一种SPH应力修正算法及自由表面流中的应用

提出了一种SPH应力修正算法,即模型中的拉应力和压应力分别采用不同的插值核函数和状态方程来处理,改善应力稳定性问题。介绍了一种改进的Quintic核函数,用于改善模型中压应力的稳定性。通过增加钟型核函数的光滑长度,改善模型中拉应力的稳定性。采用该应力修正算法模拟了无重力条件下方形液滴的震荡变形过程,对比分析了不同算法的模拟结果。此外,为进一步验证算法的适用性,模拟了溃坝算例。研究表明,改进的Quintic型核函数明显改善了粒子聚集现象,该SPH应力修正方法可以使液滴具有更均匀的粒子分布以及更光滑的自由表面,有效改善了SPH方法中的压应力不稳定作用以及自由表面流的模拟精度。

A SPH stress correction algorithm and its application in free surface flow

In order to suppress the stress unstability of SPH method,a stress correction algorithm that calculating the tensile and compressive stress with different kernel functions and state equations is proposed.Then an improved Quintic kernel function improve compressive stress stability of SPH model is introduced.The stress correction algorithm increases Bell-Shaped kernel''s smooth length to promote the tensile stresses stability.Moreover the stress correction algorithm is applied to simulate oscillation and deformation of a square droplet under weightlessness conditions.Several numerical results of different algorithms are proposed for comparative analysis.In addition,to further verify the algorithm''s applicability,this paper simulates a dam break example.Studies show that Improved Quintic kernel function significantly solved particles aggregation problem.The SPH stress correction method can make droplets having more uniform particle distribution and more smooth free surface,effectively improve the stress stability of SPH method as well as the simulation accuracy of free surface flow.