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A sequel to AUSM: AUSM\(^ +\). (English) Zbl 0870.76049
This paper describes recent progress toward improving the advection upstream splitting method (AUSM). We show that the improved scheme, termed \(\text{AUSM}^+\), features the following properties: (1) exact resolution of one-dimensional contact and shock discontinuities, (2) positivity preserving of scalar quantities such as the density, (3) free of “carbuncle phenomenon,” (4) free of oscillations at the slowly moving shock, (5) algorithmic simplicity, and (6) easy intension to treat other hyperbolic systems.

76M20 Finite difference methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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