光滑粒子动力学方法中粒子分布与数值稳定性分析

光滑粒子动力学(SPH)作为一种拉格朗日型无网格粒子方法,已经成功地应用于包括含多相流动界面以及移动边界的可压缩和不可压缩流体运动的研究中.通过对Poiseuille流动的深入研究,探索了SPH方法中粒子分布对计算精度的影响,揭示了一种因为粒子不规则分布而导致的数值不稳定现象.研究显示,这种数值不稳定性起源于SPH方法粒子近似过程中的不连续性.使用了一种新的粒子近似格式以确保SPH方法中粒子近似的连续性.计算结果表明,这种新的粒子近似格式对于规则和不规则的粒子分布都能得到稳定精度的结果.

Particle distribution and numerical stability in smoothed particle hydrodynamics method

Smoothed particle hydrodynamics(SPH) is a Lagrangian meshfree particle method, and has been widely applied to different areas including incompressible or pseudo-incompressible flows with multiphase interfaces and moving boundaries. In this paper, an instability problem has been identified when the conventional SPH method is applied to modeling the Poiseuille flow problem at long-term simulations. It is found that this instability resulted from the particle inconsistency inherent to the SPH method, which originates from the discrete particle approximation and is a fundamental cause for poor approximation accuracy. A new particle approximation approach has been used to restore the particle consistency. We show that this particle consistency restoring approach can produce stable solutions for both regular and irregular particle distributions even at long-term simulations.