General Limiting Behavior Of Riemann Solutions To The Non-isentropic Euler Equations For Modified Chaplygin Gas And Extended Chaplygin Gas

In this paper,the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas and extended Chaplygin gas are studied,and in the limiting conditions,the Riemann solutions of the two equations are converted into the Riemann solutions of the Chaplygin gas and generalized Chaplygin gas with Dirac shock waves,respectively.In the first chapter,the research status of the non-isentropic Euler equations,various Chaplygin gas models and Dirac shock waves are introduced.The second chapter mainly gives the required conclusion for the following content.The conclusion include the Riemann solutions of the non-isentropic Euler equations of the Chaplygin gas and generalized Chaplygin gas.In chapter 3,the Riemann solutions of the non-isentropic Euler equations for the modified Chaplygin gas is constructed firstly.The Riemann solutions consists of the backward(forward)centered rarefaction waves R_1,3,contact discontinuity J,and the backward(forward)shock waves S(1,3).Then we consider the limiting behavior of the Riemann solutions when the parameter A approaches 0.It is strictly proved that when the condition u--1/?-?u₊+1/?+ holds,the delta shock waves appear in the Riemann solution;when the condition u--1/?-<u₊+1/?+ holds,the Riemann solutions of the non-isentropic Euler equation for the modified Chaplygin gas will converge to three contact discontinuities of the Chaplygin gas.Finally,the numerical simulation in this chapter further verifies the correctness of the theoretical analysis in the previous part.In chapter 4,the Riemann solutions of the non-isentropic Euler equations for extended Chaplygin gas is firstly considered.The Riemann solutions consists of the backward(forward)centered rarefaction waves R'_1,3,contact discontinuity J,and the backward(forward)shock waves S'_1,3.Then,when the parameter A approaches 0,it is found that the Riemann solutions obtained will be transformed into the Riemann solutions of the non-isentropic Euler equations for the generalized Chaplygin gas.Finally,the theoretical results are demonstrated by numerical simulation.