Evaluation of euler fluxes for hypersonic flow computations

Abstract

Shock-capturing finite volume schemes often give rise to anomalous results in hypersonic flow. We present a wide-ranging survey of numerical experiments from 12 different flux functions in one- and two-dimensional contexts. Included is a recently developed function that satisfies the second law of thermodynamics. It is found here that there are at least two kinds of shock instabilities: one is one-dimensional and the other is multidimensional. According to the results, the former does not appear if a flux function satisfies the second law of thermodynamics, and the latter is suppressed by an additional dissipation with a multidimensional character. However, such dissipation has no effect on the one-dimensional mode. Among the flux functions investigated, no universally stable schemes are found that are free from both one- and multidimensional shock instabilities. The appearance of these instabilities depends on the relative positioning of the shock on the grid. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.