Regularized image system for Stokes flow outside a solid sphere

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• 作者：Jacek K. Wró ; bel^a ; ^{jwrobel@tulane.edu" class="auth_mail" title="E-mail the corresponding author} ; Ricardo Cortez^a ; ^{rcortez@tulane.edu" class="auth_mail" title="E-mail the corresponding author} ; Douglas Varela^b ; ^{dvarela@davinci-camp.com" class="auth_mail" title="E-mail the corresponding author} ; Lisa Fauci^a ; ^{fauci@tulane.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Regularized Stokeslets ; Method of images ; Flow outside a sphere
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 July 2016
• 年：2016
• 卷：317
• 期：Complete
• 页码：165-184
• 全文大小：4863 K

文摘

The image system for a three-dimensional flow generated by regularized forces outside a solid sphere is formulated and implemented as an extension of the method of regularized Stokeslets. The method is based on replacing a point force given by a delta distribution with a smooth localized function and deriving the exact velocity field produced by the forcing. In order to satisfy zero-flow boundary conditions at a solid sphere, the image system for singular Stokeslets is generalized to give exact cancellation of the regularized flow at the surface of the sphere. The regularized image system contains the same elements as the singular counterpart but with coefficients that depend on a regularization parameter. As this parameter vanishes, the expressions reduce to the image system of the singular Stokeslet. The expression relating force and velocity can be inverted to compute the forces that generate a given velocity boundary condition elsewhere in the flow. We present several examples within the context of biological flows at the microscale in order to validate and highlight the usefulness of the image system in computations.