自由面
离散化
压缩性
不可压缩流
数学分析
数学
动量(技术分析)
泊松方程
速度势
流量(数学)
矢量场
经典力学
边值问题
机械
物理
几何学
经济
财务
作者
Fan Zhang,Xiong Zhang,K. Y. Sze,Yuan Lian,Yan Liu
标识
DOI:10.1016/j.jcp.2016.10.064
摘要
To overcome the shortcomings of the weakly compressible material point method (WCMPM) for modeling the free surface flow problems, an incompressible material point method (iMPM) is proposed based on operator splitting technique which splits the solution of momentum equation into two steps. An intermediate velocity field is first obtained by solving the momentum equations ignoring the pressure gradient term, and then the intermediate velocity field is corrected by the pressure term to obtain a divergence-free velocity field. A level set function which represents the signed distance to free surface is used to track the free surface and apply the pressure boundary conditions. Moreover, an hourglass damping is introduced to suppress the spurious velocity modes which are caused by the discretization of the cell center velocity divergence from the grid vertexes velocities when solving pressure Poisson equations. Numerical examples including dam break, oscillation of a cubic liquid drop and a droplet impact into deep pool show that the proposed incompressible material point method is much more accurate and efficient than the weakly compressible material point method in solving free surface flow problems.
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