The Limit Of Riemann Solutions And Elementary Wave Interactions For Magnetohydrodynamic Euler Equations

Based on the law of mass conservation,the law of momentum conservation and the law of energy conservation,the magnetic fluid euler's equations are established.The first chapter introduces the research background,current situation,main content and structure of this paper.The second chapter,through the law of conservation of mass and momentum con-servation law to establish MHD euler equations,the first solution of the inhomogeneous generalized Chaplygin gas liquid Riemann solution of euler equations,then by using phase plane analysis and characteristic analysis study pressure and magnetic field disappear and only the magnetic field at the same time limit of Riemann solution,when pressure and magnetic field and disappear from time to tome quality concentration and vacuum phe-nomenon,only when the magnetic field disappeared,only a quality concentration,by using the software of Matlab to equations are numerically simulated to verify the limit of Riemann solution.Third chapter through the law of conservation of mass,momentum conservation law,the law of conservation of energy,the magnetic euler equations in Lagrangian coordinate system and ordered F=p+B2/2? Riemann solution of think about it,so you can put the contact discontinuities in(F,u)planar projection from a straight line to a point,thereby reducing the difficulty of the interaction of the wave,the wave of the interaction of the discussion,has left the centre-right three piece of initial value,and from the middle to consider the interaction of the wave can be divided into eight types,Moreover,the problem of wave interaction is transformed into the problem of Riemann solution.Finally,Matlab software is used to perform numerical simulation on the system of equations to verify the case of wave interaction.