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A general-purpose time-step criterion for simulations with gravity

Grudić, Michael Y. and Hopkins, Philip F. (2020) A general-purpose time-step criterion for simulations with gravity. Monthly Notices of the Royal Astronomical Society, 495 (4). pp. 4306-4313. ISSN 0035-8711. doi:10.1093/mnras/staa1453.

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We describe a new adaptive time-step criterion for integrating gravitational motion, which uses the tidal tensor to estimate the local dynamical time-scale and scales the time-step proportionally. This provides a better candidate for a truly general-purpose gravitational time-step criterion than the usual prescription derived from the gravitational acceleration, which does not respect the equivalence principle, breaks down when a=0⁠, and does not obey the same dimensional scaling as the true time-scale of orbital motion. We implement the tidal time-step criterion in the simulation code GIZMO, and examine controlled tests of collisionless galaxy and star cluster models, as well as galaxy merger simulations. The tidal criterion estimates the dynamical time faithfully, and generally provides a more efficient time-stepping scheme compared to an acceleration criterion. Specifically, the tidal criterion achieves order-of-magnitude smaller energy errors for the same number of force evaluations in potentials with inner profiles shallower than ρ ∝ r⁻¹ (i.e. where a → 0⁠), such as star clusters and cored galaxies. For a given problem these advantages must be weighed against the additional overhead of computing the tidal tensor on-the-fly, but in many cases this overhead is small.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Grudić, Michael Y.0000-0002-1655-5604
Hopkins, Philip F.0000-0003-3729-1684
Alternate Title:A general-purpose timestep criterion for simulations with gravity
Additional Information:© 2020 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Accepted 2020 May 21. Received 2020 May 19; in original form 2019 October 10. Published: 27 May 2020. We thank Dávid Guszejnov, Walter Dehnen, Oliver Hahn, and Jens Stücker for enlightening discussions, and thank the anonymous referee for helpful suggestions that improved the text. Support for MYG was provided by a CIERA Postdoctoral Fellowship. Support for MYG and PFH was provided by an Alfred P. Sloan Research Fellowship, NSF Collaborative Research grant number 1715847, NSF CAREER grant number 1455342, and NASA grants NNX15AT06G, JPL 1589742, and 17-ATP17-0214. Numerical calculations were run on the Caltech compute cluster ‘Wheeler,’. This research has made use of use of NASA’s Astrophysics Data System, IPYTHON (Pérez & Granger 2007), NUMPY, SCIPY (Jones et al. 2001), and MATPLOTLIB (Hunter 2007).
Group:Astronomy Department, TAPIR
Funding AgencyGrant Number
Northwestern UniversityUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:gravitation, hydrodynamics, methods: numerical
Issue or Number:4
Record Number:CaltechAUTHORS:20200310-111822630
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Official Citation:Michael Y Grudić, Philip F Hopkins, A general-purpose time-step criterion for simulations with gravity, Monthly Notices of the Royal Astronomical Society, Volume 495, Issue 4, July 2020, Pages 4306–4313,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101824
Deposited By: Tony Diaz
Deposited On:10 Mar 2020 18:24
Last Modified:16 Nov 2021 18:06

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