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A new class of accurate, mesh-free hydrodynamic simulation methods

Hopkins, Philip F. (2015) A new class of accurate, mesh-free hydrodynamic simulation methods. Monthly Notices of the Royal Astronomical Society, 450 (1). pp. 53-110. ISSN 0035-8711.

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We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume ‘overlap’. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code gizmo:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require ‘artificial diffusion’ terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced ‘particle noise’ and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of ‘grid alignment’ effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize ‘grid noise’. These differences are important for a range of astrophysical problems.

Item Type:Article
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URLURL TypeDescription Paper DOIArticle
Hopkins, Philip F.0000-0003-3729-1684
Alternate Title:GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods
Additional Information:© 2015 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. Accepted 2015 January 27. Received 2014 December 31; in original form 2014 September 24. First published online April 15, 2015. I thank Volker Springel, Romain Teyssier, Lars Hernquist, Jim Stone, Dusan Keres, Paul Duffell, James Wadsley, Oscar Agertz, Thorsten Naab, Richard Bower, Matthieu Schaller, Nick Gnedin, Andrey Kravtsov, Desika Narayanan, Ji-Hoon Kim, Andrew Wetzel, Eliot Quataert, Paul Torrey, Norm Murray, Claude-Andre Faucher- Giguere, and many others for conversations motivating, clarifying, and guiding the development of this work. I thank the anonymous referee for helpful comments, Bert Vandenbroucke for catching a bug in the initial public code release, Evghenii Gaburov for helpful discussions and the initial studies motivating this paper, and Ryan O’Leary for providing additional ATHENA simulations. I must express my immense debt and gratitude to the many people in the numerical development community who have made their codes and methods public, particularly Volker Springel, Evghenii Gaburov, Jim Stone, and Romain Teyssier, whose excellent codes were used throughout this project. Partial 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, and the Alfred P. Sloan Foundation through a Sloan Research Fellowship #BR2014-022. The simulations here were run on the Stampede supercomputer at TACC through NSF XSEDE allocation #TG-AST130039.
Group:TAPIR, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Gordon and Betty Moore Foundation776
Alfred P. Sloan FoundationBR2014-022
Subject Keywords:hydrodynamics; instabilities; turbulence; methods: numerical; cosmology: theory
Issue or Number:1
Record Number:CaltechAUTHORS:20141202-094306473
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Official Citation:Philip F. Hopkins A new class of accurate, mesh-free hydrodynamic simulation methods MNRAS (June 11, 2015) Vol. 450 53-110 doi:10.1093/mnras/stv195 First published online April 15, 2015
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52260
Deposited By: Joy Painter
Deposited On:02 Dec 2014 21:30
Last Modified:03 Oct 2019 07:40

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