Journal Article

rpSPH: a novel smoothed particle hydrodynamics algorithm

Tom Abel

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 413, issue 1, pages 271-285
Published in print May 2011 | ISSN: 0035-8711
Published online April 2011 | e-ISSN: 1365-2966 | DOI:
rpSPH: a novel smoothed particle hydrodynamics algorithm

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We suggest a novel discretization of the momentum equation for smoothed particle hydrodynamics (SPH) and show that it significantly improves the accuracy of the obtained solutions. Our new formulation which we refer to as relative pressure SPH, rpSPH, evaluates the pressure force with respect to the local pressure. It respects Newton’s first law of motion and applies forces to particles only when there is a net force acting upon them. This is in contrast to standard SPH which explicitly uses Newton’s third law of motion continuously applying equal but opposite forces between particles. rpSPH does not show the unphysical particle noise, the clumping or banding instability, unphysical surface tension and unphysical scattering of different mass particles found for standard SPH. At the same time, it uses fewer computational operations and only changes a single line in existing SPH codes. We demonstrate its performance on isobaric uniform density distributions, uniform density shearing flows, the Kelvin–Helmholtz and Rayleigh–Taylor instabilities, the Sod shock tube, the Sedov–Taylor blast wave and a cosmological integration of the Santa Barbara galaxy cluster formation test. rpSPH is an improvement in these cases. The improvements come at the cost of giving up exact momentum conservation of the scheme. Consequently, one can also obtain unphysical solutions particularly at low resolutions.

Keywords: hydrodynamics; instabilities; methods: numerical

Journal Article.  11316 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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