Delta Shocks and Vacuums to the Isentropic Euler Equations with the Flux Perturbation for van der Waals Gas

Abstract

In this paper, we study the isentropic Euler equations with the flux perturbation for van der Waals gas, in which the density has both lower and upper bounds due to the introduction of the flux approximation and the molecular excluded volume. First, we solve the Riemann problem of this system and construct the Riemann solutions. Second, the formation mechanisms of delta shocks and vacuums are analyzed for the Riemann solutions as the pressure, the flux approximation, and the molecular excluded volume all vanish. Finally, some numerical simulations are demonstrated to verify the theoretical analysis.