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Improving convergencein smoothed particlehydrodynamicssimulations withoutpairing instability Walter DehnenHossam Aly2012 год

Improving convergence in smoothed particle hydrodynamics simulations without pairing instability
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Аннотация: 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 NH 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 allNH, 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 NH and hence better numerical convergence (note that computational costs rise sublinear with NH). Our analysis also shows that at low NH the quartic spline kernel with NH ≈ 60 obtains much better convergence than the standard cubic spline.
Год издания: 2012
Авторы: Walter Dehnen, Hossam Aly
Издательство: Oxford University Press
Источник: Monthly Notices of the Royal Astronomical Society
Ключевые слова: Fluid Dynamics Simulations and Interactions, Fluid Dynamics and Vibration Analysis, Ship Hydrodynamics and Maneuverability
Другие ссылки: Monthly Notices of the Royal Astronomical Society (PDF)
Monthly Notices of the Royal Astronomical Society (HTML)
arXiv (Cornell University) (PDF)
arXiv (Cornell University) (HTML)
OPAL (Open@LaTrobe) (La Trobe University) (PDF)
OPAL (Open@LaTrobe) (La Trobe University) (HTML)
Leicester Research Archive (University of Leicester) (PDF)
Leicester Research Archive (University of Leicester) (HTML)
DataCite API (HTML)