General limiting behavior of Riemann solutions to the non-isentropic Euler equations for modified Chaplygin gas

Abstract

In this paper, the authors investigate the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas, which are the set of all rarefaction waves, shock waves, and contact discontinuity. For these Riemann solutions, the authors further consider their limiting behavior. In the process of analyzing the limiting behavior, the authors found that the delta shock wave is contained in the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas. Consequently, up to some appropriate conditions, there is unidirectional transformation from non-isentropic Euler equations for the modified Chaplygin gas to Chaplygin gas. On the basis of numerical simulations, the authors verified the reasonability of the theoretical analysis.