Documentation du code de simulation numérique SUNFLUIDH

• 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 : several examples

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"  /                          
                        
                       

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 * Using the namelists “Numerical_Methods” and “HomeData_PoissonSolver” === Using the namelist “Numerical_Methods” only === The 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 / The corresponding new version : &Numerical_Methods NS_NumericalMethod= “BDF2-SchemeO2”, MomentumConvection_Scheme=“Centered-O2-Conservative” , TemperatureAdvection_Scheme=“Centered-O2-Conservative” , Poisson_NumericalMethod=“Home-Multigrid-ConstantMatrixCoef”, 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 /