A multigrid method for steady incompressible NavierStokes equations based on flux difference splitting
Abstract
The steady NavierStokes equations in primitive variables are discretized in conservative form by a vertexcentered 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 firstorder formulation, flux difference splitting leads to a discretization of socalled vector positive type. This allows the use of classical relaxation methods in collective form. An alternating line GaussSeidel 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 Fcycles, bilinear prolongation, full weighting for residual restriction and injection of grid functions. Higherorder accuracy is achieved by the flux extrapolation method. In this approach the firstorder convective fluxes are modified by adding secondorder corrections involving flux limiting. Here the simple MinMod limiter is chosen. In the multigrid formulation the secondorder discrete system is solved by defect correction. Computational results are shown for the wellknown GAMM backwardfacing step problem and for a channel with a halfcircular obstruction.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 June 1992
 DOI:
 10.1002/fld.1650141104
 Bibcode:
 1992IJNMF..14.1311D
 Keywords:

 Flux Vector Splitting;
 Incompressible Flow;
 Multigrid Methods;
 NavierStokes Equation;
 Steady Flow;
 Computational Fluid Dynamics;
 Computational Geometry;
 Finite Volume Method;
 Fluid Mechanics and Heat Transfer