Astronomy and Astrophysics – Astrophysics – Instrumentation and Methods for Astrophysics
Scientific paper
2012-04-11
Astronomy and Astrophysics
Astrophysics
Instrumentation and Methods for Astrophysics
13 pages, 13 figures, submitted to MNRAS
Scientific paper
We investigate the suitability of the Wendland functions as smoothing kernels for smoothed particle hydrodynamics (SPH) and compare them with the traditional B-splines. Linear stability analysis in three dimensions and test simulations demonstrate that the Wendland kernels avoid the clumping (or pairing) instability for all neighbour numbers NH, despite having vanishing derivative at the origin. This disproves traditional ideas about the origin of this instability. Instead, we give an explanation based on the kernel Fourier transform, but also an interpretation in terms of the SPH density estimator. The Wendland kernels are computationally more convenient than the higher-order B-splines and thus allow large NH, which we show are required to obtain decent numerical accuracy for strongly shearing flows (note that computational costs rise sub-linear with NH). At low NH the quartic B-spline kernel with NH = 60 obtains much better convergence then the standard cubic B-spline with NH<=57.
Aly Hossam
Dehnen Walter
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