A numerical magnetohydrodynamic scheme using the hydrostatic approximation

TL;DR

This paper introduces a finite-difference magnetohydrodynamic scheme based on the hydrostatic approximation, suitable for modeling stratified astrophysical fluids by filtering sound waves and enabling larger timesteps.

Contribution

It presents a novel numerical scheme incorporating magnetic fields within the hydrostatic approximation framework for astrophysical fluid simulations.

Findings

Efficient filtering of sound waves in stratified fluids.

Applicable to stellar and planetary atmospheres.

Enhanced timestep size in simulations.

Abstract

In gravitationally stratified fluids, length scales are normally much greater in the horizontal direction than in the vertical one. When modelling these fluids it can be advantageous to use the hydrostatic approximation, which filters out vertically propagating sound waves and thus allows a greater timestep. We briefly review this approximation, which is commonplace in atmospheric physics, and compare it to other approximations used in astrophysics such as Boussinesq and anelastic, finding that it should be the best approximation to use in context such as radiative stellar zones, compact objects, stellar or planetary atmospheres and other contexts. We describe a finite-difference numerical scheme which uses this approximation, which includes magnetic fields.