Semi-conservative reduced speed of sound technique for low Mach number flows with large density variations

TL;DR

This paper introduces a semi-conservative formulation of the reduced speed of sound technique (RSST) that effectively handles low Mach number flows with large density variations, overcoming limitations of the original method.

Contribution

A new semi-conservative RSST formulation is proposed, enabling simulation of low Mach flows with large density variations and including variants that conserve momentum with high precision.

Findings

Original RSST is ineffective with large density variations.

New formulations successfully reduce sound speed in complex flows.

Variants conserve momentum accurately in numerical simulations.

Abstract

The reduced speed of sound technique (RSST) has been used for efficient simulation of low Mach number flows in solar and stellar convection zones. The basic RSST equations are hyperbolic, and are suitable for parallel computation by domain decomposition. The application of RSST is limited to cases where density perturbations are much smaller than the background density. In addition, non-conservative variables are required to be evolved using this method, which is not suitable in cases where discontinuities like shock waves co-exist in a single numerical domain. In this study, we suggest a new semi-conservative formulation of the RSST that can be applied to low Mach number flows with large density variations. We derive the wave speed of the original and newly suggested methods to clarify that these methods can reduce the speed of sound without affecting the entropy wave. The equations are implemented using the finite volume method. Several numerical tests are carried out to verify the suggested methods. The analysis and numerical results show that the original RSST is not applicable when mass density variations are large. In contrast, the newly suggested methods are found to be efficient in such cases. We also suggest variants of the RSST that conserve momentum in the machine precision. The newly suggested variants are formulated as semi-conservative equations, which reduce to the conservative form of the Euler equations when the speed of sound is not reduced. This property is advantageous when both high and low Mach number regions are included in the numerical domain. The newly suggested forms of RSST can be applied to a wider range of low Mach number flows.