Anisotropic Diffusion in Mesh-Free Numerical Magnetohydrodynamics

TL;DR

This paper extends mesh-free Lagrangian methods for magnetohydrodynamics to accurately simulate a wide range of anisotropic diffusion processes, demonstrating stability, correctness, and competitiveness with existing methods.

Contribution

It introduces a new mesh-free approach for anisotropic diffusion in MHD, including a stabilization scheme and applications to SPH, improving accuracy and stability.

Findings

Methods are accurate and stable with noisy fields.

Correctly recover anisotropic diffusion behavior.

Competitive with state-of-the-art AMR/moving-mesh methods.

Abstract

We extend recently-developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer-Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect), and turbulent 'eddy diffusion.' We study these as implemented in the code GIZMO for both new meshless finite-volume Godunov schemes (MFM/MFV). We show the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behavior even in arbitrarily anisotropic cases. They are competitive with state-of-the-art AMR/moving-mesh methods, and can correctly treat anisotropic diffusion-driven instabilities (e.g. the MTI and HBI, Hall MRI). We also develop a new scheme for stabilizing anisotropic tensor-valued fluxes with high-order gradient estimators and non-linear flux limiters, which is trivially generalized to AMR/moving-mesh codes. We also present applications of some of these improvements for SPH, in the form of a new integral-Godunov SPH formulation that adopts a moving-least squares gradient estimator and introduces a flux-limited Riemann problem between particles.