不同质量粒子分布SPH方法及其应用

艾孜海尔·哈力克1, 2，热合买提江·依明2，开依沙尔·热合曼2，买买提明·艾尼1

(1. 新疆大学机械工程学院，乌鲁木齐830047;2. 新疆大学数学与系统科学学院，乌鲁木齐830046)

摘要：光滑粒子流体动力学(SPH)方法是一种新发展起来的纯拉格朗日数值方法，其最大的优点是不需要对自由表面进行特殊处理，有利于模拟飞溅、破碎等高度非线性流。SPH方法的一个缺点是计算的时间复杂性高，因为需要大量粒子详细定义流体，使之计算时间相应增加。在核半径保持不变的情况下为了提高计算效率和精度提出不同质量粒子分布的方法，即在关键计算区域分布较小质量粒子，而在其它区域分布较大质量粒子。首先通过静水数值模拟，初步验证了此方法的有效性。之后，对半浸泡振荡圆筒所产生的小振幅水波进行了数值模拟。将数值模拟结果与已有的实验结果进行了对比分析。分析结果表明此方法能够明显提高计算精度的同时可以节省大量计算时间。

关键词：光滑流体动力学方法；波浪；振荡圆筒；不同质量粒子；流体与结构物相互作用

中图分类号:TP391文献标志码：A

基金项目：国家自然科学基金资助(50975036，51275064)；中央高校基本科研业务费专项资金(3132013063)；辽宁省自然科学基金(2015020136)

收稿日期：2014-11-21修改稿收到日期：2015-04-27

SPH method with different mass particle distributions and its application

AZHARHalik1,2,RAHMATJANImin2,KAYSARRahman2,MAMTIMINGeni1(1. School of Mechanical Engineering, Xinjiang University, Urumqi 830047, China; 2. Schools of Mathematics and System Science, Xinjiang University, Urumqi 830046, China)

Abstract:The smoothed particle hydrodynamic (SPH) method is a newly developed pure Lagrangian numerical method, its major advantage is that no special treatment of a free surface is required, it is beneficial for simulating highly non-linear flows to run up and splash around bodies. Its one drawback is that it has a high computational time complexity associated with a large number of particles desirable for good flow definition in order to improve the computation accuracy without substantially increasing computational time. Here, a method with different mass particle distributions was used for a pre-selected area where the high resolution was desirable. The effectiveness of the proposed method was tested and verified with a static water problem. Then, the surface waves generated by an oscillating cylinder with different wave periods and strokes were numerically simulated, and the simulation results were compared with the experimental data. The results showed that using this method brings a significant improvement in the computation accuracy without substantially increasing computational time.

Key words:smoothed particle hydrodynamic (SPH) method; wave; oscillating cylinder; different mass particle

通过欧拉计算流体动力学方法对自由表面流体问题进行处理是比较困难的，主要是因为流体不仅复杂多变，而且运动时所受力的数学模型多为空间和时间函数的偏微分方程，编程实现难度较大。……