Artículos de revistas
Performance of geometric multigrid method for coupled two-dimensional systems in CFD
Fecha
2015-05Registro en:
Applied Mathematical Modelling,Amsterdam : Elsevier,v. 39, n. 9, p. 2602-2616, Mai. 2015
0307-904X
10.1016/j.apm.2014.10.067
Autor
Souza, Leandro Franco de
Santiago, C. D.
Marchi, C. H.
Souza, Leandro Franco de
Institución
Resumen
The performance of a geometric multigrid method is analyzed for two-dimensional
Laplace, Navier, Burgers and two formulations of Navier–Stokes (streamfunction–vorticity
and streamfunction–velocity) equations. These equations are discretized with the Finite
Difference Method on uniform grids with numerical approximations of first- and secondorders
of accuracy. The systems of equations are solved with a Modified Strongly Implicit
(MSI) and a Successive Over Relaxation (SOR) solver associated with the multigrid method
with a V-cycle and a Correction Scheme (CS) and a Full Approximation Scheme (FAS). The
effect of the number of inner iterations of the solver, the number of grid levels problems
with grid sizes of 1025 1025 points, the influence of differential equations numbers
and Reynolds number up to 1000 on Central Processing Unit (CPU) time are investigated.
The results show that (1) a solution of two coupled equations (Navier or Burgers) is
obtained with the same efficiency multigrid textbook that occurs in the solution of only
one equation (Laplace), (2) the efficiency of the multigrid method in the solution of two
coupled equations (Navier–Stokes streamfunction–vorticity formulation) or only one equation
(the Navier–Stokes streamfunction–velocity formulation) decreases with increasing
Reynolds numbers, and (3) the poor performance of the multigrid method for solving
the Navier–Stokes seems to be related to the physics of the problem and not to the type
of formulation or coupling between the equations.