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A multigrid method for steady incompressible navier‐stokes equations based on flux difference splitting
Author(s) -
Dick E.,
Linden J.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650141104
Subject(s) - multigrid method , discretization , mathematics , flux limiter , finite volume method , navier–stokes equations , mathematical analysis , relaxation (psychology) , finite difference method , finite difference , compressibility , partial differential equation , mechanics , physics , psychology , social psychology
The steady Navier–Stokes equations in primitive variables are discretized in conservative form by a vertex‐centred finite volume method Flux difference splitting is applied to the convective part to obtain an upwind discretization. The diffusive part is discretized in the central way. 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 flux extrapolation 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 and for a channel with a half‐circular obstruction.