Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

TL;DR

This paper introduces a robust, second-order accurate numerical method for the compressible Euler equations that works with any equation of state, ensuring physical invariance and stability across shocks.

Contribution

It presents a novel approximation technique that is invariant-domain preserving, applicable to arbitrary equations of state, and includes an entropy surrogate functional for shock stability.

Findings

Method verified with analytical solutions

Validated on multiple computational benchmarks

Ensures nonnegative pressure and shock stability

Abstract

This paper is concerned with the approximation of the compressible Euler equations supplemented with an arbitrary or tabulated equation of state. The proposed approximation technique is robust, formally second-order accurate in space, invariant-domain preserving, and works for every equation of state, tabulated or analytic, provided the pressure is nonnegative. An entropy surrogate functional that grows across shocks is proposed. The numerical method is verified with novel analytical solutions and then validated with several computational benchmarks seen in the literature.