Différences

Ci-dessous, les différences entre deux révisions de la page.

--- sunfluidh:numerical_methods_examples [2017/09/25 15:33] – créée yann
+++ sunfluidh:numerical_methods_examples [2018/12/01 16:43] (Version actuelle) – [Example 2 : An iterative method coupled with a multigrid procedure using a in-house development] yann
@@ Ligne 1: / Ligne 1: @@
 ===== Some examples illustrating how to use the relevant namelists to set the numerical methods for solving the equations =====
-==== Context : Heat driven incompressible flow ====
+[[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)
@@ Ligne 8: / Ligne 10: @@
        * 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**__
+       * Solving Poisson's equation : see the following examples
+</WRAP>
-==== Example 1 : Solving the Poisson's equation by the partial diagonalization method ====
+==== 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.\\
@@ Ligne 28: / Ligne 31: @@
-==== Example 2 : Solving the Poisson's equation by an iterative method coupled with a multigrid procedure ====
+==== 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]]
-                       Iterative_Method_Selection         = 1    ,
-                       Number_max_Grid= 4                         ,
-                       Number_max_Cycle= 10                      ,
-                       Number_Iteration= 15,
-                       Number_Iteration_FineToCoarseGrid= 15,
-                       Number_Iteration_CoarsestGrid= 15,
-                       Number_Iteration_CoarseToFineGrid= 15,
-                       Relaxation_Coefficient              = 1.80 ,
-                       Convergence_Criterion = 1.D-08 /