NUMERICAL-SOLUTION OF THE RIEMANN PROBLEM FOR 2-DIMENSIONAL GAS-DYNAMICS

The Riemann problem for two-dimensional gas dynamics with isentropic o r polytropic gas is considered. The initial data is constant in each q uadrant and chosen so that only a rarefaction wave, shock wave, or sli p line connects two neighboring constant initial states. With this res triction sixteen (respectively, fifteen) genuinely different wave comb inations for isentropic (respectively, polytropic) gas exist. For each configuration the numerical solution is analyzed and illustrated by c ontour plots. Additionally, the required relations for the initial dat a and the symmetry properties of the solutions are given. The chosen c alculations correspond closely to the cases studied by T. Zhang and Y. Zheng [SIAM J. Math.Anal., 21 (1990), pp. 593-630], so that the analy tical theory can be directly compared to our numerical study.