The Riemann Problem Of Gas Dynamics Equations Involving Combustion

This paper mainly study the distribution of wave solutions for Riemann problem of Euler equations in the non-isentropic combustion gas.Firstly,we study the distribution of single wave solutions connecting the left and right states according to Rankine-Hugoniot conditions and Lax conditions.Then,we study the distribution of mixed wave solutions of combustion gas by using the properties of the Hugoniot curve.Finally,we get the distribution of wave solutions for the Riemann problem of Euler equations in the non-isentropic combustion gas.This paper consists of three chapters.In the first chapter,we mainly introduce the research history and current situation of the Riemann problem of the gas dynamic equa-tions,and analyze some concepts of Riemann problem of the conservation law equations of the combustion gas.This chapter also summarizes the research content of this paper.In the second chapter,we study the distribution of single wave solutions connecting left and right states of the Riemann problem in the non-isentropic combustion gas.Firstly,we find the Lax condition that the eigenvalues satisfy through variable substitution,and then find the equivalent forms of the equations satisfying Rankine-Hugoniot condition.Finally,according to the Lax condition and Rankine-Hugoniot condition satisfied by shock and rarefaction waves,the left and right connecting states of shock and rarefaction waves are determined.In the third chapter,we study the distribution of mixed wave solutions of Riemann problem for the non-isentropic combustion gas.Firstly,the properties of Hugoniot curve is analyzed simply,and the conditions of combustion wave solutions are found when the chemical energy difference between left and right states are given.Then,the distribution of the combustion wave solutions are determined according to the pressure relation.Finally,the distribution of Riemann solutions for a complete Euler equations is summarized.