Second-order invariant-domain preserving approximation to the multi-species Euler equations

TL;DR

This paper develops a second-order numerical method for multi-species Euler equations that preserves physical invariants, using Riemann problem solutions, wave speed analysis, and convex limiting, validated through benchmarks and experiments.

Contribution

It introduces a novel second-order invariant-domain preserving scheme for multi-species Euler equations, including a full Riemann problem solution and a convex limiting technique.

Findings

The method accurately preserves physical invariants.

It achieves second-order accuracy in simulations.

Validated with benchmarks and laboratory experiments.

Abstract

This work is concerned with constructing a second-order, invariant-domain preserving approximation of the compressible multi-species Euler equations where each species is modeled by an ideal gas equation of state. We give the full solution to the Riemann problem and derive its maximum wave speed. The maximum wave speed is used in constructing a first-order invariant-domain preserving approximation. We then extend the methodology to second-order accuracy and detail a convex limiting technique which is used for preserving the invariant domain. Finally, the numerical method is verified with analytical solutions and then validated with several benchmarks and laboratory experiments.