Low Mach number effect in simulation of high Mach number flow

TL;DR

This paper investigates the low Mach number effect in high Mach number flow simulations, proposing modifications to the Roe flux to improve accuracy and eliminate numerical artifacts like the carbuncle phenomenon.

Contribution

It introduces two simple modifications to the Roe flux that address low Mach number effects and improve shock simulation accuracy.

Findings

Both modifications eliminate the kinked Mach stem in tests.

The modifications reduce the impact of low Mach number effects.

Results link carbuncle phenomena to dissipation imbalance in Godunov schemes.

Abstract

In this note, we relate the two well-known difficulties of Godunov schemes: the carbuncle phenomena in simulating high Mach number flow, and the inaccurate pressure profile in simulating low Mach number flow. We introduced two simple low-Mach-number modifications for the classical Roe flux to decrease the difference between the acoustic and advection contributions of the numerical dissipation. While the first modification increases the local numerical dissipation, the second decreases it. The numerical tests on the double-Mach reflection problem show that both modifications eliminate the kinked Mach stem suffered by the original flux. These results suggest that, other than insufficient numerical dissipation near the shock front, the carbuncle phenomena is strongly relevant to the non-comparable acoustic and advection contributions of the numerical dissipation produced by Godunov schemes due to the low Mach number effect.