Two Dimensional Riemann Problem for Gas Dynamics System in Three Pieces

Abstract

The Riemann problem for two-dimensional flow of polytropic gas with three constant initial data is considered. Under the assumption that each interface of initial data outside of the origin projects exactly one planar wave of shock, rarefaction wave or contact discontinuity, it is proved that only two kinds of combinations, JRS and Js, are reasonable. Numerical solutions are obtained by using a nonsplitting second order accurate MmB Scheme, and they efficiently reflect the complicated configurations and the geometric structure of solutions of gas dynamics system.