On the invariant region for compressible Euler equations with a general equation of state

TL;DR

This paper investigates the solution space of the compressible Euler equations with a general thermodynamically consistent equation of state, identifying an invariant region and proposing an IRP limiter for high-order numerical schemes.

Contribution

It introduces a minimal-assumption invariant region for the Euler system with general equations of state and develops an IRP limiter for high-order finite-volume methods.

Findings

Invariant region is convex and physically consistent.

An IRP limiter is constructed for high-order schemes.

Applicable to a wide class of thermodynamically valid equations of state.

Abstract

The state space for solutions of the compressible Euler equations with a general equation of state is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. An invariant region of the resulting Euler system is identified and the convexity property of this region is justified by using only very minimal thermodynamical assumptions. Finally, we show how an invariant-region-preserving (IRP) limiter can be constructed for use in high order finite-volume type schemes to solve the compressible Euler equations with a general constitutive relation.