Journal Article

Dusty gas with smoothed particle hydrodynamics – II. Implicit timestepping and astrophysical drag regimes

Guillaume Laibe and Daniel J. Price

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 420, issue 3, pages 2365-2376
Published in print March 2012 | ISSN: 0035-8711
Published online February 2012 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.20201.x
Dusty gas with smoothed particle hydrodynamics – II. Implicit timestepping and astrophysical drag regimes

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In a companion paper, we have presented an algorithm for simulating two-fluid gas and dust mixtures in smoothed particle hydrodynamics (SPH). In this paper, we develop an implicit timestepping method that preserves the exact conservation of the both linear and angular momenta in the underlying SPH algorithm, but unlike previous schemes, allows the iterations to converge to arbitrary accuracy and is suited to the treatment of non-linear drag regimes. The algorithm presented in Paper I is also extended to deal with realistic astrophysical drag regimes, including both linear and non-linear Epstein and Stokes drag. The scheme is benchmarked against the test suite presented in Paper I, including (i) the analytic solutions of the dustybox problem and (ii) solutions of the dustywave, dustyshock, dustysedov and dustydisc obtained with explicit timestepping. We find that the implicit method is 1–10 times faster than the explicit temporal integration when the ratio r between the timestep and the drag stopping time is 1 ≲r≲ 1000.

Keywords: hydrodynamics; methods: numerical; planets and satellites: formation; protoplanetary discs; dust, extinction

Journal Article.  7096 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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