A note on the Riemann solutions to the isentropic Euler equations in the vanishing pressure limit
Analysis of PDEs
2018-12-03 v2
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.
Keywords
Cite
@article{arxiv.1805.04641,
title = {A note on the Riemann solutions to the isentropic Euler equations in the vanishing pressure limit},
author = {Sana Keita and Yves Bourgault},
journal= {arXiv preprint arXiv:1805.04641},
year = {2018}
}