基于四次分段光滑核函数的SPH应力修正算法

An SPH stress correction algorithm based on the quartic piecewise smooth kernel function

光滑粒子流体动力学(SPH)方法是近年来流行的一种自适应拉格朗日型无网格粒子方法.本文针对传统SPH方法的应力不稳定问题,依据应力不稳定充分条件,提出了一种新的二阶导数非负的四次分段光滑核函数,由此得到了一种SPH应力修正算法.计算结果表明,修正的SPH算法能够有效地描述二维以及三维vd W液滴的形成过程.此外,基于修正的SPH算法进一步探讨了不同物理参数对二维圆形液滴粒子分布的影响,结果表明,取适当的温度和粒子初始间距时圆形液滴的边界粒子既不聚集也不分散,且流体温度越高或者粒子初始间距越大,圆形液滴的边界粒子分布越分散,而光滑长度比例系数越大,圆形液滴的粒子分布会更均匀.

Smoothed particle hydrodynamics(SPH) is a popular adaptive Lagrangian mesh-free particle method. For the tensile instability problem in traditional SPH, according to the sufficient condition of tensile instability, a new quartic piecewise smooth kernel function with non-negative second derivative is proposed, and an SPH stress correction algorithm is obtained in this study. The numerical results show that the modified SPH algorithm can effectively describe the formation processes of 2 D and 3 D vd W liquid drops. Then, based on the modified SPH algorithm, the effects of different physical parameters on the particle distribution of 2 D circular droplets are further discussed. The results show that, with the appropriate temperature or initial particle spacing, the boundary particles of circular droplets are neither clustered nor scattered, and as the fluid temperature or initial particle spacing increases, the boundary particles will be scattered.Conversely, the particle distribution of circular droplets becomes more uniform with the increase in the smooth length proportion coefficient.