MULTI-STAGE JACOBI RELAXATION IN MULTIGRID METHODS FOR THE STEADY EULER EQUATIONS

SUMMARY Mulli-stage versions of the Jacobi relaxation methods are developed for use in multigrid methods for the steady Euler equations. The non-linear TVD-discretization, both on structured and unstructured grids, is employed. Different multigrid formulations are compared : the defect correction procedure based on the first order discretization; the mixed discretization formulation with the TVD-operator on the finest grid and a linear operator on the coarser grids; the full second order formulation employing the TVD-operator on all grids. The full second order requires the use of implicit residual weighting. Optimized coefficient sets in the multi-staging are constructed for every formulation. It is shown that the mixed discretization is, in general, the most efficient. The speed of convergence on unstructured grids is much greater than on structured grids.