Optimal Multigrid Method for Inviscid Flows

Abstract

In this paper we describe a novel approach for the solution of in-viscid flow problems both for incompressible and subsonic compressible cases. The approach is based on canonical forms of the equations in which subsystems governed by hyperbolic operators are separated from those governed by elliptic ones. The discretizations as well as the iterative techniques for the different subsystems are inherently different. Hyperbolic parts, which describe in general propagation phenomena, are discretized using upwind schemes and are solved by marching techniques. Elliptic parts, which are directionally unbiased, are discretized using h-elliptic central discretizations and are solved by pointwise relaxations together with coarse grid acceleration. The resulting discretization schemes introduce artificial viscosity only for the hyperbolic parts of the system; thus a smaller total artificial viscosity is used, while the multigrid solvers used are much more efficient. Solutions of the subsonic compressible and incompressible Euler equations are achieved at the same efficiency as the full potential and Poisson equations respectively.

This research was made possible in part by funds granted to the author through a fellowship program sponsored by the Charles H. Revson Foundation and in part by the National Aeronautics and Space Administration under NASA Contract No. NASI-19480 and NAS1-18605 while the author was in residence at ICASE, NASA Langley Research Center, Hampton, Va 23681.