2D conservative sharp interface method for compressible three-phase flows: Ternary fluid flows and interaction of two-phase flows with solid

IF 3.8 2区 物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Zhu-Jun Li , Yi Ren , Yi Shen , Hang Ding
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Abstract

In this article, we propose a 2D conservative sharp interface method to simulate compressible three-phase flows that encompasses both ternary fluid flows and two-phase flows involving complex solid geometries. The evolution of the fluid-fluid interfaces and the geometry of the solid objects are tracked by a regional level-set function, and are repeatedly reconstructed on a background Cartesian mesh using line segments at each time step. To achieve a high resolution of the interfaces, we identify triple points where the ternary fluids meet or where the interface intersects with solid walls during the reconstruction process. Additionally, by exploiting the symmetry and rotational symmetry of fluid (and solid) positions within a cut cell (i.e., a Cartesian cell containing at least two phases), we reduce the configurations of the cut cells from 96 to 6 basic ones for two-dimensional simulations. Special treatment is also implemented for the cell assembly process in the vicinity of triple points. To ensure a unified approach to boundary conditions, we first identify the specific properties of the reconstructed interfaces, and subsequently enforce appropriate boundary conditions (i.e., jump conditions for interfaces and no-penetration conditions for solid walls) through the solution of a local 1D Riemann problem along the direction normal to the corresponding reconstructed interface. We employ a second-order finite volume method within the arbitrary Lagrange-Eulerian framework to discretize the Euler equations, thereby ensuring that the conservation of mass, momentum, and energy is maintained during the flow computation. The accuracy and robustness of the method are evaluated through numerous numerical experiments, including the compressible triple point problem, the interaction between a shock wave and a multi-medium bubble, high-speed droplet impingement on curved surfaces, and the water entry of a sphere at a uniform speed. The numerical results are validated against benchmark solutions available in the literature. Furthermore, the method is shown to effectively preserve the physical symmetry of ternary fluid flows, primarily due to the geometric resolution of the triple points and second-order accuracy in resolving interfaces.
可压缩三相流的二维保守锐界面法:三元流体流动及两相流与固体的相互作用
在本文中,我们提出了一种二维保守锐界面方法来模拟可压缩三相流动,包括三元流体流动和涉及复杂固体几何形状的两相流动。通过区域水平集函数跟踪流体-流体界面的演变和固体物体的几何形状,并在每个时间步长使用线段在背景笛卡尔网格上重复重建。为了获得界面的高分辨率,我们在重建过程中确定了三元流体相遇或界面与固体壁相交的三点。此外,通过利用切割细胞(即包含至少两个相的笛卡尔细胞)内流体(和固体)位置的对称性和旋转对称性,我们将切割细胞的配置从96个减少到6个基本的二维模拟。在三相点附近的电池装配过程中也实施了特殊处理。为了确保边界条件的统一方法,我们首先确定重建界面的具体属性,然后通过求解相应重建界面法向的局部1D黎曼问题,强制执行适当的边界条件(即界面的跳跃条件和实体壁的无穿透条件)。我们在任意拉格朗日-欧拉框架内采用二阶有限体积法离散欧拉方程,从而确保在流动计算过程中保持质量、动量和能量的守恒。通过大量的数值实验,包括可压缩三相点问题、激波与多介质气泡的相互作用、液滴在曲面上的高速撞击以及水以匀速进入球体等,评估了该方法的准确性和鲁棒性。数值结果与文献中可用的基准解进行了验证。此外,该方法有效地保持了三元流体流动的物理对称性,这主要归功于三点的几何分辨率和解析界面的二阶精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Computational Physics
Journal of Computational Physics 物理-计算机:跨学科应用
CiteScore
7.60
自引率
14.60%
发文量
763
审稿时长
5.8 months
期刊介绍: Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.
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