The invariant domain of Riemann solution for 1D non-isentropic gas dynamics equations

Abstract

In this paper, we get the invariant domain of 1D non-isentropic gas dynamics equations. First of all, we construct the elementary waves with the characteristic analysis method. According to the characteristic of elementary waves, we divide the u–p plane into five areas. By analyzing the structure of Riemann solutions in each area, we find a new convex bounded domain where if the Riemann data belong to the domain, then the Riemann solutions also belong to the domain. Moreover, it is used to prove the uniform boundedness of approximate solutions built by the difference scheme, so it is the basis for the Riemann problem to be applied to the Cauchy problem.