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Anisotropic Diffusion in Mesh-Free Numerical Magnetohydrodynamics

Hopkins, Philip F. (2017) Anisotropic Diffusion in Mesh-Free Numerical Magnetohydrodynamics. Monthly Notices of the Royal Astronomical Society, 466 (3). pp. 3387-3405. ISSN 0035-8711. doi:10.1093/mnras/stw3306.

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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.

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Hopkins, Philip F.0000-0003-3729-1684
Additional Information:© 2017 The Author. Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2016 December 15. Received 2016 December 15; in original form 2016 January 3. Published: 20 December 2016. We thank Eliot Quataert for several helpful suggestions of interesting test problems. Support for PFH was provided by the Gordon and Betty Moore Foundation through grant no. 776 to the Caltech Moore Center for Theoretical Cosmology and Physics, an Alfred P. Sloan Research Fellowship, NASA ATP Grant NNX14AH35G and NSF Collaborative Research Grant no. 1411920. Numerical calculations were run on the Caltech compute cluster ‘Zwicky’ (NSF MRI award no. PHY-0960291) and allocation TG-AST130039 granted by the Extreme Science and Engineering Discovery Environment (XSEDE) supported by the NSF.
Group:TAPIR, Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics, Astronomy Department
Funding AgencyGrant Number
Gordon and Betty Moore Foundation776
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:conduction, diffusion, hydrodynamics, instabilities, MHD, methods: numerical
Issue or Number:3
Record Number:CaltechAUTHORS:20160317-141936363
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Official Citation:Philip F. Hopkins; Anisotropic diffusion in mesh-free numerical magnetohydrodynamics. Mon Not R Astron Soc 2017; 466 (3): 3387-3405. doi: 10.1093/mnras/stw3306
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:65451
Deposited By: Joy Painter
Deposited On:17 Mar 2016 21:53
Last Modified:10 Nov 2021 23:45

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