A Vector Potential implementation for Smoothed Particle Magnetohydrodynamics

TL;DR

This paper introduces a stable vector potential formulation for smoothed particle magnetohydrodynamics (SPMHD) that effectively preserves magnetic field solenoidality, improving simulation accuracy of astrophysical processes.

Contribution

It presents a novel vector potential implementation in Coulomb gauge for SPMHD, overcoming previous instability issues and enhancing magnetic field evolution accuracy.

Findings

Successfully reproduces classical test cases stably.

Demonstrates failure of direct magnetic field integration methods.

Highlights importance of vector potential approach for stability.

Abstract

The development of smooth particle magnetohydrodynamic (SPMHD) has significantly improved the simulation of complex astrophysical processes. However, the preservation the solenoidality of the magnetic field is still a severe problem for the MHD. A formulation of the induction equation with a vector potential would solve the problem. Unfortunately all previous attempts suffered from instabilities. In the present work, we evolve the vector potential in the Coulomb gauge and smooth the derived magnetic field for usage in the momentum equation. With this implementation we could reproduce classical test cases in a stable way. A simple test case demonstrates the possible failure of widely used direct integration of the magnetic field, even with the usage of a divergence cleaning method.