The method of images for regularized Stokeslets
The method of images for regularized Stokeslets
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DOI：
10.1016/j.jcp.2008.01.032
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发表时间：
2008-04-20
影响因子：
4.1
通讯作者：
Cortez, Ricardo
中科院分区：
文献类型：
--
作者：
Ainley, Josephine;Durkin, Sandra;Cortez, Ricardo
开发并实现了正则化Stokeslets方法的图像系统。该方法使用光滑的局部化函数来近似由于集中力引起的流体流动的导数中的δ分布。为了满足零流边界条件在一个平面壁，图像的方法导出一个标准的（奇异）Stokeslet的扩展，以精确取消的正则化流在壁。当正则化参数为零时，表达式退化为奇异Stokeslets的已知图像。正则化方法的优点是，即使对于孤立的力或力沿着曲线的分布，它也能给出有界的速度场。这些在纤毛跳动、鞭毛运动和粒子悬浮的模拟中是有用的。力和速度的关系式可以通过求逆来求出产生给定速度边界条件的力。后者是通过将纤毛建模为在三维流动中移动的细丝来举例说明的。根据已知的数据构建不同时间的纤毛速度，并用于确定沿着细丝的力场。然后，这些力量可以在各处复制流动。通过计算球体在壁面附近运动时所受的阻力，验证了该方法的有效性。与已知的阻力表达式的比较表明，该方法给出了准确的结果，即使在距离壁等于表面离散尺寸的范围内的球体。(C)2008年爱思唯尔公司All rights reserved.
The image system for the method of regularized Stokeslets is developed and implemented. The method uses smooth localized functions to approximate a delta distribution in the derivation of the fluid flow due to a concentrated force. In order to satisfy zero-flow boundary conditions at a plane wall, the method of images derived for a standard (singular) Stokeslet is extended to give exact cancellation of the regularized flow at the wall. As the regularization parameter vanishes, the expressions reduce to the known images for singular Stokeslets. The advantage of the regularized method is that it gives bounded velocity fields even for isolated forces or for distributions of forces along curves. These are useful in the simulation of ciliary beats, flagellar motion, and particle suspensions. The expression relating force and velocity can be inverted to find the forces that generate a given velocity boundary condition. The latter is exemplified by modeling a cilium as a filament moving in a three-dimensional flow. The cilium velocity at various times is constructed from known data and used to determine the force field along the filament. Those forces can then reproduce the flow everywhere. The validity of the method is evaluated by computing the drag on a sphere moving near a wall. Comparisons with known expressions for the drag show that the method gives accurate results for spheres even within a distance from the wall equal to the surface discretization size. (C) 2008 Elsevier Inc. All rights reserved.