A SEQUEL TO AUSM - AUSM(+)

While enjoying demonstrated improvement in accuracy, efficiency, and r obustness over existing schemes, the advection upstream splitting meth od (AUSM) has been found to have deficiencies in some cases. This pape r describes recent progress toward improving the AUSM. We show that th e improved scheme, termed AUSM(+), features the following properties: (1) exact resolution of 1D contact and shock discontinuities, (2) posi tivity preserving of scalar quantity such as the density, (3) free of ''carbuncle phenomenon,'' (4) free of oscillations at the slowly movin g shock, (5) algorithmic simplicity, and (6) easy entension to treat o ther hyperbolic systems. In this paper, we lay out a general construct ion for the AUSM(+) scheme and prove its heretofore unreported mathema tical properties. Especially a CFL-like condition for positivity-prese rving property is derived. This positivity-preserving proves to be tig htly related to the capability of calculating strong rarefaction and n ear 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. (C) 1996 Academic Press, Inc.