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Title: Improving convergence in smoothed particle hydrodynamics simulations without pairing instability
Authors: Dehnen, Walter
Aly, Hossam
First Published: 1-Sep-2012
Publisher: Oxford University Press (OUP)
Citation: Monthly Notices of the Royal Astronomical Society, 2012, 425 (2), pp. 1068-1082
Abstract: The numerical convergence of smoothed particle hydrodynamics (SPH) can be severely restricted by random force errors induced by particle disorder, especially in shear flows, which are ubiquitous in astrophysics. The increase in the number N[subscript: H] of neighbours when switching to more extended smoothing kernels at fixed resolution (using an appropriate definition for the SPH resolution scale) is insufficient to combat these errors. Consequently, trading resolution for better convergence is necessary, but for traditional smoothing kernels this option is limited by the pairing (or clumping) instability. Therefore, we investigate the suitability of the Wendland functions as smoothing kernels and compare them with the traditional B-splines. Linear stability analysis in three dimensions and test simulations demonstrate that the Wendland kernels avoid the pairing instability for all N[subscript: H], despite having vanishing derivative at the origin (disproving traditional ideas about the origin of this instability; instead, we uncover a relation with the kernel Fourier transform and give an explanation in terms of the SPH density estimator). The Wendland kernels are computationally more convenient than the higher order B-splines, allowing large N[subscript: H] and hence better numerical convergence (note that computational costs rise sublinear with N[subscript: H]). Our analysis also shows that at low N[subscript: H] the quartic spline kernel with N[subscript: H] ≈ 60 obtains much better convergence than the standard cubic spline.
DOI Link: 10.1111/j.1365-2966.2012.21439.x
ISSN: 0035-8711
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 ©: 2012 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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