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Title: Resolving mixing in smoothed particle hydrodynamics
Authors: Read, J. I.
Agertz, O.
Hayfield, T.
First Published: 1-Jul-2010
Publisher: Oxford University Press (OUP)
Citation: Monthly Notices of the Royal Astronomical Society, 2010, 405 (3), pp. 1513-1530
Abstract: Standard formulations of smoothed particle hydrodynamics (SPH) are unable to resolve mixing at fluid boundaries. We use an error and stability analysis of the generalized SPH equations of motion to prove that this is due to two distinct problems. The first is a leading order error in the momentum equation. This should decrease with an increasing neighbour number, but does not because numerical instabilities cause the kernel to be irregularly sampled. We identify two important instabilities: the clumping instability and the banding instability, and we show that both are cured by a suitable choice of kernel. The second problem is the local mixing instability (LMI). This occurs as particles attempt to mix on the kernel scale, but are unable to due to entropy conservation. The result is a pressure discontinuity at boundaries that pushes fluids of different entropies apart. We cure the LMI by using a weighted density estimate that ensures that pressures are single-valued throughout the flow. This also gives a better volume estimate for the particles, reducing errors in the continuity and momentum equations. We demonstrate mixing in our new optimized smoothed particle hydrodynamics (OSPH) scheme using a Kelvin–Helmholtz instability (KHI) test with a density contrast of 1:2, and the ‘blob test’– a 1:10 density ratio gas sphere in a wind tunnel – finding excellent agreement between OSPH and Eulerian codes.
DOI Link: 10.1111/j.1365-2966.2010.16577.x
ISSN: 0035-8711
eISSN: 1365-2966
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2010 the authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved. Deposited with reference to the publisher’s archiving policy available on the SHERPA/RoMEO website.
Appears in Collections:Published Articles, Dept. of Physics and Astronomy

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