A general system of images for regularized Stokeslets and other elements near a plane wall
A general system of images for regularized Stokeslets and other elements near a plane wall
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DOI：
10.1016/j.jcp.2015.01.019
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发表时间：
2015-03-15
影响因子：
4.1
通讯作者：
Varela, Douglas
中科院分区：
文献类型：
--
作者：
Cortez, Ricardo;Varela, Douglas
我们从一个任意正则化核（blob）开始，推导出正则化源、stokeslet和其他相关元素的一般图像系统，该正则化核（blob）用于模拟以平面为界的三维Stokes流。这是对以前的工作的推广，在以前的工作中，已经为一个特定的blob导出了Stokeslet图像系统。这种推广的意义在于，最近关于正则化方法的工作要求使用设计来满足某些特性的blob，例如零矩条件和快速衰减，因此从任意blob开始的图像系统是绝对必要的。正则化元素的图像系统由几个元素组成，通常是高阶的，这些元素在边界平面上产生零流。为了使所产生的流动在壁上解析地消失，必须使用两个不同但相关的斑点。对于任意给定的blob，我们给出了完成消去的伴生blob的公式，并导出了正则化stokeslet、源和偶极子图像系统的系统计算方法。其他元素可以从这些元素中衍生出来。取正则化参数趋近于零时的极限，求出对应奇异元素的图像系统。(C) 2015爱思唯尔公司版权所有。
We derive a general system of images for regularized sources, Stokeslets, and other related elements starting from an arbitrary regularization kernel (blob) used in the simulation of Stokes flows in three dimensions bounded by a plane. This generalizes previous work in which the image system for a Stokeslet had been derived for one specific blob. The significance of this generalization is that recent work on regularization methods requires the use of blobs designed to satisfy certain properties, such as zero moment conditions and fast decay, and thus it is absolutely necessary to have the system of images starting from an arbitrary blob. The system of images for a regularized element consists of a set of several elements, usually of higher order, that produce a flow that is zero at the bounding plane. In order for the resultant flow to vanish analytically at the wall, two different but related blobs must be used. For any given blob, we provide the formula for the companion blob that accomplishes the cancellation and we derive a systematic way to compute the image system of regularized Stokeslets, sources and dipoles. Other elements can be derived from these. By taking the limit as the regularization parameter approaches zero, the system of images for the corresponding singular elements is found. (C) 2015 Elsevier Inc. All rights reserved.