We remind the user the equations are solved with a projection method. The numerical methods used in the code SUNFLUIDH are commented in the documents for the full version or documents for the educative version.
For solving the conservation equations for velocity and temperature, we choose a 2nd order scheme in space and time.
The Poisson's equation is solved a Successive Over-Relaxation method coupled with a nV-cycle multigrid method for accelerating the convergence. As the flow is incompressible, a solver version with constant coefficient matrix can be selected.
The data setup is made with the following namelists :
&Numerical_Methods NS_NumericalMethod= "BDF2-SchemeO2" , !--- BDF2 + 2nd order centered scheme MomentumConvection_Scheme="Centered-O2-Conservative" , !--- conservative form for solving the velocity (momentum) equation TemperatureAdvection_Scheme="Centered-O2-Conservative" , !--- conservative form for solving the temperature (enthalpy) equation Poisson_NumericalMethod="Home-SORMultigrid-ConstantMatrixCoef" / !--- SOR + multigrid method (homemade release) for solving the Poisson's equation with constant coefficient matrix
As the used solver is a “homemade” release (directly implemented in the code SUNFLUIDH without invoking any external scientific library), the parameters of the SOR + multigrid method are set in the namelist
&HomeData_PoissonSolver SolverName="SOR-Redblack",!--- Successive Over-Relaxation (SOR) method based on the red-black algorithm Relaxation_Coefficient= 1.7 , !--- Relaxation coefficient of the SOR method ( 1 <= Relaxation_Coefficient < 2) Number_max_Grid= 5, !--- Number of grid levels Number_max_Cycle= 10, !--- Number of multigrid cycles Number_Iteration= 0, !--- Maximum number of SOR iterations method applied for any grid level, if 0 (or removed) the 3 next data are considered Number_Iteration_FineToCoarseGrid= 3, !--- number of SOR iterations applied on any grid level during the restriction step (before the coarsest grid computation) Number_Iteration_CoarseToFineGrid= 15, !--- number of SOR iterations applied on any grid level during the prolongation step (after the Coarsest grid computation) Number_Iteration_CoarsestGrid= 15 , !--- number of SOR iterations applied on the coarsest grid Convergence_Criterion= 1.D-08 / !--- convergence tolerance on the residu of the Poisson's equation