The Perturbation Riemann Problem For The Isentropic Drift-flux Flow Equations

In this paper,a isentropy-based drift-flux model is presented,and the perturbation Riemann problem with Chaplygin gas and extended Chaplygin gas is respectively taken as the equation of state.Firstly,the characteristics of the Chaplygin gas equation are analyzed to determine the possible wave conditions.Secondly,the interaction of the wave generated by the equation is described in detail by using the method of characteristic lines.On this basis,the Riemann problem of changing the equation of state from Chaplygin gas to extended Chaplygin gas is studied.On this basis,the main content of the article is arranged as follows:The first chapter mainly expounds the research background of drift-flux flow model,the research situation at home and abroad and the main content of this paper.The second chapter mainly introduces the definitions and theorems related to this paper.In chapter three,the perturbation Riemann problem of a simplified isentropy-based drift-flux model of Chaplygin gas is studied and it is found that the Riemann solution consists of a Dirac shock wave or three contact discontinuity.On this basis,specific generalized Rankine-Hugoniot conditions are derived to analytically calculate the intensity and propagation velocity of the Dirac shock wave,and it is strictly proved that the obtained Dirac shock solution satisfies this equation in the sense of the generalized function.In addition,for the Riemann problem with the initial values of three constant states,the interaction of the basic waves that may occur is discussed in detail by using the characteristic line method.In chapter four,the perturbation Riemann problem in an extended Chaplygin gas is studied,and its Riemann solution is composed of Dirac shock waves or a combination of shock waves and rarefaction waves.The phase plane method is used to solve the generation condition of Dirac shock wave.In addition,in the Dirac shock solution,it is found that the Dirac function is superimposed on the density of the gas phase and the liquid phase at the same time,and the generalized Rankine-Hugoniot condition is used to solve the Dirac shock analytically.