最优输运无网格方法及其在液滴表面张力效应模拟中的应用

Optimized transportation meshfree method and its apllication in simulating droplet surface tension effect

基于网格的数值方法(如有限元、有限体积、有限差分等)在大变形、不连续等问题中遇到挑战,因此人们提出了多种无网格方法.最优输运无网格方法是一种新型拉格朗日无网格方法,但是继承了有限元方法在边界表征、边界处理等方面的优势,在表面张力模拟中具有较大潜力.基于拉格朗日方程,通过将表面张力势能加入拉格朗日函数,得到的表面张力广义力精确地作用在流体表面,而且表面张力系数是唯一的输入参数.给出了最优输运无网格方法轴对称离散格式.通过对二维/三维泊肃叶流、静止和振动的液滴、液滴变形等典型问题的仿真分析,验证了最优输运无网格方法在表面张力问题模拟中的精度和收敛性.

Owing to challenges encountered by mesh-based CFD methods when simulating large material deformation,a number of meshfree methods have been presented. The optimized transportation meshfree method is a newly developed meshfree method, but it inherits the advantage of the finite element method in boundary treatment and thus having great potential applications in surface tension effect simulation. By adding the surface tension potential into the Lagrangian, the resulting generalized force acts on fluid surfaces exactly. The axial symmetry treatment is also discussed. By simulating several benchmark cases such as two-and three-dimensional Poiseuille flow, static and vibrating drop and drop deformation, the advantages like precision and convergence of the optimized transportation meshfree method in simulating surface tension effect are verified.