The Riemann Problem Of A Kind Of Aerodynamic System And The Interaction Between Fundamental Waves

In this paper,the Riemann.problem of.gas dynamics Euler equation with the pres-sure law p=ln p and the interactions of elem.entary wave are studied.First,we analyze the solution of the Riemann problem with initial value being of two piecewise constants.The forward and backward shock waves are obtained by using R,H conditions and entropy inequalities,and the forward rarefaction wave and the backward rarefaction wave are ob-tained by the self-similar transformation.In the meanwhile,the solvability of the problem under various initial value conditions is studied.Then,we study the perturbed Riemann problem of the initial values of the three piecewise constant.The following results are obtained:two shock waves are generated after the interaction of shock waves of different families;a family of shock waves and a family of rarefaction waves are generated after the interaction between shock waves of same family;and after the interaction of the shock waves and the rarefaction waves of same family,the shock waves and the rarefaction waves weaken each other,and the criterion of whether the shock waves can completely eliminat.e the rarefaction wavesis clarified;after the interaction of shock wave and the rarefaction wave of different families will completely penetrate each other,and then produce new shock wave and rarefaction wave.