中文摘要：

介绍了使用LevelSet方法对界面的运动情况进行精确追踪，采用Taylor-Galerkin（TG）有限元方法离散LevelSet方程，易于处理复杂边界。利用不可压缩流体性质，避免求解重新初始化方程。采用有限元方法对剪切流场中界面的运动变化进行数值模拟，并与有限差分方法离散LevelSet方程，修正的Godunov方法求解重新初始化方程的计算结果，进行对比。结果验证TG有限元方法具有简单灵活和易于编程的特点，求解LevelSet方程是可行的。

英文摘要：

Above all, LevelSet method is introduced. Then Taylor-Galerkin （TG）finite element method is used to solve the LevelSet equations. For taking advantage of incompressible flow characteristic, Reinitializtion of Level Set function is avoided. For using finite method, it is easy to handle complicated boundary conditions.By simulating the interface move in the constant, revolving and shear velocity flow fields, as well as comparing with the results by 5th order WENO method and revisement Godnov method, TG method is proved to be the effective method to simulate moving interfaces, and it is easy to write codes.