Anisotropic diffusion in mesh-free numerical magnetohydrodynamics
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 that the MFM/MFV methods are accurate and stable even with noisy fields and irregular particle arrangements, and recover the correct behaviour 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.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- April 2017
- DOI:
- 10.1093/mnras/stw3306
- arXiv:
- arXiv:1602.07703
- Bibcode:
- 2017MNRAS.466.3387H
- Keywords:
-
- conduction;
- diffusion;
- hydrodynamics;
- instabilities;
- MHD;
- methods: numerical;
- Astrophysics - Instrumentation and Methods for Astrophysics;
- Astrophysics - Solar and Stellar Astrophysics;
- Physics - Computational Physics
- E-Print:
- 18 pages, 17 figures, MNRAS (replaced with accepted version). A public version of the GIZMO code is available at http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html