Smoothed Particle Magnetohydrodynamics: A State of the Union

TL;DR

This paper reviews the challenges and limitations of implementing stable magnetohydrodynamics in smoothed particle hydrodynamics, highlighting the numerical issues that hinder progress despite corrective measures.

Contribution

It provides a comprehensive overview of SPMHD implementation, discusses the failures of current methods, and identifies fundamental numerical limitations.

Findings

Current corrective methods are insufficient for stable MHD in SPH.

Numerical issues significantly limit the accuracy of SPMHD.

Stable MHD calculations in SPH remain challenging at the state-of-the-art level.

Abstract

Obtaining a stable magnetohydrodynamical (MHD) formalism in SPH - i.e. smoothed particle magnetohydrodynamics (SPMHD) - has proven remarkably difficult. To implement MHD requires two steps: a modification to the momentum equation and an induction equation, and both present challenges. We first provide an overview of how SPMHD is implemented, and then discuss how this implementation fails and the limitation of various corrective methods - with particular reference to the effects of particle disorder. Although there are many problems for which, with careful choice of corrective measures, good results can be obtained, we then show that, at the very limits of the state of the art, the ability to perform stable MHD calculations in SPH is curtailed by numerical issues.