COMPARISON OF RIEMANN SOLUTIONS TO THE EULER EQUATIONS FOR MODIFIED AND GENERALIZED CHAPLYGIN GAS DYNAMICS

In this article, utilizing the method of characteristic analysis, we construct the Riemann solutions of the Euler equations for the modified and the generalized Chaplygin gas, which contains rarefaction waves, shock waves, contact discontinuities and $ \delta- $ shock waves. For the $ \delta- $ shock waves, we propose generalized Rankine-Hugoniot relation and entropy conditon. Moreover, by studing the limiting behaviour, we find that the Riemann solutions of modified Chaplygin gas is the same as generalized Chaplygin gas including the $ \delta- $shock waves. Moreover, we give some numerical simulations to verify the theoretical analysis.