Journal Article

Dusty gas with smoothed particle hydrodynamics – I. Algorithm and test suite

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 2345-2364
Published in print March 2012 | ISSN: 0035-8711
Published online February 2012 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.20202.x
Dusty gas with smoothed particle hydrodynamics – I. Algorithm and test suite

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We present a new algorithm for simulating two-fluid gas and dust mixtures in smoothed particle hydrodynamics (SPH), systematically addressing a number of key issues including the generalized SPH density estimate in multifluid systems, the consistent treatment of variable smoothing-length terms, finite particle size, timestep stability, thermal coupling terms and the choice of kernel and smoothing length used in the drag operator. We find that using double-hump-shaped kernels improves the accuracy of the drag interpolation by a factor of several hundred compared to the use of standard SPH bell-shaped kernels, at no additional computational expense. In order to benchmark our algorithm, we have developed a comprehensive suite of standardized, simple test problems for gas and dust mixtures: dustybox, dustywave, dustyshock, dustysedov and dustydisc, the first three of which have known analytic solutions.

We present the validation of our algorithm against all of these tests. In doing so, we show that the spatial resolution criterion Δ≲csts is a necessary condition in all gas+dust codes that becomes critical at high drag (i.e. small stopping time ts) in order to correctly predict the dynamics. Implicit timestepping and the implementation of realistic astrophysical drag regimes are addressed in a companion paper.

Keywords: hydrodynamics; methods: numerical; planets and satellites: formation; proto-planetary discs; dust, extinction

Journal Article.  12207 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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