A partially dimensionally-split approach to numerical MHD

TL;DR

This paper presents a modified dimensionally-split magnetohydrodynamics algorithm that ensures divergence-free magnetic fields and is compatible with existing hydrodynamics codes, facilitating easier integration into complex astrophysical simulations.

Contribution

It introduces a partially dimensionally-split MHD algorithm compatible with existing codes, using a cell-centered grid and constrained transport for divergence-free magnetic fields.

Findings

Accurate results demonstrated on multiple test problems.

Algorithm easily integrates into existing hydrodynamics codes.

Source code is publicly available for adoption.

Abstract

We modify an existing magnetohydrodynamics algorithm to make it more compatible with a dimensionally-split (DS) framework. It is based on the standard reconstruct-solve-average strategy (using a Riemann solver), and relies on constrained transport to ensure that the magnetic field remains divergence-free (div B = 0). The DS approach, combined with the use of a single, cell-centred grid (for both the fluid quantities and the magnetic field), means that the algorithm can be easily added to existing DS hydrodynamics codes. This makes it particularly useful for mature astrophysical codes, which often model more complicated physical effects on top of an underlying DS hydrodynamics engine, and therefore cannot be restructured easily. Several test problems have been included to demonstrate the accuracy of the algorithm, and illustrative source code has been made freely available online.