A Study of the Numerical Instability of the AUSM Scheme

Abstract

This paper presents a study of the numerical instability of the Advection Upstream Splitting Method (AUSM) for inviscid compressible flow analysis on two-dimensional structured triangular grids. The composition of the AUSM flux-vector splitting scheme for the solution of the Euler equations is reviewed. Mach number splitting functions operating with values from adjacent cells are used to determine numerical convective fluxes, and the pressure splitting is used for the evaluation of numerical pressure fluxes. The scheme is further extended to obtain higher-order spatial and temporal solution accuracy. A computational model for shock wave problems is presented to investigate the numerical stability of the scheme. The performance and efficiency of the AUSM scheme are evaluated by solving three high-speed compressible flow problems.

Keywords: AUSM Scheme; Explicit Scheme; Higher-order Scheme; Numerical Instability.