An accurate and robust flux splitting scheme for shock and contact discontinuities

A flux splitting scheme (AUSMDV) has been constructed with an aim at removing numerical dissipation of the Van Leer-type flux vector splittings on a contact discontinuity. The obtained scheme is also recognized as an improved advection upstream splitting method (AUSM) by Lieu and Steffen. The proposed scheme has the following favorable properties: accurate and robust resolution for shock and contact (steady and moving) discontinuities; conservation of enthalpy for steady flows; algorithmic simplicity; and easy extension to general conservation laws such as that for chemically reacting flows. A simple shock fix is presented to cure the numerical shock instability associated with the ''carbuncle phenomenon'' and an entropy dr to remove an expansion shock or glitch at the sonic point. Extensive numerical experiments were conducted to validate the proposed scheme for a wide range of problems, and the results are compiled for comparison with several recent upwind methods.