Improving convergence in smoothed particle hydrodynamics simulations without pairing instability
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_{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 Bsplines. Linear stability analysis in three dimensions and test simulations demonstrate that the Wendland kernels avoid the pairing instability for all N_{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 Bsplines, allowing large N_{H} and hence better numerical convergence (note that computational costs rise sublinear with N_{H}). Our analysis also shows that at low N_{H} the quartic spline kernel with N_{H} ≈ 60 obtains much better convergence than the standard cubic spline.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 September 2012
 DOI:
 10.1111/j.13652966.2012.21439.x
 arXiv:
 arXiv:1204.2471
 Bibcode:
 2012MNRAS.425.1068D
 Keywords:

 hydrodynamics;
 methods: numerical;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Physics  Computational Physics;
 Physics  Fluid Dynamics
 EPrint:
 substantially revised version, accepted for publication in MNRAS, 15 pages, 13 figures