Add V&V for the 2D Backward facing step

TestCases/vandv/inc_bfs/docs/su2validation_inc_bfs.md

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+---
+title: 2D Backward Facing Step Validation Case
+permalink: /docs/su2validation_inc_bfs.md
+---
+
+# 2D Backward Facing Step Validation Case
+
+
+<style>
+table th:first-of-type {
+    width: 50%;
+}
+table th:nth-of-type(2) {
+    width: 30%;
+}
+</style>
+
+| Solver | Version |
+| --- | --- |
+| INC_RANS |  8.1.0 "Harrier"  |
+
+---
+
+The 2D Backward-Facing Step (BFS) is a classical benchmark case for validating turbulence models. In this configuration, a fully developed turbulent boundary layer encounters a sudden back step, leading to flow separation and recirculation zones downstream. The experimental data provided by Driver and Seegmiller serves as the reference for this validation case.
+
+## Problem Setup
+
+Geometry: The BFS model consists of a channel with a sudden expansion due to a step. The step height (H) is the primary geometric parameter and in this case it is set to $0.0127m$. This corresponds to a Reynolds number of approximately 36,000 based on step height H. Geometry of the testcase is shown in the following image.
+
+![geometry](../images/bfsw-geom.png)
+
+The simulation is performed with the following boundary conditions:
+
+- Inlet: A specified velocity profile representing the turbulent boundary layer.
+- Walls: No-slip conditions on both the upper and lower walls.
+- Outlet: pressure outlet condition.
+
+## Mesh Description
+
+To ensure accurate resolution of the flow features, particularly in the recirculation region downstream of the step, a sequence of structured nested grids is used. These grids are designed to effectively capture adverse pressure gradients and flow separation. The approximate mesh sizes are:
+
+- L1 "coarse" - 20k quadrilaterals
+- L2 "medium" - 104k quadrilaterals
+- L3 "fine" - 210k quadrilaterals
+
+## Results
+
+The SST turbulence model demonstrates excellent agreement with experimental results for velocity and turbulent kinetic energy. However, the pressure coefficient appears to be slightly under-predicted, as seen in the comparison figures below.
+
+![Velocity](../images/Velocity.png)
+![tke](../images/tke.png)
+![Cp](../images/Cp.png)

TestCases/vandv/inc_bfs/inc_bfs.cfg

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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                              %
+% SU2 configuration file                                                       %
+% Case description: Backward Facing Step of Driver (incompressible)            %
+%                   http://turbmodels.larc.nasa.gov/backstep_val.html          %
+% Author: Nijso Beishuizen                                                     %
+% Institution: TU Eindhoven                                                    %
+% Date: Dec 8th, 2024                                                          %
+% File Version 8.1.0 "Harrier"                                                 %
+%                                                                              %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% ------------- DIRECT, ADJOINT, AND LINEARIZED PROBLEM DEFINITION ------------%
+%
+SOLVER= INC_RANS
+KIND_TURB_MODEL= SST
+SST_OPTIONS= V2003m
+
+RESTART_SOL= YES
+
+% ---------------- INCOMPRESSIBLE FLOW CONDITION DEFINITION -------------------%
+%
+INC_DENSITY_INIT= 1.2
+INC_DENSITY_REF = 1.2
+
+INC_VELOCITY_INIT= ( 44.2, 0.0, 0.0 )
+INC_VELOCITY_REF = 44.2
+INC_NONDIM= DIMENSIONAL
+
+% --------------------------- VISCOSITY MODEL ---------------------------------%
+%
+VISCOSITY_MODEL= CONSTANT_VISCOSITY
+MU_CONSTANT= 1.8e-05
+
+% ---------------------- REFERENCE VALUE DEFINITION ---------------------------%
+%
+REF_ORIGIN_MOMENT_X = 0.25
+REF_ORIGIN_MOMENT_Y = 0.00
+REF_ORIGIN_MOMENT_Z = 0.00
+REF_LENGTH= 0.0127
+REF_AREA= 1.0
+% -------------------- BOUNDARY CONDITION DEFINITION --------------------------%
+%
+INC_INLET_TYPE= VELOCITY_INLET
+INC_INLET_DAMPING= 0.05
+INC_OUTLET_TYPE= PRESSURE_OUTLET
+SPECIFIED_INLET_PROFILE= YES
+INLET_FILENAME= inlet.dat
+MARKER_HEATFLUX= ( wall_upper, 0.0, wall_lower_left, 0.0, wall_vertical, 0.0, wall_lower_right, 0.0)
+MARKER_INLET= ( inlet, 300.0, 44.2, 1.0, 0.0, 0.0 )
+MARKER_INLET_TURBULENT= (inlet, 0.10, 100.0)
+MARKER_OUTLET= ( outlet, 0.0)
+INLET_MATCHING_TOLERANCE = 1e-3
+%
+
+% ------------- COMMON PARAMETERS DEFINING THE NUMERICAL METHOD ---------------%
+%
+NUM_METHOD_GRAD= WEIGHTED_LEAST_SQUARES
+CFL_NUMBER= 10.0
+CFL_ADAPT= YES
+CFL_ADAPT_PARAM= ( 0.95, 1.01, 1.0, 100.0 )
+ITER= 50000
+
+% ----------------------- SLOPE LIMITER DEFINITION ----------------------------%
+%
+VENKAT_LIMITER_COEFF= 0.01
+ADJ_SHARP_LIMITER_COEFF= 3.0
+REF_SHARP_EDGES= 3.0
+SENS_REMOVE_SHARP= NO
+
+% ------------------------ LINEAR SOLVER DEFINITION ---------------------------%
+%
+LINEAR_SOLVER= FGMRES
+LINEAR_SOLVER_PREC= LU_SGS
+LINEAR_SOLVER_ERROR= 1E-4
+LINEAR_SOLVER_ITER= 5
+
+% -------------------- FLOW NUMERICAL METHOD DEFINITION -----------------------%
+%
+CONV_NUM_METHOD_FLOW= FDS
+MUSCL_FLOW= NO
+SLOPE_LIMITER_FLOW= VENKATAKRISHNAN
+JST_SENSOR_COEFF= ( 0.5, 0.02 )
+TIME_DISCRE_FLOW= EULER_IMPLICIT
+
+% -------------------- TURBULENT NUMERICAL METHOD DEFINITION ------------------%
+%
+CONV_NUM_METHOD_TURB= BOUNDED_SCALAR
+MUSCL_TURB= NO
+CFL_REDUCTION_TURB= 0.5
+SLOPE_LIMITER_TURB= VENKATAKRISHNAN
+TIME_DISCRE_TURB= EULER_IMPLICIT
+
+% --------------------------- CONVERGENCE PARAMETERS --------------------------%
+%
+CONV_RESIDUAL_MINVAL= -10
+CONV_STARTITER= 10
+CONV_CAUCHY_ELEMS= 500
+CONV_CAUCHY_EPS= 1E-6
+
+% ------------------------- INPUT/OUTPUT INFORMATION --------------------------%
+%
+MESH_FILENAME= mesh_fine_200k.su2
+
+MESH_FORMAT= SU2
+MESH_OUT_FILENAME= ./mesh_out.su2
+SOLUTION_FILENAME= solution_flow.dat
+TABULAR_FORMAT= CSV
+CONV_FILENAME= history
+RESTART_FILENAME= restart_flow.dat
+VOLUME_FILENAME= flow
+SURFACE_FILENAME= surface_flow
+OUTPUT_WRT_FREQ= 100
+SCREEN_OUTPUT= (INNER_ITER, RMS_PRESSURE, RMS_DENSITY, RMS_VELOCITY-X, RMS_VELOCITY-Y, RMS_TKE, RMS_DISSIPATION, LIFT, DRAG, AVG_CFL)
+OUTPUT_FILES= RESTART, PARAVIEW_MULTIBLOCK, CSV
+VOLUME_OUTPUT= SOLUTION, PRIMITIVE, RESIDUAL