A stabilized finite element formulation to solve high and low speed flows

Abstract

AbstractIt is well known that numerical methods designed to solve the compressible Euler equations, when written in terms of conservation variables behave poorly in the incompressible limit, that is, when density variations are negligible. However, a change to pressure based variables seem to, partly, eliminate the problem by making the Jacobian matrices fully invertible whatever the flow regime may be. Despite this apparent benefit, the stabilization matrix plus discontinuity capturing operator (for the compressible regime) still need attention, since they tend to be ill behaved for either conservation or pressure variables. In this paper, we introduce a simple way of balancing two stabilizing matrices, one of them suitable for low Mach flows and the other one for supersonic flows, so that a wide range of flow regimes are covered with only one formulation. Comparison between conservation and pressure variables is made and numerical examples are shown to validate the method. Copyright © 2005 John Wiley & Sons, Ltd.