Computation of Deformable Interface Two-Phase Flows: A Semi-Lagrangian Finite Element Approach

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Daniel B. V. Santos, Rafael Vidal, Prashant Valluri, Gustavo R. Anjos
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Abstract

This work aims at presenting a new computational approach to study two and three dimensional two-phase flows and two dimensional coalescence phenomenon using direct numerical simulation. The flows are modeled by the incompressible Navier–Stokes equations, which are approximated by the finite element method. The Galerkin formulation is used to discretize the Navier–Stokes equations in the spatial domain and the semi-Lagrangian method is used to discretize the material derivative. In order to satisfy the Ladyzhenskaya–Babuška–Brezzi condition, high-order stable pair of elements are used, with pressure and velocity fields being calculated on different degrees of freedom in the unstructured mesh nodes. The interface is modeled by an unfitted adaptive moving mesh, where interface nodes are tracked in a Lagrangian fashion and moved with the velocity solution of the fluid motion equations. The surface tension is computed using the interface curvature and the gradient of a Heaviside function, and added in the momentum equations as a body force. In order to avoid undesired spurious modes at the interface due to high property ratios, a smooth transition between fluid properties is defined on the interface region. Several benchmark tests have been carried out to validate the proposed approach, and the obtained results have demonstrated agreement with analytical solutions and numerical results reported in the literature. A coalescence model is also proposed based on geometric criteria and results show interesting dynamics.

Abstract Image

本工作旨在提出一种新的计算方法来研究二维和三维两相流和二维聚结现象。流动用不可压缩的Navier-Stokes方程来模拟,该方程用有限元法近似。采用伽辽金公式对空间域内的Navier-Stokes方程进行离散化,采用半拉格朗日方法对材料导数进行离散化。为了满足Ladyzhenskaya-Babuška-Brezzi条件,采用高阶稳定单元对,在非结构化网格节点上计算不同自由度的压力场和速度场。采用非拟合自适应运动网格对界面进行建模,其中界面节点以拉格朗日方式跟踪,并随流体运动方程的速度解移动。利用界面曲率和Heaviside函数的梯度计算表面张力,并将其作为体力加入动量方程中。为了避免由于高性质比而在界面处产生不希望的杂散模式,在界面区域上定义了流体性质之间的平滑过渡。已经进行了几个基准测试来验证所提出的方法,所获得的结果与文献中报道的解析解和数值结果一致。提出了一种基于几何准则的聚结模型,结果显示出有趣的动力学特性。
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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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