Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing
Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing
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DOI：
10.1016/j.jcp.2006.03.016
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发表时间：
2006-11-20
影响因子：
4.1
通讯作者：
Hu, Howard H.
中科院分区：
文献类型：
--
作者：
Yue, Pengtao;Zhou, Chunfeng;Hu, Howard H.
本文描述了一种新的模拟非牛顿流体界面动力学的数值算法。两种不混相流体之间的界面被视为一个薄的混合层，其物理性质在其上急剧而连续地变化。界面层的性质和演化是由相场变量0控制的，它服从Cahn-Hilliard型对流扩散方程。这规避了直接跟踪界面的任务，并从存储在混合层中的自由能产生正确的界面张力。粘弹性和其他类型的本构方程可以很容易地纳入变分相场框架。这种方法最大的挑战是解决界面上的急剧梯度。这是通过使用一种有效的自适应网格方案来实现的，该方案由相场变量控制。有限元方案易于适应复杂的流动几何形状，自适应网格划分使模拟复杂流体的大型两相系统成为可能。在二维和轴对称的三维实现中，数值工具包在这里应用于剪切和拉长流动中的液滴变形，液滴的上升和液滴和鸟窝的收缩。其中一些解决方案验证了该方法并说明了其关键特征，而其他解决方案则探索了界面变形和演化中的粘弹性新物理。(c) 2006爱思唯尔公司版权所有。
This paper describes a novel numerical algorithm for simulating interfacial dynamics of non-Newtonian fluids. The interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously. The property and evolution of the interfacial layer is governed by a phase-field variable 0 that obeys a Cahn-Hilliard type of convection-diffusion equation. This circumvents the task of directly tracking the interface, and produces the correct interfacial tension from the free energy stored in the mixing layer. Viscoelasticity and other types of constitutive equations can be incorporated easily into the variational phase-field framework. The greatest challenge of this approach is in resolving the sharp gradients at the interface. This is achieved by using an efficient adaptive meshing scheme governed by the phase-field variable. The finite-element scheme easily accommodates complex flow geometry and the adaptive meshing makes it possible to simulate large-scale two-phase systems of complex fluids. In two-dimensional and axisymmetric three-dimensional implementations, the numerical toolkit is applied here to drop deformation in shear and elongational flows, rise of drops and retraction of drops and torii. Some of these solutions serve as validation of the method and illustrate its key features, while others explore novel physics of viscoelasticity in the deformation and evolution of interfaces. (c) 2006 Elsevier Inc. All rights reserved.