New numerical solver for flows at various Mach numbers

TL;DR

This paper introduces a new numerical scheme based on a modified Roe solver that accurately simulates flows across a wide range of Mach numbers, especially low Mach flows in astrophysics, reducing dissipation and capturing flow structures effectively.

Contribution

The authors develop a novel scheme that maintains low Mach number accuracy while preserving compressibility effects, improving upon existing methods in astrophysical hydrodynamics.

Findings

Successfully reproduces slow flow structures at moderate resolution

Maintains accuracy across a wide Mach number range

Offers a promising tool for stellar evolution simulations

Abstract

Many problems in stellar astrophysics feature flows at low Mach numbers. Conventional compressible hydrodynamics schemes frequently used in the field have been developed for the transonic regime and exhibit excessive numerical dissipation for these flows. While schemes were proposed that solve hydrodynamics strictly in the low Mach regime and thus restrict their applicability, we aim at developing a scheme that correctly operates in a wide range of Mach numbers. Based on an analysis of the asymptotic behavior of the Euler equations in the low Mach limit we propose a novel scheme that is able to maintain a low Mach number flow setup while retaining all effects of compressibility. This is achieved by a suitable modification of the well-known Roe solver. Numerical tests demonstrate the capability of this new scheme to reproduce slow flow structures even in moderate numerical resolution. Our scheme provides a promising approach to a consistent multidimensional hydrodynamical treatment of astrophysical low Mach number problems such as convection, instabilities, and mixing in stellar evolution.