The Riemann Problem Of Euler Equations In Fluid Mechanics

In this paper,we investigate the analytic and geometric properties of the connections of wave and wave in the solution to the Riemann problem of Euler equations.We study the monotonicity and convexity of these wave curves.After considering the gas combustion,we analyze the connected wave and the geometric properties of the states to the corresponding Riemann problem of Euler equation.This paper is arranged as follows.In the first chapter we mainly introduce the history and development of the Riemann problem of the conservation laws and the main content of this paper.Then we introduce the relevant knowledge of the Riemann problem of conservation system in chapter 2.In chapter 3,we consider the mixed waves of the Riemann problem to the non-isentropic gas dynamic equations.We investigate the properties,such as monotonicity,and convexity of the wave cures connected the left state and the right state according to the mixed Rankine-Hugoniot conditions and the Lax conditions of shock wave.Especially,we give the necessary and sufficient conditions of existence of solutions made up of a mixture of shock waves,contact discontinuities and rarefaction waves.In chapter 4,we investigate the Riemann problem of the non-isentropic gas dynamic Euler equations with combustion.We get the H-curve of the relations of the pressure and the density according to Rankine-Hugoniot conditions.We also investigate the shock and the rarefaction solutions to the Riemann problem of Euler equations with combustion.