Numerical investigations of the XFEM for solving two-phase incompressible flows
Numerical investigations of the XFEM for solving two-phase incompressible flows
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DOI：
10.1080/10618562.2017.1322200
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发表时间：
2017-03
影响因子：
1.3
通讯作者：
Adil Fahsi;A. Soulaïmani
中科院分区：
文献类型：
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作者：
Adil Fahsi;A. Soulaïmani
本文讨论了扩展有限元方法在求解两相不可压缩流动中的应用。Navier-Stokes方程采用Taylor-Hood有限元离散。为了捕捉界面上不同的不连续面，速度场和/或压力场采用了扭结或跳跃富集法。然而，这些丰富可能会导致不适当的内插组合。研究了不同的多项式富化阶数和不同的富化函数；之后只使用稳定的组合。在有表面张力的情况下，精度主要取决于法线和曲率的精确计算。提出了一种计算界面法向量的新方法。该方法在切割元素内部使用连续的网格细化。与解析解和数值解的比较表明，该方法是有效的。此外，网格细化改进了XFEM中的子积分，并允许精确的重新初始化过程。
ABSTRACT This paper discusses the application of the extended finite element method (XFEM) to solve two-phase incompressible flows. The Navier–Stokes equations are discretised using the Taylor–Hood finite element. To capture the different discontinuities across the interface, kink or jump enrichments are used for the velocity and/or pressure fields. However, these enrichments may lead to an inappropriate combination of interpolations. Different polynomial enrichment orders and different enrichment functions are investigated; only the stable combination will be used afterward. In cases with a surface tension force, the accuracy mainly relies on the precise computation of the normal and curvature. A novel method for computing normal vectors to the interface is proposed. This method employs successive mesh refinements inside the cut elements. Comparisons with analytical and numerical solutions demonstrate that the method is effective. Moreover, the mesh refinement improves the sub-integration in the XFEM and allows for a precise re-initialisation procedure.