A Sequel to AUSM

While enjoying demonstrated improvement in accuracy, efficiency, and robustness over existing schemes, the advection upstream splitting method (AUSM) has been found to have deficiencies in some cases. This paper describes recent progress toward improving the AUSM. We show that the improved scheme, termed AUSM+, features the following properties: (1) exact resolution of 1D contact and shock discontinuities, (2) positivity preserving of scalar quantity such as the density, (3) free of “carbuncle phenomenon,” (4) free of oscillations at the slowly moving shock, (5) algorithmic simplicity, and (6) easy entension to treat other hyperbolic systems. In this paper, we lay out a general construction for the AUSM+scheme and prove its heretofore unreported mathematical properties. Especially a CFL-like condition for positivity-preserving property is derived. This positivity-preserving proves to be tightly related to the capability of calculating strong rarefaction and near vacuum flows. Finally, results of numerical tests on many problems are given to confirm the capability and improvements on a variety of problems including those failed by other well-known schemes.

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