# Divergence-Free Magnetohydrodynamics on Conformally Moving, Adaptive Meshes Using a Vector Potential Method

## TL;DR

This paper introduces a novel divergence-free magnetohydrodynamics method that employs a vector potential to evolve magnetic fields on adaptive, conformally moving meshes, ensuring high accuracy and maintaining divergence-free conditions.

## Contribution

The paper presents a new vector potential-based approach for MHD simulations on adaptive, moving meshes, improving divergence control and computational flexibility.

## Key findings

- Maintains divergence-free magnetic fields to machine precision.
- Successfully tested on a variety of MHD problems, including relativistic cases.
- Produces accurate results across different grid configurations.

## Abstract

We present a new method for evolving the equations of magnetohydrodynamics (both Newtonian and relativistic) that is capable of maintaining a divergence-free magnetic field ($\nabla \cdot \mathbf{B} = 0$) on adaptively refined, conformally moving meshes. The method relies on evolving the magnetic vector potential and then using it to reconstruct the magnetic fields. The advantage of this approach is that the vector potential is not subject to a constraint equation in the same way the magnetic field is, and so can be refined and moved in a straightforward way. We test this new method against a wide array of problems from simple Alfven waves on a uniform grid to general relativistic MHD simulations of black hole accretion on a nested, spherical-polar grid. We find that the code produces accurate results and in all cases maintains a divergence-free magnetic field to machine precision.