Limit Behavior Of Riemann Solutions To The Nonisentropic Magnetogasdynamics

Nonisentropic magnetogasdynamics can be used to model the motion of compressible fluids with transverse magnetic fields under nonisentropic situations.This thesis studies the one-dimensional nonisentropic magnetogasdynamics in Eulerian coordiantes.Firstly,the Riemann problem of the nonisentropic magnetogasdynamics is solved.Secondly,the limit behavior of Riermann solutions is studied when the pressure and magnetic field vanish.The first chapter introduces the research status of nonisentropic magnetogasdynamics and zero-pressure gas dynamics,and briefly summarizes the main research content of this thesis.The second chapter introduces the ?-shock solution,and vacuum solution of the zero-pressure gas dynamics with total internal energy.An obvious feature is that the density and total internal energy simultaneously develop into ?-measure.The third chapter studies the limit behavior of Riemann solutions of the nonisen-tropic magnetogasdynamics when both the pressure and magnetic field vanish.First,the dependence of Riemann solutions of the nonisentropic magnetogasdynamics on the parameters is discussed,and the corresponding Riemann problem is solved by using the parametric explicit formulas of the elementary wave curves.Then,it is proved that when the pressure and magnetic field vanish,any Riemann solution including two shocks waves and a possibly one-contact-discontinuity to the nonisentropic magnetogasdynamics tends to a ?-shock solution to the zero-pressure gas dynamics with total internal energy.At the same time,the intermediate density and the intermediate total internal energy between the two shocks converge to the sum of a step function and a weighted ?-measure function.In addition,any Riemann solution including two rarefaction waves and a possibly two-contact-discontinuity to the nonisentropic magnetogasdynamics tends to a two-contact-discontinuity solution to the zero-pressure gas dy-namics with total internal energy,and the intermediate density as well as the intermediate total internal energy between the two rarefaction waves tend to the vacuum state.The fourth chapter is numerical calculation,which simulates the forming process of?-shocks of the intermediate density and the intermediate total energy between the two shocks and a possibly one-contact-discontinuity,and the forming process of vacuum states of the intermediate density and the intermediate total energy between the two rarefac-tion waves and a possibly two-contact-discontinuity.It is observed that the numerical simulation results are consistent with the theoretical analysis in the third chapter.