Concentration and cavitation in the Euler equations for nonisentropic fluids with the flux approximation

Abstract

In this paper, by introducing a two-parameter flux approximation including pressure in the Euler equations for nonisentropic compressible fluids, we analyze the phenomena of concentration and cavitation in Riemann solutions. It is rigorously proved that, as the double parameter flux perturbation vanishes, any Riemann solution containing two shock waves and a possibly one-contact-discontinuity tends to a delta shock solution to the transport equations, and the intermediate density between the two shocks tends to a weighted δ-measure which forms the delta shock wave; any Riemann solution containing two rarefaction waves and a possibly one-contact-discontinuity tends to a two-contact-discontinuity solution to the transport equations, and the nonvacuum intermediate state in between tends to a vacuum state. Some numerical results are also given to present the processes of concentration and cavitation as the flux perturbation decreases.