水珠滴落的最小二乘粒子有限元方法模拟  

Numerical simulation of liquid drop phenomenon by least square particle finite element method

作　　者：汤波[1] 李俊峰[1] 王天舒[1] 

机构地区：[1]清华大学航天航空学院,北京100084

出　　处：《物理学报》2008年第11期6722-6729,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10302013;10572022)资助的课题~~

摘　　要：提出了一种最小二乘粒子有限元方法,用其模拟了二维水珠滴落水面并飞溅散开的过程.该法基于拉格朗日描述,在每个时间步上使用扩展的Delaunay划分更新计算网格,并应用α形方法识别自由面形状;用最小二乘有限元方法离散流体运动的Navier-Stokes方程,并推导了一种自适应时间步长方案以提高计算效率和鲁棒性;引入网格拉伸技术修正减小流体质量误差.对水滴飞溅进行仿真,得到了与商用软件Flow-3d比较符合的结果,且具有更清晰锐利的自由面.A least square particle finite element method is presented and used to simulate the impact and splash of 2D water droplets on the water surface.This algorithm is based on an upgraded Lagrangian framework.An extended Delaunay triangulation method is used to get the new mesh at every time step.An alpha-shape method is used to deal with the splash and impact of the free surface.The least square finite element method is applied to solve the Navier-Stokes equations.An adaptive time step algorithm is derived to improve the efficiency and the robustness of calculation,and a mesh pulling scheme is introduced to improve the conservation of the total mass.Finally,when compared with the commercial Flow-3d code,the computational results achieve good agreement.Moreover,the free surface is more accurate and more clearcut than that of the Eulerian description based Flow-3d code.

关 键 词：滴落 网格划分 α形 最小二乘有限元 

分 类 号：O411.3[理学—理论物理]