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arXiv 1204.2471astro-ph.IMphysics.comp-phphysics.flu-dyn
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无配对不稳定性的光滑粒子流体动力学模拟中的收敛性改进

Improving convergence in smoothed particle hydrodynamics simulations without pairing instability

Walter Dehnen, Hossam Aly

摘要:

光滑粒子流体动力学(SPH)的数值收敛会受到粒子无序引起的随机力误差的严重限制,特别是在天体物理中普遍存在的剪切流中。当切换到固定分辨率的更扩展的平滑内核时(使用SPH分辨率尺度的适当定义),邻居的数量NH的增加不足以对抗这些错误。因此,为了更好的收敛而交易分辨率是必要的,但是对于传统的平滑内核,这种选择受到配对(或聚集)不稳定性的限制。因此,我们调查的适宜性的Wendland函数平滑内核,并比较它们与传统的B样条。在三维和测试模拟的线性稳定性分析表明,文德兰内核避免配对不稳定的所有NH,尽管有消失的衍生物在原点(反驳传统的想法,这种不稳定的起源;相反,我们发现的关系与内核傅立叶变换,并给出解释的SPH密度估计)。Wendland核在计算上比高阶B样条更方便,允许较大的NH,因此具有更好的数值收敛性(注意计算成本随NH呈次线性上升)。我们的分析还表明,在低的NH ~= 60的四次样条核得到更好的收敛比标准的三次样条。

英文摘要:

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 all NH, 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 sub-linear with NH). Our analysis also shows that at low NH the quartic spline kernel with NH ~= 60 obtains much better convergence then the standard cubic spline.

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