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Accurate, meshless methods for magnetohydrodynamics

Hopkins, Philip F. and Raives, Matthias J. (2016) Accurate, meshless methods for magnetohydrodynamics. Monthly Notices of the Royal Astronomical Society, 455 (1). pp. 51-88. ISSN 0035-8711. doi:10.1093/mnras/stv2180.

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Recently, we explored new 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. We extend these to include ideal magnetohydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains ∇⋅B≈0∇⋅B≈0. We implement these in the code GIZMO, together with state-of-the-art SPH MHD. We consider a large test suite, and show that on all problems the new methods are competitive with AMR using constrained transport (CT) to ensure ∇⋅B=0∇⋅B=0. They correctly capture the growth/structure of the magnetorotational instability, MHD turbulence, and launching of magnetic jets, in some cases converging more rapidly than state-of-the-art AMR. Compared to SPH, the MFM/MFV methods exhibit convergence at fixed neighbour number, sharp shock-capturing, and dramatically reduced noise, divergence errors, and diffusion. Still, ‘modern’ SPH can handle most test problems, at the cost of larger kernels and ‘by hand’ adjustment of artificial diffusion. Compared to non-moving meshes, the new methods exhibit enhanced ‘grid noise’ but reduced advection errors and diffusion, easily include self-gravity, and feature velocity-independent errors and superior angular momentum conservation. They converge more slowly on some problems (smooth, slow-moving flows), but more rapidly on others (involving advection/rotation). In all cases, we show divergence control beyond the Powell 8-wave approach is necessary, or all methods can converge to unphysical answers even at high resolution.

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URLURL TypeDescription Paper ItemCode
Hopkins, Philip F.0000-0003-3729-1684
Alternate Title:Accurate, Meshless Methods for Magneto-Hydrodynamics
Additional Information:© 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2015 September 17. Received 2015 September 17; in original form 2015 April 17. First published online November 2, 2015. We thank Paul Duffell, Jim Stone, Evghenii Gaburov, Ryan O'Leary, Romain Teyssier, Colin McNally, our referee Daniel Price, and many others for enlightening discussions and the initial studies motivating this paper. Support for PFH was provided by the Gordon and Betty Moore Foundation through Grant #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 #1411920. Numerical calculations were run on the Caltech compute cluster ‘Zwicky’ (NSF MRI award #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
Funding AgencyGrant Number
Gordon and Betty Moore Foundatino776
Alfred P. Sloan FoundationUNSPECIFIED
Caltech Moore Center for Theoretical Cosmology and PhysicsUNSPECIFIED
Subject Keywords:hydrodynamics – instabilities – turbulence – methods: numerical – cosmology: theory
Issue or Number:1
Record Number:CaltechAUTHORS:20150615-061712828
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:58228
Deposited By: Joy Painter
Deposited On:15 Jun 2015 14:49
Last Modified:10 Nov 2021 22:01

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