An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flows
An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flows
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DOI：
10.1016/j.jcp.2013.10.018
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发表时间：
2014-01-15
影响因子：
4.1
通讯作者：
Lai, Ming-Chih
中科院分区：
文献类型：
--
作者：
Hu, Wei-Fan;Kim, Yongsam;Lai, Ming-Chih
本文发展了一种简单的浸没边界方法来模拟三维轴对称不可伸缩小泡在Navier-Stokes流动中的动力学。我们没有引入拉格朗日乘子来加强囊泡的不可延伸性约束，而是采用了弹簧式的张力来修正模型，使囊泡的边界几乎是不可展的，从而避免了求解未知张力的问题。我们还从修改的囊泡能量中得到了一个新的弹性力，并得到了与原始未修改的完全相同的形式。为了表示囊泡边界，我们使用了傅立叶谱近似，这样可以更精确地计算界面上的几何量。对该格式进行了一系列数值试验，以说明该方法的适用性和可靠性。我们首先对界面的几何参数进行精度检验，并对不同的刚度数和流体变量进行收敛检验。然后，我们研究了静态流和重力下的囊泡动力学。最后，对Poiseuille流中气泡的形状进行了详细的研究，研究了折合体积、约束和平均流速对气泡形状的影响。数值计算结果与文献结果吻合较好。(C)2013 Elsevier Inc.保留所有权利。
In this paper, we develop a simple immersed boundary method to simulate the dynamics of three-dimensional axisymmetric inextensible vesicles in Navier-Stokes flows. Instead of introducing a Lagrange's multiplier to enforce the vesicle inextensibility constraint, we modify the model by adopting a spring-like tension to make the vesicle boundary nearly inextensible so that solving for the unknown tension can be avoided. We also derive a new elastic force from the modified vesicle energy and obtain exactly the same form as the originally unmodified one. In order to represent the vesicle boundary, we use Fourier spectral approximation so we can compute the geometrical quantities on the interface more accurately. A series of numerical tests on the present scheme have been conducted to illustrate the applicability and reliability of the method. We first perform the accuracy check of the geometrical quantities of the interface, and the convergence check for different stiffness numbers as well as fluid variables. Then we study the vesicle dynamics in quiescent flow and in gravity. Finally, the shapes of vesicles in Poiseuille flow are investigated in detail to study the effects of the reduced volume, the confinement, and the mean flow velocity. The numerical results are shown to be in good agreement with those obtained in literature. (C) 2013 Elsevier Inc. All rights reserved.