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Variationally derived interface stabilization for discrete multiphase flows and relation with the ghost-penalty method
Computer Methods in Applied Mechanics and Engineering ( IF 6.9 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.cma.2020.113404
Lixing Zhu , Arif Masud

Abstract This paper presents an interface stabilized method for moving and deforming interface problems in immiscible, discrete, multi-phase flows. The evolution of the interface is represented in the momentum balance equations written in an Eulerian frame via the dependence of the local value of density and viscosity of the fluids on the spatial location of the interphase boundary. The motion of the interface is tracked via a hyperbolic equation that is driven by the velocity field furnished by the Navier–Stokes equations. Zero contour of the level set field marks the boundary which is permitted to traverse through the elements. The jump in viscosity and density of the fluids across the arbitrarily deforming phase boundaries can trigger numerical instabilities in the solution. A main contribution in this work is the mathematical analysis of interface stabilization terms that appear naturally when the Variational Multiscale (VMS) method is applied to the coupled system of partial differential equations (PDEs). Two specific forms are developed: full gradient form in R n sd over subdomain Ω I around the embedded interface, and a reduced form in R n sd − 1 for face stabilization at the embedded interface Γ I . Benchmark problems in 2D and 3D are presented to highlight the salient features of the proposed interface stabilization method and to show its range of application.

中文翻译:

离散多相流的变分导出界面稳定性及其与重影惩罚法的关系

摘要 本文提出了一种用于非混相、离散、多相流中移动和变形界面问题的界面稳定方法。通过流体密度和粘度的局部值对界面边界空间位置的依赖性,界面的演化在以欧拉坐标系写成的动量平衡方程中表示。界面的运动通过一个双曲方程来跟踪,该方程由 Navier-Stokes 方程提供的速度场驱动。水平集域的零轮廓标记了允许穿过元素的边界。跨越任意变形相边界的流体粘度和密度的跳跃会引发解中的数值不稳定性。这项工作的主要贡献是对当变分多尺度 (VMS) 方法应用于偏微分方程 (PDE) 耦合系统时自然出现的界面稳定项的数学分析。开发了两种特定形式:R n sd 中嵌入界面周围子域Ω I 上的全梯度形式,以及 R n sd - 1 中用于在嵌入界面 Γ I 处稳定面的简化形式。提出了 2D 和 3D 中的基准问题,以突出所提出的界面稳定方法的显着特征并展示其应用范围。R n sd 中嵌入界面周围子域Ω I 上的全梯度形式,以及 R n sd − 1 中的简化形式,用于嵌入界面 Γ I 处的面稳定。提出了 2D 和 3D 中的基准问题,以突出所提出的界面稳定方法的显着特征并展示其应用范围。嵌入界面周围子域Ω I 上的 R n sd 中的全梯度形式,以及用于嵌入界面 Γ I 处的面稳定的 R n sd − 1 中的简化形式。提出了 2D 和 3D 中的基准问题,以突出所提出的界面稳定方法的显着特征并展示其应用范围。
更新日期:2021-01-01
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