3D meshfree magnetohydrodynamics

TL;DR

This paper introduces a novel meshfree method for simulating magnetohydrodynamics using Euler potentials within a 3D SPH framework, ensuring divergence-free magnetic fields and demonstrating improved performance.

Contribution

The paper presents a new meshfree MHD method employing Euler potentials in SPH, ensuring divergence-free magnetic fields and enhanced accuracy over previous methods.

Findings

Successful implementation in the MAGMA code.

Demonstrated superiority through various tests.

Ensured divergence-free magnetic fields by construction.

Abstract

We describe a new method to include magnetic fields into smooth particle hydrodynamics. The derivation of the self-gravitating hydrodynamics equations from a variational principle is discussed in some detail. The non-dissipative magnetic field evolution is instantiated by advecting so-called Euler potentials. This approach enforces the crucial $\nabla\cdot\vec{B}=0$-constraint by construction. These recent developments are implemented in our three-dimensional, self-gravitating magnetohydrodynamics code MAGMA. A suite of tests is presented that demonstrates the superiority of this new approach in comparison to previous implementations.