Accurately simulating anisotropic thermal conduction on a moving mesh

TL;DR

This paper introduces a new anisotropic thermal conduction solver for moving meshes that preserves extrema and is suitable for complex astrophysical simulations, improving stability and accuracy in modeling heat transport.

Contribution

The paper presents a novel extremum preserving anisotropic diffusion solver on unstructured moving Voronoi meshes, with a robust interpolation scheme and efficient implicit time integration.

Findings

The method is stable and accurate in various tests.

It effectively models heat conduction in heterogeneous, anisotropic environments.

Suitable for astrophysical phenomena like galaxy clusters and supernova remnants.

Abstract

We present a novel implementation of an extremum preserving anisotropic diffusion solver for thermal conduction on the unstructured moving Voronoi mesh of the AREPO code. The method relies on splitting the one-sided facet fluxes into normal and oblique components, with the oblique fluxes being limited such that the total flux is both locally conservative and extremum preserving. The approach makes use of harmonic averaging points and a simple, robust interpolation scheme that works well for strong heterogeneous and anisotropic diffusion problems. Moreover, the required discretisation stencil is small. Efficient fully implicit and semi-implicit time integration schemes are also implemented. We perform several numerical tests that evaluate the stability and accuracy of the scheme, including applications such as point explosions with heat conduction and calculations of convective instabilities in conducting plasmas. The new implementation is suitable for studying important astrophysical phenomena, such as the conductive heat transport in galaxy clusters, the evolution of supernova remnants, or the distribution of heat from blackhole-driven jets into the intracluster medium.