On the modelling of compressible inviscid flow problems using AUSM schemes

During last decades, upwind schemes have become a popular method in the field of computational fluid dynamics. Although they are only first order accurate, AUSM (Advection Upstream Splitting Method) schemes proved to be well suited for modelling of compressible flows due to their robustness and ability of capturing shock discontinuities. In this paper, we review the composition of the AUSM flux-vector splitting scheme and its improved version noted AUSM+, proposed by Liou, for the solution of the Euler equations. Mach number splitting functions operating with values from adjacent cells are used to determine numerical convective fluxes and pressure splitting is used for the evaluation of numerical pressure fluxes. Both versions of the AUSM scheme are applied for solving some test problems such as one-dimensional shock tube problem and three-dimensional GAMM channel. Features of the schemes are discussed in comparison with some explicit central schemes of the first order accuracy (Lax-Friedrichs) and of the second order accuracy (MacCormack)