Stable Finite Volume Methods for the Isentropic Euler Equations

Abstract

We developed an entropy conservative and entropy stable finite volume scheme for the isentropic Euler schemes for polytropic, ideal gases with any degrees of freedom. The schemes were developed for one space dimension, and the generalized to account for the two-dimensional case. Numerical experiments showed that the EEC scheme has a decent computational cost, even though it's higher than that of the popularly used methods. It is also second order accurate. The ESRD scheme adds dissipation around shocks to avoid growing oscillations, and is stable, but only first-order accurate.