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 Liou 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 fix 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.