Accurate Flux Vector Splitting for Shocks and Shear Layers.

Abstract

The Advection Upstream Splitting Method (AUSM) recently developed by Liou and Steffen is improved towards more accurate predictions of viscous flows. The special merits of AUSM compared to other upwind schemes are the low computational complexity and the low numerical diffusion. However, it is known that the original method also has several deficiencies. It locally produces pressure oscillations in the vicinity of shocks and in cases of adverse grid situations and flow alignment. In this paper a hybrid flux vector splitting scheme is proposed which switches from AUSM to van Leer at shock waves ensuring a sharp and clean resolution of strong shocks. In order to achieve sufficient damping, a modified dissipative term is introduced, which prevents the scheme from being undamped as Mach number approaches zero. Various modifications of the standard MUSCL implementations for second-order accuracy are proposed, which.