Generalized finite difference method for non-linear free-surface problems of liquid sloshing

Abstract

The generalized finite difference method (GFDM) is a newly developed domain type meshless method,which could truly get rid of time consuming meshing generation and numerical quadrature at every time step and be adopted to simulate the non linear moving boundary physical problems.According to the Lagrangian approach,the GFDM and the leap frog approach were adopted for spatial and temporal discretizations of the sloshing problem in a two dimensional numerical tank,respectively.Results and comparisons via the numerical examples of free sloshing and forced sloshing verified the accuracy,efficiency and stability of the proposed meshless numerical scheme.广义有限差分法属新发展的区域型无网格法，在每个演算时间层内可避免重建网格及数值积分等工作，可用于模拟非线性动态边界的物理问题。针对2维矩形水槽的自由液面晃动问题，以Lagrangia法为基础，采用广义有限差分法配合蛙跳法对于此移动边界问题分别在空间上和时间上进行离散。通过水槽液体自由晃动和受迫振动的数值案例对比，结果表明提出的数值模式在处理自由液面的液体晃动问题的准确性、有效性以及稳定性。