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

  • E. Dick
  • J. Linden
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


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.


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Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • E. Dick
    • 1
  • J. Linden
    • 2
  1. 1.Department of MachineryState University of GhentGentBelgium
  2. 2.Gesellschaft für Mathematik und DatenverarbeitungSt. Augustin-BirlinghovenGermany

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