Preserving the minimum principle on the entropy for the compressible Euler Equations with general equations of state
Numerical Analysis
2025-09-09 v3 Numerical Analysis
Abstract
This paper is concerned with constructing an invariant-domain preserving approximation technique for the compressible Euler equations with general equations of state that preserves the minimum principle on the physical entropy. We derive a sufficient wave speed estimate for the Riemann problem under some mild thermodynamic assumptions on the equation of state. This minimum principle is guaranteed through the use of discrete auxiliary states which are in the invariant domain when using this new wave speed estimate. Finally, we numerically illustrate the proposed methodology.
Keywords
Cite
@article{arxiv.2503.10612,
title = {Preserving the minimum principle on the entropy for the compressible Euler Equations with general equations of state},
author = {Bennett Clayton and Eric J. Tovar},
journal= {arXiv preprint arXiv:2503.10612},
year = {2025}
}