The Research On Riemann Solutions Of Euler System With Chaplygin,generalized Chaplygin And Modified Chaplygin Gas Equations

In this paper,firstly,we considered the comparison of Riemann solutions between Chaplygin and generalized Chaplygin gas Euler equations.Secondly,the stability of the Riemann solutions for Cha.plygin gas Euler equations with a source term are present-ed.Thirdly,we focused on the vanishing pressure limits of Riemann solutions to modified Chaplygin gas Euler equat,ions with a source term.Different from the homogeneous Chap-lygin gas Euler equations,the Riemann solutions of inhomogeneous modified Chaplygin gas Euler equations are no longer self-similar.In the first chapter,we introduced the research background and st,atus of this paper.Meanwhile,the context and structure of this paper will be presented.In the second chapter,we considered the comparison of Riemann solutions for Chaply-gin and generalized Chaplygin gas Euler equations.The Riemann solut,ions for Chaplygin gas Euler equations consist of J+ J and delta shock wave.While,the Riemann solutions of generalized Chaplygin gas Euler equations are made up of R+R、R+S、S+R、S+S and delta shock wave.By the characteristic analxysis and the phase plane analysis,when a→1-we conclude that the Riemann solutions for generalized Chaplygin gas Euler equat,ions turn into the Riemann solutions of Cha.plygin gas Euler equations.In the third cha.pter,we are concentrated on the stability of Riemann solutions for Chaplygin gas Euler equations with a source term.It is distinct from the homogeneous Chaplygin gas Euler equations that the Riemann solutions for inhomogeneous Euler e-quations are no longer self-similar.Meanwhile,we find that the Riemann solutions for Chaplygin gas equations with a coulomb-like friction term are stable as the parameter ε-tends to zero even in the density tends to infinity.In the fourth chapter,we investigated the vanishing pressure limits of Riemann solu-tions to modified Chaplygin gas Euler equations with a source term.Due to the influence of source term,the Riemann solutions of inhomogeneous modified Chaplygin gas Euler equat,ions are no longer self-similar.With the method of speed transformation,the inho-mogeneous modified Chaplygin gas Euler equations turn into conservation laws.In the way of characteristic analysis and phase plane analysis,we studied the delta shock wave and vacuum phenomenon.As the pressure vanishes,we found that the Riemann solutions of inhomogeneous modified Chaplygin gas Euler equations converge to Riemann solutions of pressureless Euler system with a source term.