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

[[new_numerical_methods_setup_namelist |Click here to come back to the previous page]]

==== Context : Heat driven incompressible flow ====
<WRAP info>
   * 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
</WRAP>

==== 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 ====                         

<WRAP info>

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 
</WRAP>                         
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 ====                         

<WRAP info>

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 
</WRAP>                         

=== 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 /                         
                          
                         
 [[new_numerical_methods_setup_namelist |Click here to come back to the previous page]]