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-   -   best setting for SU2 (https://www.cfd-online.com/Forums/su2/133576-best-setting-su2.html)

mechy April 17, 2014 02:19

best setting for SU2
 
Hi all

I want to simulate an airfoil with a small flap at its end. the FLUENT and OpenFoam give similar steady results and in their results the Drag coefficient reaches a constant value. but in the SU2 the Drag coefficient has an oscillation about the OpenFoam result. how I can remove this oscillation and get a steady results from SU2 ?
the config file is attached.


Code:


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                              %
% Stanford University unstructured (SU2) configuration file                    %
% Case description: Transonic inviscid flow around a NACA0012 airfoil          %
% Author: Thomas D. Economon                                                  %
% Institution: Stanford University                                            %
% Date: 2012.10.07                                                            %
% File Version 1.0.12 January 5th, 2012                                        %
%                                                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ------------- DIRECT, ADJOINT, AND LINEARIZED PROBLEM DEFINITION ------------%
%
% Physical governing equations (POTENTIAL_FLOW, EULER, NAVIER_STOKES,
%                              MULTI_SPECIES_NAVIER_STOKES, TWO_PHASE_FLOW,
%                              COMBUSTION)
PHYSICAL_PROBLEM= NAVIER_STOKES
%
% Mathematical problem (DIRECT, ADJOINT, LINEARIZED, ONE_SHOT_ADJOINT)
MATH_PROBLEM= DIRECT
%
% If Navier-Stokes, kind of turbulent model (NONE, SA)
KIND_TURB_MODEL= SA
%
% Restart solution (NO, YES)
RESTART_SOL= NO
%
% Console output (VERBOSE, CONCISE, QUIET)
CONSOLE= CONCISE

% ----------- COMPRESSIBLE AND INCOMPRESSIBLE FREE-STREAM DEFINITION ----------%
%
% Mach number (non-dimensional, based on the free-stream values)
MACH_NUMBER= 0.3
%
% Angle of attack (degrees)
AoA=5
%
% Free-stream pressure (101325.0 N/m^2 by default, only Euler flows) 
FREESTREAM_PRESSURE= 101325.0
%
% Free-stream temperature (273.15 K by default)
FREESTREAM_TEMPERATURE= 273.15
%
% Reynolds number (non-dimensional, based on the free-stream values)
REYNOLDS_NUMBER= 7.16E6
%
% Reynolds length (1 m by default)
REYNOLDS_LENGTH= 1.0
%
% Free-stream Turbulence Intensity
FREESTREAM_TURBULENCEINTENSITY = 0.01
%
% Free-stream Turbulent to Laminar viscosity ratio
FREESTREAM_TURB2LAMVISCRATIO = 2.0

% -------------- COMPRESSIBLE AND INCOMPRESSIBLE FLUID CONSTANTS --------------%
%
% Ratio of specific heats (1.4 (air), only for compressible flows)
GAMMA_VALUE= 1.4
%
% Specific gas constant (287.87 J/kg*K (air), only for compressible flows)
GAS_CONSTANT= 287.87
%
% Laminar Prandtl number (0.72 (air), only for compressible flows)
PRANDTL_LAM= 0.72
%
% Turbulent Prandtl number (0.9 (air), only for compressible flows)
PRANDTL_TURB= 0.9

% ---------------------- REFERENCE VALUE DEFINITION ---------------------------%
%
% Conversion factor for converting the grid to meters
CONVERT_TO_METER= 1.0
%
% Reference origin for moment computation
REF_ORIGIN_MOMENT_X = 0.25
REF_ORIGIN_MOMENT_Y = 0.00
REF_ORIGIN_MOMENT_Z = 0.00
%
% Reference length for pitching, rolling, and yawing non-dimensional moment
REF_LENGTH_MOMENT= 1.0
%
% Reference area for force coefficients (0 implies automatic calculation)
REF_AREA= 1.0
%
% Reference pressure (101325.0 N/m^2 by default)
REF_PRESSURE= 1.0
%
% Reference temperature (273.15 K by default)
REF_TEMPERATURE= 1.0
%
% Reference density (1.2886 Kg/m^3 (air), 998.2 Kg/m^3 (water))
REF_DENSITY= 1.0

% ----------------------- BOUNDARY CONDITION DEFINITION -----------------------%
%
% Marker of the Euler boundary (0 = no marker)
MARKER_HEATFLUX= ( airfoil,0.0,plate,0.0 )
%
% Marker of the far field (0 = no marker)
MARKER_FAR= ( inlet,outlet,farfield )
%
% ------------------------ SURFACES IDENTIFICATION ----------------------------%
%
% Marker of the surface which is going to be plotted or designed
MARKER_PLOTTING= ( airfoil,plate )
%
% Marker of the surface where the functional (Cd, Cl, etc.) will be evaluated
MARKER_MONITORING= ( airfoil,plate )
%
% Marker(s) of the surface where obj. func. (design problem) will be evaluated
MARKER_DESIGNING = ( airfoil )
%
% ------------- COMMON PARAMETERS TO DEFINE THE NUMERICAL METHOD --------------%
%
% Numerical method for spatial gradients (GREEN_GAUSS, WEIGHTED_LEAST_SQUARES)
NUM_METHOD_GRAD= GREEN_GAUSS
%
% Courant-Friedrichs-Lewy condition of the finest grid
CFL_NUMBER= 1.0
%
% CFL ramp (factor, number of iterations, CFL limit)
CFL_RAMP= ( 1.1, 100, 4.0 )
%
% Runge-Kutta alpha coefficients
RK_ALPHA_COEFF= ( 0.66667, 0.66667, 1.000000 )
%
% Number of total iterations
EXT_ITER= 4000
%
% ------------------------ LINEAR SOLVER DEFINITION ---------------------------%
%
% Linear solver for the implicit (or discrete adjoint) formulation (BCGSTAB, FGMRES)
LINEAR_SOLVER= FGMRES
%
% Preconditioner of the Krylov linear solver (JACOBI, LINELET, LU_SGS)
%LINEAR_SOLVER_PREC= LU_SGS
%
% Min error of the linear solver for the implicit formulation
LINEAR_SOLVER_ERROR= 1E-6
%
% Max number of iterations of the linear solver for the implicit formulation
LINEAR_SOLVER_ITER= 30
%
% Relaxation coefficient
%LINEAR_SOLVER_RELAX= 1.0
% -------------------------- MULTIGRID PARAMETERS -----------------------------%
%
% Full Multigrid (NO, YES)
FULLMG= NO
%
% Start up iterations using the fine grid
START_UP_ITER= 0
%
% Multi-Grid Levels (0 = no multi-grid)
MGLEVEL= 0
%
% Multi-Grid Cycle (0 = V cycle, 1 = W Cycle)
MGCYCLE= 1
%
% Reduction factor of the CFL coefficient on the coarse levels
MG_CFL_REDUCTION= 0.9
%
% Maximum number of children in the agglomeration stage
MAX_CHILDREN= 250
%
% Maximum length of an agglomerated element (compared with the domain)
MAX_DIMENSION= 0.1
%
% Multi-Grid PreSmoothing Level
MG_PRE_SMOOTH= ( 1, 2, 3, 3 )
%
% Multi-Grid PostSmoothing Level
MG_POST_SMOOTH= ( 1, 1, 1, 1 )
%
% Jacobi implicit smoothing of the correction
MG_CORRECTION_SMOOTH= ( 1, 1, 1, 1 )
%
% Damping factor for the residual restriction
MG_DAMP_RESTRICTION= 0.9
%
% Damping factor for the correction prolongation
MG_DAMP_PROLONGATION= 0.9

% --------------------- FLOW NUMERICAL METHOD DEFINITION ----------------------%
%
% Convective numerical method (JST, LAX-FRIEDRICH, ROE-1ST_ORDER,
%                              ROE-2ND_ORDER)
%
CONV_NUM_METHOD_FLOW= ROE-2ND_ORDER
%
% Slope limiter (NONE, VENKATAKRISHNAN)
SLOPE_LIMITER_FLOW= VENKATAKRISHNAN
%
% Coefficient for the limiter (smooth regions)
LIMITER_COEFF= 0.1
%
% 1st, 2nd and 4th order artificial dissipation coefficients
AD_COEFF_FLOW= ( 0.15, 0.5, 0.02 )
%
% Viscous numerical method (AVG_GRAD, AVG_GRAD_CORRECTED, GALERKIN)
VISC_NUM_METHOD_FLOW= AVG_GRAD_CORRECTED
%
% Source term numerical method (PIECEWISE_CONSTANT)
SOUR_NUM_METHOD_FLOW= PIECEWISE_CONSTANT
%
% Time discretization (RUNGE-KUTTA_EXPLICIT, EULER_IMPLICIT, EULER_EXPLICIT)
TIME_DISCRE_FLOW= EULER_IMPLICIT

% -------------------- TURBULENT NUMERICAL METHOD DEFINITION ------------------%
%
% Convective numerical method (SCALAR_UPWIND-1ST_ORDER,
%                              SCALAR_UPWIND-2ND_ORDER)
CONV_NUM_METHOD_TURB= SCALAR_UPWIND-1ST_ORDER
%
% Slope limiter (NONE, VENKATAKRISHNAN)
SLOPE_LIMITER_TURB= NONE
%
% Viscous numerical method (AVG_GRAD, AVG_GRAD_CORRECTED)
VISC_NUM_METHOD_TURB= AVG_GRAD_CORRECTED
%
% Source term numerical method (PIECEWISE_CONSTANT)
SOUR_NUM_METHOD_TURB= PIECEWISE_CONSTANT
%
% Time discretization (EULER_IMPLICIT)
TIME_DISCRE_TURB= EULER_IMPLICIT

% ---------------- ADJOINT-FLOW NUMERICAL METHOD DEFINITION -------------------%
% Adjoint problem boundary condition (DRAG, LIFT, SIDEFORCE, MOMENT_X,
%                                    MOMENT_Y, MOMENT_Z, EFFICIENCY,
%                                    EQUIVALENT_AREA, NEARFIELD_PRESSURE,
%                                    FORCE_X, FORCE_Y, FORCE_Z, THRUST,
%                                    TORQUE, FREE_SURFACE)
ADJ_OBJFUNC= DRAG
%
% Convective numerical method (JST, LAX-FRIEDRICH, ROE-1ST_ORDER,
%                              ROE-2ND_ORDER)
CONV_NUM_METHOD_ADJ= JST
%
% Slope limiter (NONE, VENKATAKRISHNAN, SHARP_EDGES)
SLOPE_LIMITER_ADJFLOW= SHARP_EDGES
%
% Coefficient for the sharp edges limiter
SHARP_EDGES_COEFF= 3.0
%
% 1st, 2nd, and 4th order artificial dissipation coefficients
AD_COEFF_ADJ= ( 0.15, 0.0, 0.01 )
%
% Reduction factor of the CFL coefficient in the adjoint problem
ADJ_CFL_REDUCTION= 0.9
%
% Limit value for the adjoint variable
ADJ_LIMIT= 1E6
%
% Remove sharp edges from the sensitivity evaluation (NO, YES)
SENS_REMOVE_SHARP= YES
%
% Viscous numerical method (AVG_GRAD, AVG_GRAD_CORRECTED, GALERKIN)
VISC_NUM_METHOD_ADJ= AVG_GRAD_CORRECTED
%
% Source term numerical method (PIECEWISE_CONSTANT)
SOUR_NUM_METHOD_ADJ= PIECEWISE_CONSTANT
%
% Time discretization (RUNGE-KUTTA_EXPLICIT, EULER_IMPLICIT)
TIME_DISCRE_ADJ= EULER_IMPLICIT
%
% Adjoint frozen viscosity (NO, YES)
FROZEN_VISC= YES
%
% --------------------------- PARTITIONING STRATEGY ---------------------------%
% Write a paraview file for each partition (NO, YES)
VISUALIZE_PART= NO

% ----------------------- GEOMETRY EVALUATION PARAMETERS ----------------------%
%
% Geometrical evaluation mode (FUNCTION, GRADIENT)
GEO_MODE= FUNCTION

% ------------------------- GRID ADAPTATION STRATEGY --------------------------%
%
% Percentage of new elements (% of the original number of elements)
NEW_ELEMS= 15
%
% Kind of grid adaptation (NONE, FULL, FULL_FLOW, GRAD_FLOW, FULL_ADJOINT,
%                          GRAD_ADJOINT, GRAD_FLOW_ADJ, ROBUST,
%                          FULL_LINEAR, COMPUTABLE, COMPUTABLE_ROBUST,
%                          REMAINING, WAKE, HORIZONTAL_PLANE)
KIND_ADAPT= FULL_FLOW
%
% Scale factor for the dual volume
DUALVOL_POWER= 0.5
%
% Use analytical definition for surfaces (NONE, NACA0012_airfoil, BIPARABOLIC,
%                                        NACA4412_airfoil, CYLINDER)
ANALYTICAL_SURFDEF= NACA0012_airfoil
%
% Before each computation do an implicit smoothing of the nodes coord (NO, YES)
SMOOTH_GEOMETRY= YES

% ------------------------ GRID DEFORMATION PARAMETERS ------------------------%
% Kind of deformation (NO_DEFORMATION, HICKS_HENNE, HICKS_HENNE_NORMAL, PARABOLIC,
%                      HICKS_HENNE_SHOCK, NACA_4DIGITS, DISPLACEMENT, ROTATION,
%                      FFD_CONTROL_POINT, FFD_DIHEDRAL_ANGLE, FFD_TWIST_ANGLE,
%                      FFD_ROTATION)
DV_KIND= HICKS_HENNE
%
% Marker of the surface in which we are going apply the shape deformation
DV_MARKER= ( airfoil )
%
% Parameters of the shape deformation
%        - HICKS_HENNE_FAMILY ( Lower(0)/Upper(1) side, x_Loc )
%        - NACA_4DIGITS ( 1st digit, 2nd digit, 3rd and 4th digit )
%        - PARABOLIC ( 1st digit, 2nd and 3rd digit )
%        - DISPLACEMENT ( x_Disp, y_Disp, z_Disp )
%        - ROTATION ( x_Orig, y_Orig, z_Orig, x_End, y_End, z_End )
DV_PARAM= ( 1, 0.5 )
%
% Old value of the deformation for incremental deformations
DV_VALUE= 0.05
%
% Grid deformation technique (SPRING, TORSIONAL_SPRING, ALGEBRAIC)
GRID_DEFORM_METHOD= FEA
%
% Visualize the deformation (NO, YES)
VISUALIZE_DEFORMATION= YES

% --------------------------- CONVERGENCE PARAMETERS --------------------------%
% Convergence criteria (CAUCHY, RESIDUAL)
%
CONV_CRITERIA= RESIDUAL
%
% Residual reduction (order of magnitude with respect to the initial value)
RESIDUAL_REDUCTION= 8
%
% Min value of the residual (log10 of the residual)
RESIDUAL_MINVAL= -9
%
% Start Cauchy criteria at iteration number
STARTCONV_ITER= 10
%
% Number of elements to apply the criteria
CAUCHY_ELEMS= 100
%
% Epsilon to control the series convergence
CAUCHY_EPS= 1E-6
%
% Function to apply the criteria (LIFT, DRAG, SENS_GEOMETRY, SENS_MACH,
%                                DELTA_LIFT, DELTA_DRAG)
CAUCHY_FUNC_FLOW= DRAG
CAUCHY_FUNC_ADJ= SENS_GEOMETRY
%
% Epsilon for full multigrid method evaluation
FULLMG_CAUCHY_EPS= 1E-3

% ------------------------- INPUT/OUTPUT INFORMATION --------------------------%
% Mesh input file
MESH_FILENAME= airfoilPlateLarge184_2per.su2
%
% Mesh input file format (SU2, CGNS, NETCDF_ASCII)
MESH_FORMAT= SU2
%
% Convert a CGNS mesh to SU2 format (YES, NO)
CGNS_TO_SU2= NO
%
% Mesh output file
MESH_OUT_FILENAME= mesh_out.su2
%
% Restart flow input file
SOLUTION_FLOW_FILENAME= solution_flow.dat
%
% Restart adjoint input file
SOLUTION_ADJ_FILENAME= solution_adj.dat
%
% Output file format (PARAVIEW, TECPLOT)
OUTPUT_FORMAT= PARAVIEW
%
% Output file convergence history (w/o extension)
CONV_FILENAME= history
%
% Output file restart flow
RESTART_FLOW_FILENAME= restart_flow.dat
%
% Output file restart adjoint
RESTART_ADJ_FILENAME= restart_adj.dat
%
% Output file flow (w/o extension) variables
VOLUME_FLOW_FILENAME= flow
%
% Output file adjoint (w/o extension) variables
VOLUME_ADJ_FILENAME= adjoint
%
% Output Objective function gradient (using continuous adjoint)
GRAD_OBJFUNC_FILENAME= of_grad.dat
%
% Output file surface flow coefficient (w/o extension)
SURFACE_FLOW_FILENAME= surface_flow
%
% Output file surface adjoint coefficient (w/o extension)
SURFACE_ADJ_FILENAME= surface_adjoint
%
% Writing solution file frequency
WRT_SOL_FREQ= 500
%
% Writing solution file frequency for physical time steps (dual time)
WRT_SOL_FREQ_DUALTIME= 1
%
% Writing convergence history frequency
WRT_CON_FREQ= 10
%
% Writing convergence history frequency (dual time, only written to screen)
WRT_CON_FREQ_DUALTIME= 10
%
% Writing linear solver history frequency
WRT_LIN_CON_FREQ= 1
%
% Output rind layers in the solution files
WRT_HALO= NO
% --------------------- OPTIMAL SHAPE DESIGN DEFINITION -----------------------%
% Available flow based objective functions or constraint functions
%    DRAG, LIFT, SIDEFORCE, EFFICIENCY,
%    FORCE_X, FORCE_Y, FORCE_Z,
%    MOMENT_X, MOMENT_Y, MOMENT_Z,
%    THRUST, TORQUE, FIGURE_OF_MERIT,
%    EQUIVALENT_AREA, NEARFIELD_PRESSURE,
%    FREE_SURFACE
%
% Available geometrical based objective functions or constraint functions
%    MAX_THICKNESS, 1/4_THICKNESS, 1/2_THICKNESS, 3/4_THICKNESS, AREA, AOA, CHORD,
%    MAX_THICKNESS_SEC1, MAX_THICKNESS_SEC2, MAX_THICKNESS_SEC3, MAX_THICKNESS_SEC4, MAX_THICKNESS_SEC5,
%    1/4_THICKNESS_SEC1, 1/4_THICKNESS_SEC2, 1/4_THICKNESS_SEC3, 1/4_THICKNESS_SEC4, 1/4_THICKNESS_SEC5,
%    1/2_THICKNESS_SEC1, 1/2_THICKNESS_SEC2, 1/2_THICKNESS_SEC3, 1/2_THICKNESS_SEC4, 1/2_THICKNESS_SEC5,
%    3/4_THICKNESS_SEC1, 3/4_THICKNESS_SEC2, 3/4_THICKNESS_SEC3, 3/4_THICKNESS_SEC4, 3/4_THICKNESS_SEC5,
%    AREA_SEC1, AREA_SEC2, AREA_SEC3, AREA_SEC4, AREA_SEC5,
%    AOA_SEC1, AOA_SEC2, AOA_SEC3, AOA_SEC4, AOA_SEC5,
%    CHORD_SEC1, CHORD_SEC2, CHORD_SEC3, CHORD_SEC4, CHORD_SEC5
%
% Available design variables
%    HICKS_HENNE        (  1, Scale | Mark. List | Lower(0)/Upper(1) side, x_Loc )
%    COSINE_BUMP        (  2, Scale | Mark. List | Lower(0)/Upper(1) side, x_Loc, x_Size )
%    SPHERICAL                (  3, Scale | Mark. List | ControlPoint_Index, Theta_Disp, R_Disp )
%    NACA_4DIGITS        (  4, Scale | Mark. List |  1st digit, 2nd digit, 3rd and 4th digit )
%    DISPLACEMENT        (  5, Scale | Mark. List | x_Disp, y_Disp, z_Disp )
%    ROTATION                (  6, Scale | Mark. List | x_Axis, y_Axis, z_Axis, x_Turn, y_Turn, z_Turn )
%    FFD_CONTROL_POINT        (  7, Scale | Mark. List | Chunk, i_Ind, j_Ind, k_Ind, x_Mov, y_Mov, z_Mov )
%    FFD_DIHEDRAL_ANGLE        (  8, Scale | Mark. List | Chunk, x_Orig, y_Orig, z_Orig, x_End, y_End, z_End )
%    FFD_TWIST_ANGLE        (  9, Scale | Mark. List | Chunk, x_Orig, y_Orig, z_Orig, x_End, y_End, z_End )
%    FFD_ROTATION        ( 10, Scale | Mark. List | Chunk, x_Orig, y_Orig, z_Orig, x_End, y_End, z_End )
%    FFD_CAMBER        ( 11, Scale | Mark. List | Chunk, i_Ind, j_Ind )
%    FFD_THICKNESS        ( 12, Scale | Mark. List | Chunk, i_Ind, j_Ind )
%    FFD_VOLUME        ( 13, Scale | Mark. List | Chunk, i_Ind, j_Ind )
%    FOURIER                ( 14, Scale | Mark. List | Lower(0)/Upper(1) side, index, cos(0)/sin(1) )
%
% Optimization objective function with scaling factor
% ex= Objective * Scale
OPT_OBJECTIVE= DRAG * 0.001
%
% Optimization constraint functions with scaling factors, separated by semicolons
% ex= (Objective = Value ) * Scale, use '>','<','='
OPT_CONSTRAINT= ( MAX_THICKNESS > 0.08 ) * 0.001
%
% Optimization design variables, separated by semicolons
DEFINITION_DV= ( 1, 1.0 | airfoil | 0, 0.05 ); ( 1, 1.0 | airfoil | 0, 0.10 ); ( 1, 1.0 | airfoil | 0, 0.15 ); ( 1, 1.0 | airfoil | 0, 0.20 ); ( 1, 1.0 | airfoil | 0, 0.25 ); ( 1, 1.0 | airfoil | 0, 0.30 ); ( 1, 1.0 | airfoil | 0, 0.35 ); ( 1, 1.0 | airfoil | 0, 0.40 ); ( 1, 1.0 | airfoil | 0, 0.45 ); ( 1, 1.0 | airfoil | 0, 0.50 ); ( 1, 1.0 | airfoil | 0, 0.55 ); ( 1, 1.0 | airfoil | 0, 0.60 ); ( 1, 1.0 | airfoil | 0, 0.65 ); ( 1, 1.0 | airfoil | 0, 0.70 ); ( 1, 1.0 | airfoil | 0, 0.75 ); ( 1, 1.0 | airfoil | 0, 0.80 ); ( 1, 1.0 | airfoil | 0, 0.85 ); ( 1, 1.0 | airfoil | 0, 0.90 ); ( 1, 1.0 | airfoil | 0, 0.95 ); ( 1, 1.0 | airfoil | 1, 0.05 ); ( 1, 1.0 | airfoil | 1, 0.10 ); ( 1, 1.0 | airfoil | 1, 0.15 ); ( 1, 1.0 | airfoil | 1, 0.20 ); ( 1, 1.0 | airfoil | 1, 0.25 ); ( 1, 1.0 | airfoil | 1, 0.30 ); ( 1, 1.0 | airfoil | 1, 0.35 ); ( 1, 1.0 | airfoil | 1, 0.40 ); ( 1, 1.0 | airfoil | 1, 0.45 ); ( 1, 1.0 | airfoil | 1, 0.50 ); ( 1, 1.0 | airfoil | 1, 0.55 ); ( 1, 1.0 | airfoil | 1, 0.60 ); ( 1, 1.0 | airfoil | 1, 0.65 ); ( 1, 1.0 | airfoil | 1, 0.70 ); ( 1, 1.0 | airfoil | 1, 0.75 ); ( 1, 1.0 | airfoil | 1, 0.80 ); ( 1, 1.0 | airfoil | 1, 0.85 ); ( 1, 1.0 | airfoil | 1, 0.90 ); ( 1, 1.0 | airfoil | 1, 0.95 )


fpalacios April 18, 2014 09:25

Quote:

Originally Posted by mechy (Post 486627)
Hi all

I want to simulate an airfoil with a small flap at its end. the FLUENT and OpenFoam give similar steady results and in their results the Drag coefficient reaches a constant value. but in the SU2 the Drag coefficient has an oscillation about the OpenFoam result. how I can remove this oscillation and get a steady results from SU2 ?
the config file is attached.


Code:


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                              %
% Stanford University unstructured (SU2) configuration file                    %
% Case description: Transonic inviscid flow around a NACA0012 airfoil          %
% Author: Thomas D. Economon                                                  %
% Institution: Stanford University                                            %
% Date: 2012.10.07                                                            %
% File Version 1.0.12 January 5th, 2012                                        %
%                                                                              %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% ------------- DIRECT, ADJOINT, AND LINEARIZED PROBLEM DEFINITION ------------%
%
% Physical governing equations (POTENTIAL_FLOW, EULER, NAVIER_STOKES,
%                              MULTI_SPECIES_NAVIER_STOKES, TWO_PHASE_FLOW,
%                              COMBUSTION)
PHYSICAL_PROBLEM= NAVIER_STOKES
%
% Mathematical problem (DIRECT, ADJOINT, LINEARIZED, ONE_SHOT_ADJOINT)
MATH_PROBLEM= DIRECT
%
% If Navier-Stokes, kind of turbulent model (NONE, SA)
KIND_TURB_MODEL= SA
%
% Restart solution (NO, YES)
RESTART_SOL= NO
%
% Console output (VERBOSE, CONCISE, QUIET)
CONSOLE= CONCISE

% ----------- COMPRESSIBLE AND INCOMPRESSIBLE FREE-STREAM DEFINITION ----------%
%
% Mach number (non-dimensional, based on the free-stream values)
MACH_NUMBER= 0.3
%
% Angle of attack (degrees)
AoA=5
%
% Free-stream pressure (101325.0 N/m^2 by default, only Euler flows) 
FREESTREAM_PRESSURE= 101325.0
%
% Free-stream temperature (273.15 K by default)
FREESTREAM_TEMPERATURE= 273.15
%
% Reynolds number (non-dimensional, based on the free-stream values)
REYNOLDS_NUMBER= 7.16E6
%
% Reynolds length (1 m by default)
REYNOLDS_LENGTH= 1.0
%
% Free-stream Turbulence Intensity
FREESTREAM_TURBULENCEINTENSITY = 0.01
%
% Free-stream Turbulent to Laminar viscosity ratio
FREESTREAM_TURB2LAMVISCRATIO = 2.0

% -------------- COMPRESSIBLE AND INCOMPRESSIBLE FLUID CONSTANTS --------------%
%
% Ratio of specific heats (1.4 (air), only for compressible flows)
GAMMA_VALUE= 1.4
%
% Specific gas constant (287.87 J/kg*K (air), only for compressible flows)
GAS_CONSTANT= 287.87
%
% Laminar Prandtl number (0.72 (air), only for compressible flows)
PRANDTL_LAM= 0.72
%
% Turbulent Prandtl number (0.9 (air), only for compressible flows)
PRANDTL_TURB= 0.9

% ---------------------- REFERENCE VALUE DEFINITION ---------------------------%
%
% Conversion factor for converting the grid to meters
CONVERT_TO_METER= 1.0
%
% Reference origin for moment computation
REF_ORIGIN_MOMENT_X = 0.25
REF_ORIGIN_MOMENT_Y = 0.00
REF_ORIGIN_MOMENT_Z = 0.00
%
% Reference length for pitching, rolling, and yawing non-dimensional moment
REF_LENGTH_MOMENT= 1.0
%
% Reference area for force coefficients (0 implies automatic calculation)
REF_AREA= 1.0
%
% Reference pressure (101325.0 N/m^2 by default)
REF_PRESSURE= 1.0
%
% Reference temperature (273.15 K by default)
REF_TEMPERATURE= 1.0
%
% Reference density (1.2886 Kg/m^3 (air), 998.2 Kg/m^3 (water))
REF_DENSITY= 1.0

% ----------------------- BOUNDARY CONDITION DEFINITION -----------------------%
%
% Marker of the Euler boundary (0 = no marker)
MARKER_HEATFLUX= ( airfoil,0.0,plate,0.0 )
%
% Marker of the far field (0 = no marker)
MARKER_FAR= ( inlet,outlet,farfield )
%
% ------------------------ SURFACES IDENTIFICATION ----------------------------%
%
% Marker of the surface which is going to be plotted or designed
MARKER_PLOTTING= ( airfoil,plate )
%
% Marker of the surface where the functional (Cd, Cl, etc.) will be evaluated
MARKER_MONITORING= ( airfoil,plate )
%
% Marker(s) of the surface where obj. func. (design problem) will be evaluated
MARKER_DESIGNING = ( airfoil )
%
% ------------- COMMON PARAMETERS TO DEFINE THE NUMERICAL METHOD --------------%
%
% Numerical method for spatial gradients (GREEN_GAUSS, WEIGHTED_LEAST_SQUARES)
NUM_METHOD_GRAD= GREEN_GAUSS
%
% Courant-Friedrichs-Lewy condition of the finest grid
CFL_NUMBER= 1.0
%
% CFL ramp (factor, number of iterations, CFL limit)
CFL_RAMP= ( 1.1, 100, 4.0 )
%
% Runge-Kutta alpha coefficients
RK_ALPHA_COEFF= ( 0.66667, 0.66667, 1.000000 )
%
% Number of total iterations
EXT_ITER= 4000
%
% ------------------------ LINEAR SOLVER DEFINITION ---------------------------%
%
% Linear solver for the implicit (or discrete adjoint) formulation (BCGSTAB, FGMRES)
LINEAR_SOLVER= FGMRES
%
% Preconditioner of the Krylov linear solver (JACOBI, LINELET, LU_SGS)
%LINEAR_SOLVER_PREC= LU_SGS
%
% Min error of the linear solver for the implicit formulation
LINEAR_SOLVER_ERROR= 1E-6
%
% Max number of iterations of the linear solver for the implicit formulation
LINEAR_SOLVER_ITER= 30
%
% Relaxation coefficient
%LINEAR_SOLVER_RELAX= 1.0
% -------------------------- MULTIGRID PARAMETERS -----------------------------%
%
% Full Multigrid (NO, YES)
FULLMG= NO
%
% Start up iterations using the fine grid
START_UP_ITER= 0
%
% Multi-Grid Levels (0 = no multi-grid)
MGLEVEL= 0
%
% Multi-Grid Cycle (0 = V cycle, 1 = W Cycle)
MGCYCLE= 1
%
% Reduction factor of the CFL coefficient on the coarse levels
MG_CFL_REDUCTION= 0.9
%
% Maximum number of children in the agglomeration stage
MAX_CHILDREN= 250
%
% Maximum length of an agglomerated element (compared with the domain)
MAX_DIMENSION= 0.1
%
% Multi-Grid PreSmoothing Level
MG_PRE_SMOOTH= ( 1, 2, 3, 3 )
%
% Multi-Grid PostSmoothing Level
MG_POST_SMOOTH= ( 1, 1, 1, 1 )
%
% Jacobi implicit smoothing of the correction
MG_CORRECTION_SMOOTH= ( 1, 1, 1, 1 )
%
% Damping factor for the residual restriction
MG_DAMP_RESTRICTION= 0.9
%
% Damping factor for the correction prolongation
MG_DAMP_PROLONGATION= 0.9

% --------------------- FLOW NUMERICAL METHOD DEFINITION ----------------------%
%
% Convective numerical method (JST, LAX-FRIEDRICH, ROE-1ST_ORDER,
%                              ROE-2ND_ORDER)
%
CONV_NUM_METHOD_FLOW= ROE-2ND_ORDER
%
% Slope limiter (NONE, VENKATAKRISHNAN)
SLOPE_LIMITER_FLOW= VENKATAKRISHNAN
%
% Coefficient for the limiter (smooth regions)
LIMITER_COEFF= 0.1
%
% 1st, 2nd and 4th order artificial dissipation coefficients
AD_COEFF_FLOW= ( 0.15, 0.5, 0.02 )
%
% Viscous numerical method (AVG_GRAD, AVG_GRAD_CORRECTED, GALERKIN)
VISC_NUM_METHOD_FLOW= AVG_GRAD_CORRECTED
%
% Source term numerical method (PIECEWISE_CONSTANT)
SOUR_NUM_METHOD_FLOW= PIECEWISE_CONSTANT
%
% Time discretization (RUNGE-KUTTA_EXPLICIT, EULER_IMPLICIT, EULER_EXPLICIT)
TIME_DISCRE_FLOW= EULER_IMPLICIT

% -------------------- TURBULENT NUMERICAL METHOD DEFINITION ------------------%
%
% Convective numerical method (SCALAR_UPWIND-1ST_ORDER,
%                              SCALAR_UPWIND-2ND_ORDER)
CONV_NUM_METHOD_TURB= SCALAR_UPWIND-1ST_ORDER
%
% Slope limiter (NONE, VENKATAKRISHNAN)
SLOPE_LIMITER_TURB= NONE
%
% Viscous numerical method (AVG_GRAD, AVG_GRAD_CORRECTED)
VISC_NUM_METHOD_TURB= AVG_GRAD_CORRECTED
%
% Source term numerical method (PIECEWISE_CONSTANT)
SOUR_NUM_METHOD_TURB= PIECEWISE_CONSTANT
%
% Time discretization (EULER_IMPLICIT)
TIME_DISCRE_TURB= EULER_IMPLICIT

% ---------------- ADJOINT-FLOW NUMERICAL METHOD DEFINITION -------------------%
% Adjoint problem boundary condition (DRAG, LIFT, SIDEFORCE, MOMENT_X,
%                                    MOMENT_Y, MOMENT_Z, EFFICIENCY,
%                                    EQUIVALENT_AREA, NEARFIELD_PRESSURE,
%                                    FORCE_X, FORCE_Y, FORCE_Z, THRUST,
%                                    TORQUE, FREE_SURFACE)
ADJ_OBJFUNC= DRAG
%
% Convective numerical method (JST, LAX-FRIEDRICH, ROE-1ST_ORDER,
%                              ROE-2ND_ORDER)
CONV_NUM_METHOD_ADJ= JST
%
% Slope limiter (NONE, VENKATAKRISHNAN, SHARP_EDGES)
SLOPE_LIMITER_ADJFLOW= SHARP_EDGES
%
% Coefficient for the sharp edges limiter
SHARP_EDGES_COEFF= 3.0
%
% 1st, 2nd, and 4th order artificial dissipation coefficients
AD_COEFF_ADJ= ( 0.15, 0.0, 0.01 )
%
% Reduction factor of the CFL coefficient in the adjoint problem
ADJ_CFL_REDUCTION= 0.9
%
% Limit value for the adjoint variable
ADJ_LIMIT= 1E6
%
% Remove sharp edges from the sensitivity evaluation (NO, YES)
SENS_REMOVE_SHARP= YES
%
% Viscous numerical method (AVG_GRAD, AVG_GRAD_CORRECTED, GALERKIN)
VISC_NUM_METHOD_ADJ= AVG_GRAD_CORRECTED
%
% Source term numerical method (PIECEWISE_CONSTANT)
SOUR_NUM_METHOD_ADJ= PIECEWISE_CONSTANT
%
% Time discretization (RUNGE-KUTTA_EXPLICIT, EULER_IMPLICIT)
TIME_DISCRE_ADJ= EULER_IMPLICIT
%
% Adjoint frozen viscosity (NO, YES)
FROZEN_VISC= YES
%
% --------------------------- PARTITIONING STRATEGY ---------------------------%
% Write a paraview file for each partition (NO, YES)
VISUALIZE_PART= NO

% ----------------------- GEOMETRY EVALUATION PARAMETERS ----------------------%
%
% Geometrical evaluation mode (FUNCTION, GRADIENT)
GEO_MODE= FUNCTION

% ------------------------- GRID ADAPTATION STRATEGY --------------------------%
%
% Percentage of new elements (% of the original number of elements)
NEW_ELEMS= 15
%
% Kind of grid adaptation (NONE, FULL, FULL_FLOW, GRAD_FLOW, FULL_ADJOINT,
%                          GRAD_ADJOINT, GRAD_FLOW_ADJ, ROBUST,
%                          FULL_LINEAR, COMPUTABLE, COMPUTABLE_ROBUST,
%                          REMAINING, WAKE, HORIZONTAL_PLANE)
KIND_ADAPT= FULL_FLOW
%
% Scale factor for the dual volume
DUALVOL_POWER= 0.5
%
% Use analytical definition for surfaces (NONE, NACA0012_airfoil, BIPARABOLIC,
%                                        NACA4412_airfoil, CYLINDER)
ANALYTICAL_SURFDEF= NACA0012_airfoil
%
% Before each computation do an implicit smoothing of the nodes coord (NO, YES)
SMOOTH_GEOMETRY= YES

% ------------------------ GRID DEFORMATION PARAMETERS ------------------------%
% Kind of deformation (NO_DEFORMATION, HICKS_HENNE, HICKS_HENNE_NORMAL, PARABOLIC,
%                      HICKS_HENNE_SHOCK, NACA_4DIGITS, DISPLACEMENT, ROTATION,
%                      FFD_CONTROL_POINT, FFD_DIHEDRAL_ANGLE, FFD_TWIST_ANGLE,
%                      FFD_ROTATION)
DV_KIND= HICKS_HENNE
%
% Marker of the surface in which we are going apply the shape deformation
DV_MARKER= ( airfoil )
%
% Parameters of the shape deformation
%        - HICKS_HENNE_FAMILY ( Lower(0)/Upper(1) side, x_Loc )
%        - NACA_4DIGITS ( 1st digit, 2nd digit, 3rd and 4th digit )
%        - PARABOLIC ( 1st digit, 2nd and 3rd digit )
%        - DISPLACEMENT ( x_Disp, y_Disp, z_Disp )
%        - ROTATION ( x_Orig, y_Orig, z_Orig, x_End, y_End, z_End )
DV_PARAM= ( 1, 0.5 )
%
% Old value of the deformation for incremental deformations
DV_VALUE= 0.05
%
% Grid deformation technique (SPRING, TORSIONAL_SPRING, ALGEBRAIC)
GRID_DEFORM_METHOD= FEA
%
% Visualize the deformation (NO, YES)
VISUALIZE_DEFORMATION= YES

% --------------------------- CONVERGENCE PARAMETERS --------------------------%
% Convergence criteria (CAUCHY, RESIDUAL)
%
CONV_CRITERIA= RESIDUAL
%
% Residual reduction (order of magnitude with respect to the initial value)
RESIDUAL_REDUCTION= 8
%
% Min value of the residual (log10 of the residual)
RESIDUAL_MINVAL= -9
%
% Start Cauchy criteria at iteration number
STARTCONV_ITER= 10
%
% Number of elements to apply the criteria
CAUCHY_ELEMS= 100
%
% Epsilon to control the series convergence
CAUCHY_EPS= 1E-6
%
% Function to apply the criteria (LIFT, DRAG, SENS_GEOMETRY, SENS_MACH,
%                                DELTA_LIFT, DELTA_DRAG)
CAUCHY_FUNC_FLOW= DRAG
CAUCHY_FUNC_ADJ= SENS_GEOMETRY
%
% Epsilon for full multigrid method evaluation
FULLMG_CAUCHY_EPS= 1E-3

% ------------------------- INPUT/OUTPUT INFORMATION --------------------------%
% Mesh input file
MESH_FILENAME= airfoilPlateLarge184_2per.su2
%
% Mesh input file format (SU2, CGNS, NETCDF_ASCII)
MESH_FORMAT= SU2
%
% Convert a CGNS mesh to SU2 format (YES, NO)
CGNS_TO_SU2= NO
%
% Mesh output file
MESH_OUT_FILENAME= mesh_out.su2
%
% Restart flow input file
SOLUTION_FLOW_FILENAME= solution_flow.dat
%
% Restart adjoint input file
SOLUTION_ADJ_FILENAME= solution_adj.dat
%
% Output file format (PARAVIEW, TECPLOT)
OUTPUT_FORMAT= PARAVIEW
%
% Output file convergence history (w/o extension)
CONV_FILENAME= history
%
% Output file restart flow
RESTART_FLOW_FILENAME= restart_flow.dat
%
% Output file restart adjoint
RESTART_ADJ_FILENAME= restart_adj.dat
%
% Output file flow (w/o extension) variables
VOLUME_FLOW_FILENAME= flow
%
% Output file adjoint (w/o extension) variables
VOLUME_ADJ_FILENAME= adjoint
%
% Output Objective function gradient (using continuous adjoint)
GRAD_OBJFUNC_FILENAME= of_grad.dat
%
% Output file surface flow coefficient (w/o extension)
SURFACE_FLOW_FILENAME= surface_flow
%
% Output file surface adjoint coefficient (w/o extension)
SURFACE_ADJ_FILENAME= surface_adjoint
%
% Writing solution file frequency
WRT_SOL_FREQ= 500
%
% Writing solution file frequency for physical time steps (dual time)
WRT_SOL_FREQ_DUALTIME= 1
%
% Writing convergence history frequency
WRT_CON_FREQ= 10
%
% Writing convergence history frequency (dual time, only written to screen)
WRT_CON_FREQ_DUALTIME= 10
%
% Writing linear solver history frequency
WRT_LIN_CON_FREQ= 1
%
% Output rind layers in the solution files
WRT_HALO= NO
% --------------------- OPTIMAL SHAPE DESIGN DEFINITION -----------------------%
% Available flow based objective functions or constraint functions
%    DRAG, LIFT, SIDEFORCE, EFFICIENCY,
%    FORCE_X, FORCE_Y, FORCE_Z,
%    MOMENT_X, MOMENT_Y, MOMENT_Z,
%    THRUST, TORQUE, FIGURE_OF_MERIT,
%    EQUIVALENT_AREA, NEARFIELD_PRESSURE,
%    FREE_SURFACE
%
% Available geometrical based objective functions or constraint functions
%    MAX_THICKNESS, 1/4_THICKNESS, 1/2_THICKNESS, 3/4_THICKNESS, AREA, AOA, CHORD,
%    MAX_THICKNESS_SEC1, MAX_THICKNESS_SEC2, MAX_THICKNESS_SEC3, MAX_THICKNESS_SEC4, MAX_THICKNESS_SEC5,
%    1/4_THICKNESS_SEC1, 1/4_THICKNESS_SEC2, 1/4_THICKNESS_SEC3, 1/4_THICKNESS_SEC4, 1/4_THICKNESS_SEC5,
%    1/2_THICKNESS_SEC1, 1/2_THICKNESS_SEC2, 1/2_THICKNESS_SEC3, 1/2_THICKNESS_SEC4, 1/2_THICKNESS_SEC5,
%    3/4_THICKNESS_SEC1, 3/4_THICKNESS_SEC2, 3/4_THICKNESS_SEC3, 3/4_THICKNESS_SEC4, 3/4_THICKNESS_SEC5,
%    AREA_SEC1, AREA_SEC2, AREA_SEC3, AREA_SEC4, AREA_SEC5,
%    AOA_SEC1, AOA_SEC2, AOA_SEC3, AOA_SEC4, AOA_SEC5,
%    CHORD_SEC1, CHORD_SEC2, CHORD_SEC3, CHORD_SEC4, CHORD_SEC5
%
% Available design variables
%    HICKS_HENNE        (  1, Scale | Mark. List | Lower(0)/Upper(1) side, x_Loc )
%    COSINE_BUMP        (  2, Scale | Mark. List | Lower(0)/Upper(1) side, x_Loc, x_Size )
%    SPHERICAL                (  3, Scale | Mark. List | ControlPoint_Index, Theta_Disp, R_Disp )
%    NACA_4DIGITS        (  4, Scale | Mark. List |  1st digit, 2nd digit, 3rd and 4th digit )
%    DISPLACEMENT        (  5, Scale | Mark. List | x_Disp, y_Disp, z_Disp )
%    ROTATION                (  6, Scale | Mark. List | x_Axis, y_Axis, z_Axis, x_Turn, y_Turn, z_Turn )
%    FFD_CONTROL_POINT        (  7, Scale | Mark. List | Chunk, i_Ind, j_Ind, k_Ind, x_Mov, y_Mov, z_Mov )
%    FFD_DIHEDRAL_ANGLE        (  8, Scale | Mark. List | Chunk, x_Orig, y_Orig, z_Orig, x_End, y_End, z_End )
%    FFD_TWIST_ANGLE        (  9, Scale | Mark. List | Chunk, x_Orig, y_Orig, z_Orig, x_End, y_End, z_End )
%    FFD_ROTATION        ( 10, Scale | Mark. List | Chunk, x_Orig, y_Orig, z_Orig, x_End, y_End, z_End )
%    FFD_CAMBER        ( 11, Scale | Mark. List | Chunk, i_Ind, j_Ind )
%    FFD_THICKNESS        ( 12, Scale | Mark. List | Chunk, i_Ind, j_Ind )
%    FFD_VOLUME        ( 13, Scale | Mark. List | Chunk, i_Ind, j_Ind )
%    FOURIER                ( 14, Scale | Mark. List | Lower(0)/Upper(1) side, index, cos(0)/sin(1) )
%
% Optimization objective function with scaling factor
% ex= Objective * Scale
OPT_OBJECTIVE= DRAG * 0.001
%
% Optimization constraint functions with scaling factors, separated by semicolons
% ex= (Objective = Value ) * Scale, use '>','<','='
OPT_CONSTRAINT= ( MAX_THICKNESS > 0.08 ) * 0.001
%
% Optimization design variables, separated by semicolons
DEFINITION_DV= ( 1, 1.0 | airfoil | 0, 0.05 ); ( 1, 1.0 | airfoil | 0, 0.10 ); ( 1, 1.0 | airfoil | 0, 0.15 ); ( 1, 1.0 | airfoil | 0, 0.20 ); ( 1, 1.0 | airfoil | 0, 0.25 ); ( 1, 1.0 | airfoil | 0, 0.30 ); ( 1, 1.0 | airfoil | 0, 0.35 ); ( 1, 1.0 | airfoil | 0, 0.40 ); ( 1, 1.0 | airfoil | 0, 0.45 ); ( 1, 1.0 | airfoil | 0, 0.50 ); ( 1, 1.0 | airfoil | 0, 0.55 ); ( 1, 1.0 | airfoil | 0, 0.60 ); ( 1, 1.0 | airfoil | 0, 0.65 ); ( 1, 1.0 | airfoil | 0, 0.70 ); ( 1, 1.0 | airfoil | 0, 0.75 ); ( 1, 1.0 | airfoil | 0, 0.80 ); ( 1, 1.0 | airfoil | 0, 0.85 ); ( 1, 1.0 | airfoil | 0, 0.90 ); ( 1, 1.0 | airfoil | 0, 0.95 ); ( 1, 1.0 | airfoil | 1, 0.05 ); ( 1, 1.0 | airfoil | 1, 0.10 ); ( 1, 1.0 | airfoil | 1, 0.15 ); ( 1, 1.0 | airfoil | 1, 0.20 ); ( 1, 1.0 | airfoil | 1, 0.25 ); ( 1, 1.0 | airfoil | 1, 0.30 ); ( 1, 1.0 | airfoil | 1, 0.35 ); ( 1, 1.0 | airfoil | 1, 0.40 ); ( 1, 1.0 | airfoil | 1, 0.45 ); ( 1, 1.0 | airfoil | 1, 0.50 ); ( 1, 1.0 | airfoil | 1, 0.55 ); ( 1, 1.0 | airfoil | 1, 0.60 ); ( 1, 1.0 | airfoil | 1, 0.65 ); ( 1, 1.0 | airfoil | 1, 0.70 ); ( 1, 1.0 | airfoil | 1, 0.75 ); ( 1, 1.0 | airfoil | 1, 0.80 ); ( 1, 1.0 | airfoil | 1, 0.85 ); ( 1, 1.0 | airfoil | 1, 0.90 ); ( 1, 1.0 | airfoil | 1, 0.95 )



Could you please provide more details about the grid and convergence history (some pictures would be great)? Anyway, If I were you I would remove the CFL ramping
CFL_RAMP= ( 1.0, 100, 4.0 )

, and run the problem at a constant CFL 1 (to be conservative), furthermore LINEAR_SOLVER_ITER= 2 is a much better value to reduce the computational time.

It seems that you are using an old version of SU2. If you switch to the latest one (3.1), please remember that the name of some tags in the config file have changed.

Best Regards,

Francisco

mechy April 18, 2014 14:28

3 Attachment(s)
thanks so much for your answer
I have used a structural mesh and I used the version 3 of SU2.
I have attached the drag coefficient and some details.

fpalacios April 20, 2014 19:13

I think it is in the process to converge, as I told you, a constant and conservative value of the CFL would help.

What is the plate marker?

Cheers,
Francisco


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