A note on the Riemann solutions to the isentropic Euler equations in the vanishing pressure limit

2018/05/12 by Keita, Sana, Bourgault, Yves
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.04641

Abstract

The behaviour of the solutions to the Riemann problem for the isentropic Euler equations when the pressure vanishes is analysed. It is shown that any solution composed of a 1-shock wave and a 2-rarefaction wave tends to a two-shock wave when the pressure gets smaller than a fixed value determined by the Riemann data; by contrast, any solution composed of a 1-rarefaction wave and a 2-shock wave tends to a two-rarefaction wave. The two situations are illustrated with numerical tests.

Related

• The Vanishing Pressure Limits of Riemann Solutions to the Chaplygin Euler Equations
• Well-posedness of the Riemann problem with two shocks for the isentropic Euler system in a class of vanishing physical viscosity limits
• The pressureless limits of Riemann solutions to the Euler equations of one-dimensional compressible fluid flow with a source term
• Fluid Dynamic Limit to the Riemann Solutions of Euler Equations: I. Superposition of rarefaction waves and contact discontinuity
• The Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems