Accurate, Meshless Methods for Magneto-Hydrodynamics

TL;DR

This paper extends meshless finite-volume methods to magneto-hydrodynamics, demonstrating their accuracy, efficiency, and advantages over traditional SPH and AMR schemes in various test problems.

Contribution

The authors develop and implement a divergence-cleaning meshless MHD method that outperforms SPH and is competitive with AMR in accuracy and convergence.

Findings

Methods accurately capture MRI, turbulence, and magnetic jets.

Meshless methods show sharper shocks and reduced noise.

Convergence rates vary depending on flow type.

Abstract

Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics (SPH) and adaptive mesh-refinement (AMR) schemes. Here, we extend these to include ideal magneto-hydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains div*B~0 to high accuracy. We implement these in the code GIZMO, together with a state-of-the-art implementation of SPH MHD. In every one of a large suite of test problems, the new methods are competitive with moving-mesh and AMR schemes using constrained transport (CT) to ensure div*B=0. They are able to correctly capture the growth and structure of the magneto-rotational instability (MRI), MHD turbulence, and the launching of magnetic jets, in some cases converging more rapidly than AMR codes. Compared to SPH, the MFM/MFV methods exhibit proper convergence at fixed neighbor number, sharper shock capturing, and dramatically reduced noise, div*B errors, and diffusion. Still, 'modern' SPH is able to handle most of our tests, at the cost of much larger kernels and 'by hand' adjustment of artificial diffusion parameters. Compared to AMR, the new meshless methods exhibit enhanced 'grid noise' but reduced advection errors and numerical diffusion, velocity-independent errors, and superior angular momentum conservation and coupling to N-body gravity solvers. As a result they converge more slowly on some problems (involving smooth, slowly-moving flows) but more rapidly on others (involving advection or rotation). In all cases, divergence-control beyond the popular Powell 8-wave approach is necessary, or else all methods we consider will systematically converge to unphysical solutions.