A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows
A stabilized finite element method using a discontinuous level set approach for solving two phase incompressible flows
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DOI：
10.1016/j.jcp.2006.04.015
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发表时间：
2006-12
期刊：
影响因子：
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通讯作者：
E. Marchandise;J. Remacle
中科院分区：
文献类型：
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作者：
E. Marchandise;J. Remacle
提出了一种模拟三维不可压缩两相流的数值方法。所提出的算法将用于解决不可压缩两相流问题的隐式压力稳定有限元方法与使用无求积间断伽辽金 (DG) 方法实现的水平集方法结合起来 [E.马尚迪斯，J.-F. Remacle, N. Chevaugeon，水平集方程的自由不连续伽辽金方法，计算物理学杂志 212 (2006) 338–357]。快速轮廓算法的使用[N. Chevaugeon，E. Marchandise，C. Geuzaine，J.-F。 Remacle，高阶有限元的高效可视化，国际工程数值方法杂志]使我们能够准确地定位界面。通过这样做，我们可以计算不连续积分，而无需引入界面厚度或重新初始化水平集。通过“大规模”数值示例（自由表面流：溃坝、晃动）和“小规模”数值示例（两相泊肃叶、瑞利-泰勒不稳定性）证明了所得算法的能力。
A numerical method for the simulation of three-dimensional incompressible two-phase flows is presented. The proposed algorithm combines an implicit pressure stabilized finite element method for the solution of incompressible two-phase flow problems with a level set method implemented with a quadrature-free discontinuous Galerkin (DG) method [E. Marchandise, J.-F. Remacle, N. Chevaugeon, A quadrature free discontinuous Galerkin method for the level set equation, Journal of Computational Physics 212 (2006) 338–357]. The use of a fast contouring algorithm [N. Chevaugeon, E. Marchandise, C. Geuzaine, J.-F. Remacle, Efficient visualization of high order finite elements, International Journal for Numerical Methods in Engineering] permits us to localize the interface accurately. By doing so, we can compute the discontinuous integrals without neither introducing an interface thickness nor reinitializing the level set. The capability of the resulting algorithm is demonstrated with “large scale” numerical examples (free surface flows: dam break, sloshing) and “small scale” ones (two phase Poiseuille, Rayleigh–Taylor instability).