Sub-shock formation in shock structure of a binary mixture of polyatomic gases

Abstract

The differential system of the field equations of a binary mixture of Eulerian gases is hyperbolic and, according to a general theorem of Boillat and Ruggeri, the shock-structure solution is not always regular and a discontinuous jump (sub-shock) may appear depending on the velocity of the shock wave. In this paper, we give all the necessary conditions for the subshock formation and we identify for prescribed values of the mass ratio of the constituents and degrees of freedom of molecules four regions depending on the concentration and the Mach number in which there may exist the sub-shock for one or both constituents or not. Preliminary numerical tests calculating the shock-structure solution in these regions confirm the qualitative analysis.