A Multigrid Flux-Difference Splitting Method for Steady Incompressible Navier-Stokes Equations

Summary

The steady Navier-Stokes equations in primitive variables are discretized in conservative form by a vertex-centered finite volume method. Flux-difference splitting is applied to the convective part.

In its first order formulation flux-difference splitting leads to a discretization of so-called vector positive type. This allows the use of classical relaxation methods in collective form. An alternating line-Gauss-Seidel relaxation method is chosen here. This relaxation method is used as a smoother in a multigrid method. The components of this multigrid method are: full-approximation scheme with F-cycles, bilinear prolongation, full-weighting for residual restriction and injection of grid functions.

Higher order accuracy is achieved by the Chakravarthy-Osher method. In this approach the first order convective fluxes are modified by adding second order corrections involving flux-limiting. Here, the simple minmod-limiter is chosen. In the multigrid formulation, the second order discrete system is solved by defect correction.

Computational results are shown for the well-known GAMM-backward facing step problem. The relaxation is performed on two blocks.