The limiting behavior of the Riemann solutions of non-isentropic modified Chaplygin gas dynamics

Abstract

In this article, we construct the Riemann solutions of the compressible Euler equations in non-isentropic modified Chaplygin gas. In order to compare the Riemann solutions of modified and pure Chaplygin gas, we extend the solvable region of the Riemann solution of the pure Chaplygin gas state and discover the formation of the δ-shock waves. By studying the limiting behavior, we find that the limit of the Riemann solutions of modified Chaplygin gas is the same as pure Chaplygin gas including the δ-shock waves. Finally, we perform some numerical simulations to verify the theoretical analysis.