模拟两相流动问题的修正扩展有限元方法

Corrected extended finite element method for two phase flow

基于SUPG/PSPG稳定化方法,在处理两相流不连续问题时,引入修正扩展有限元方法使混合单元附加形函数满足单位分解原理,给出一种模拟两相流体流动问题的扩展有限元方法。在模拟两相流体流动过程中采用水平集方法捕捉流体运动界面。利用编制的计算程序模拟液体自由晃动问题,数值模拟结果与理论解一致。进一步采用本文方法和有限元方法模拟了溃坝流动问题,并将数值结果与实验结果进行比较,结果表明本文方法更有效。本文方法能够准确捕捉流体运动过程中两相界面的变化,且具有在计算过程中无需进行网格重构的优点。

An extended finite element method based on SUPG/PSPG is proposed to simulate the two phase flow problems.A corrected XFEM is introduced to ensure the blending element to satisfy the Partition of Unity in processing the discontinuity of the interface.Level set method is adopted to track the kinetic phase interface as the fluid flow.Free oscillation is numerically simulated with the presented method.The obtained numerical results are in consistent with the analytical and experimental results.Additionally,breaking dam problem is considered,the numerical solutions agree well with experimental results which illustrate the correctness and efficiency of the proposed method.No re-meshing is needed during the simulation of the two phase fluid flow and the moving interface can be accurately tracked by means of the presented method.