Numerical investigation of Mach number consistent Roe solvers for the Euler equations of gas dynamics

TL;DR

This paper explores a new approach to gas dynamics simulations that maintains Mach number consistency by adaptively balancing numerical viscosity across different wave types, improving accuracy at low Mach numbers.

Contribution

It introduces a novel adaptive method that combines viscosity adjustments for entropy, shear, and acoustic waves to ensure Mach number consistency in Roe solvers.

Findings

Achieves Mach number consistency across all waves

Reduces numerical viscosity at low Mach numbers

Improves simulation accuracy near shocks

Abstract

While traditional approaches to prevent the carbuncle phenomenon in gas dynamics simulations increase the viscosity on entropy and shear waves near shocks, it was quite recently suggested to instead decrease the viscosity on the acoustic waves for low Mach numbers. The goal is to achieve what, in this paper, we call Mach number consistency: for all waves, the numerical viscosity decreases with the same order of the Mach number when the Mach number tends to zero. We take the simple approach that was used for the proof of concept together with the simple model for the increased numerical viscosity on linear waves and investigate the possibilities of combining both in an adaptive manner while locally maintaining Mach number consistency.