Meshless Methods for Magnetohydrodynamics with Vector Potential

TL;DR

This paper introduces a novel meshless method for magnetohydrodynamics that evolves the magnetic vector potential, ensuring divergence control and improved accuracy over existing meshless codes.

Contribution

A new meshless scheme for MHD using vector potential evolution, divergence restriction, and stabilization techniques, validated through multiple complex test problems.

Findings

Method is robust and stable for long-term simulations.

Achieves better precision than existing meshless code GIZMO.

Successfully applied to complex MHD test problems.

Abstract

We present a meshless method for magnetohydrodynamics by evolving the vector potential of magnetic fields. A novel scheme and numerical techniques are developed to restrict the divergence of magnetic field, based on the Meshless Finite Mass/Volume with HLLD Riemann solver for conservative flux calculation. We found the magnetic field could be stabilized by a proper smoothing process and so the long-term evolution becomes available. To verify the new scheme, we perform the Brio-Wu shock tube, 2D and 3D Orszag-Tang vortex and Magnetorotational Instability test problems. Our results suggest that our method is robust and has better precision on central offset, amplitude and detailed pattern than an existing meshless code$-$GIZMO.