Shock stability of a combined method of advection upstream splitting and time-accurate momentum interpolation

Abstract

A combined finite volume method of advection upstream splitting (AUSM) and time-accurate momentum interpolation (TAMI), which we developed earlier for flows with very low Mach number, especially for simulation of acoustic wave propagation, is extended by shock-stability terms. The combined method, which we call AUSM-TAMI, is suitable for flows with very low Mach number, thanks to the transporting velocity in the convection part of the flow equations, derived from time-accurate momentum interpolation. The shock-stability terms are velocity difference terms that are added to the pressure force components, made similar to the shock-stability terms of a modern AUSM-method. We show with three test cases, with very different character, two unsteady flows and a steady flow, that the combined method, extended with the shock-stability terms, produces solutions without shock-induced oscillations in flows with high Mach number and strong shock waves.