Low Mach Number Modeling of Type Ia Supernovae

TL;DR

This paper presents a low Mach number model for simulating Type Ia supernovae, enabling more accurate and computationally efficient large-scale simulations of white dwarf thermonuclear deflagrations.

Contribution

The authors derive a low Mach number equation set from fully compressible equations, validated against traditional models, improving accuracy and efficiency in supernova simulations.

Findings

The low Mach number model matches fully compressible simulations in applicable regimes.

It agrees with the anelastic approximation where valid.

The model handles finite amplitude density and temperature variations.

Abstract

We introduce a low Mach number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach number flows with potentially finite amplitude variations in density and temperature, the low Mach number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.