The stable XFEM for two-phase flows
The stable XFEM for two-phase flows
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DOI：
10.1016/j.compfluid.2012.10.017
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发表时间：
2013-10
影响因子：
2.8
通讯作者：
H. Sauerland;T. Fries
中科院分区：
文献类型：
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作者：
H. Sauerland;T. Fries
扩展有限元法（XFEM）是将不连续解的性质纳入近似空间的常用方法。元件内部的不连续，如它们发生在两相/自由表面流动中，具有隐式界面描述，因此可以适当地解释。然而，XFEM往往容易出现全局系统矩阵的病态，这大大降低了迭代求解技术的性能。本文介绍并研究了利用XFEM规避病态问题的新方法。本文采用了最近提出的稳定XFEM方法进行研究。系统地比较了不同方法的逼近性质和迭代求解器的性能，以改进条件。最后采用两种推荐的设置来解决三维自由面流基准问题和经典两相流问题。据我们所知，这是第一次将稳定的XFEM应用于工业相关的流动问题。
The extended finite element method (XFEM) is frequently used in order to incorporate discontinuous solution properties into the approximation space. Discontinuities inside elements, as theye.g.occur in two-phase/free-surface flows with implicit interface descriptions, can thereby be accounted for appropriately. Yet, the XFEM is often prone to ill-conditioning of the global system matrix which reduces the performance of iterative solution techniques significantly. This paper introduces and studies new approaches to circumvent the problem of ill-conditioning with the XFEM. The stable XFEM, a recently proposed approach, is employed and studied in this work. Approximation properties and iterative solver performance are systematically compared for the different approaches which should improve the conditioning. Two recommended settings are finally used to solve a 3D free-surface flow benchmark problem and a classical two-phase flow problem. To our best knowledge, this is the first time that the stable XFEM is applied to industrially relevant flow problems.