A multigrid method for steady incompressible Navier–Stokes equations based on partial flux splitting

Abstract

AbstractFlux splitting is applied to the convective part of the steady Navier–Stokes equations for incompressible flow. Partial upwind differences are introduced in the split first‐order part, while central differences are used in the second‐order part. The discrete set of equations obtained is positive, so that it can be solved by collective variants of relaxation methods. The partial upwinding is optimized in the same way as for a scalar convection–diffusion equation, but involving several Peclet numbers. It is shown that with the optimum partial upwinding accurate results can be obtained. A full multigrid method in W‐cycle form, using red–black successive under‐relaxation, injection and bilinear interpolation, is described. The efficiency of this method is demonstrated.