Documentation du code de simulation numérique SUNFLUIDH

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Some examples illustrating how to use the relevant namelists to set the numerical methods for solving the equations

Some examples illustrating how to use the relevant namelists to set the numerical methods for solving the equations

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Context : Heat driven incompressible flow

Numerical scheme for solving the governing equations of velocity and temperature
- Time discretization : semi-implicit formulation with the 2nd order Backward Differentiation formula (BDF2)
- Viscous and conduction fluxes (2nd order centered scheme selected by default with BDF2)
- convective flux for momentum equation : 2nd order centered scheme, conservative form
- advective flux for temperature equation : 2nd order centered scheme, conservative form
- Solving Poisson's equation : see the following examples

Example 1 : Partial diagonalization method

Only one namelist is required : “Numerical_Methods”. You first find the old version and then the new one. The both versions are strictly equivalent.
The old version :

    &Numerical_Methods  Numerical_Scheme= 1,
                        Convective_Flux_Discretization_Type            = 1 , 
                        Temperature_Advective_Flux_Discretization_Type = 1 ,  
                        Numerical_Method_Poisson_Equation   = 3    /

The corresponding new version :

  &Numerical_Methods  NS_NumericalMethod= "BDF2-SchemeO2",
                      MomentumConvection_Scheme="Centered-O2-Conservative" , 
                      TemperatureAdvection_Scheme="Centered-O2-Conservative" ,  
                      Poisson_NumericalMethod="Home-PartialDiagonalization"  /

Example 2 : An iterative method coupled with a multigrid procedure using a "in-house" development

Suitable setting :

A SOR solver with a relaxation coefficient of 1.7, using a red-black alogorithm in a MPI-parallel context.
The nV-cycle multigrid procedure is composed of 5 grid levels, with a maximum number of cycles n= 10.
The number of SOR iterations is :
- 5 on the restriction step (going from finnest to the coarsest grid)
- 20 on the coarsest grid
- 15 on the prolongation step (going from coarsest to the finnest grid)
The stopping criterion based on the residu of the computation is 1E-08

As the fluid is incompressible, the matrix coefficients of the Poisson's equation are constant.
As a “homemade” method is used, two ways are possible :

Using the namelist “Numerical_Methods” only (old version).
Using the namelists “Numerical_Methods” and “HomeData_PoissonSolver” (new version)

Using the namelist "Numerical_Methods" only (old version)

               
                        
    &Numerical_Methods  Numerical_Scheme= 1,
                        Convective_Flux_Discretization_Type            = 1 , 
                        Temperature_Advective_Flux_Discretization_Type = 1 , 
                         
                        Numerical_Method_Poisson_Equation   = 1   
                        Iterative_Method_Selection          = 3   ,
                        Number_max_Grid = 5                         ,
                        Number_max_Cycle= 10                      ,
                        Number_Iteration= 15,
                        Number_Iteration_FineToCoarseGrid= 5,
                        Number_Iteration_CoarsestGrid    = 15,
                        Number_Iteration_CoarseToFineGrid= 10,
                        Relaxation_Coefficient           = 1.70 , 
                        Convergence_Criterion            = 1.D-08 /

Using the namelists "Numerical_Methods" and "HomeData_PoissonSolver" (new version)

    &Numerical_Methods  NS_NumericalMethod= "BDF2-SchemeO2",
                        MomentumConvection_Scheme="Centered-O2-Conservative" , 
                        TemperatureAdvection_Scheme="Centered-O2-Conservative" ,  
                        Poisson_NumericalMethod="Home-SORMultigrid-ConstantMatrixCoef"/
                        
    &HomeData_PoissonSolver   SolverName="SOR",
                              Number_max_Grid = 5                         ,
                              Number_max_Cycle= 10                      ,
                              Number_Iteration= 15,
                              Number_Iteration_FineToCoarseGrid= 5,
                              Number_Iteration_CoarsestGrid    = 15,
                              Number_Iteration_CoarseToFineGrid= 10,
                              Relaxation_Coefficient           = 1.70 , 
                              Convergence_Criterion            = 1.D-08 /

Example 3 : An iterative method coupled with a multigrid procedure using the HYPRE library

Suitable setting :

Selection of the PFMG method using a SOR relaxation method for non symmetrical matrix (even though the Poisson's operator could be symmetric in this context)
The number of iterations is :
- The maximum iteration number is 20
- 5 relaxation sweeps before coarse-grid correction
- 10 relaxation sweeps after coarse-grid correction
The tolerance convergence is 1E-08

Using the namelists "Numerical_Methods" and "HypreData_PoissonSolver" (new version only)

               
         
    &Numerical_Methods  NS_NumericalMethod= "BDF2-SchemeO2",
                        MomentumConvection_Scheme="Centered-O2-Conservative" , 
                        TemperatureAdvection_Scheme="Centered-O2-Conservative" ,  
                        Poisson_NumericalMethod="Home-Multigrid-ConstantMatrixCoef"/
                        
    &HypreData_PoissonSolver  SolverName="SOR-Redblack-Nonsym",
                              Number_Iteration                 = 20 ,
                              Number_Iteration_FineToCoarseGrid= 5, 
                              Number_Iteration_CoarseToFineGrid= 10, 
                              Convergence_Criterion            = 1.D-08 /

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