sum_{n_{tr}}^{N} w\left(\frac{n-n_{tr}}{N-n_{tr}}\right)C_D(\sigma,n) $$
-$$ s.t. R(u^n) = 0 \qquad \forall n=1,\dots,N $$
-$$ s.t. \sum_{n_{tr}}^{N} w\left(\frac{n-n_{tr}}{N-n_{tr}}\right)C_L(\sigma,n) \geq c$$
+$$ s.t. \qquad R(u^n) = 0 \qquad \forall n=1,\dots,N $$
+$$ \qquad\qquad\sum_{n_{tr}}^{N} w\left(\frac{n-n_{tr}}{N-n_{tr}}\right)C_L(\sigma,n) \geq c$$
 
 The optimization constraint is given by the windowed time-averaged lift, that should be greater than a specific value $$c$$. We choose arbitrarily as $$c=0.96$$, which is the windowed
 time-averaged lift of the baseline geometry.