Method of regularized stokeslets: flow analysis and improvement of convergence

Boan Zhao, Eric Lauga, Lyndon Koens

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Since their development in 2001, regularized stokeslets have become a popular nu- merical tool for low-Reynolds-number flows since the replacement of a point force by a smoothed blob overcomes many computational difficulties associated with flow singularities [Cortez, SIAM J. Sci. Comput. 23, 1204 (2001)]. The physical changes to the flow resulting from this process are, however, unclear. In this paper, we analyze the flow induced by general regularized stokeslets. An explicit formula for the flow from any regularized stokeslet is first derived, which is shown to simplify for spherically symmetric blobs. Far from the center of any regularized stokeslet we show that the flow can be written in terms of an infinite number of singularity solutions provided the blob decays sufficiently rapidly. This infinite number of singularities reduces to a point force and source dipole for spherically symmetric blobs. Slowly decaying blobs induce additional flow resulting from the nonzero body forces acting on the fluid. We also show that near the center of spherically symmetric regularized stokeslets the flow becomes isotropic, which contrasts with the flow anisotropy fundamental to viscous systems. The concepts developed are used to identify blobs that reduce regularization errors. These blobs contain regions of negative force in order to counter the flows produced in the regularization process but still retain a form convenient for computations.

LanguageEnglish
Article number084104
Pages1-21
Number of pages21
JournalPhysical Review Fluids
Volume4
Issue number8
DOIs
Publication statusPublished - Aug 2019

Bibliographical note

Copyright American Physical Society 2019. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Cite this

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abstract = "Since their development in 2001, regularized stokeslets have become a popular nu- merical tool for low-Reynolds-number flows since the replacement of a point force by a smoothed blob overcomes many computational difficulties associated with flow singularities [Cortez, SIAM J. Sci. Comput. 23, 1204 (2001)]. The physical changes to the flow resulting from this process are, however, unclear. In this paper, we analyze the flow induced by general regularized stokeslets. An explicit formula for the flow from any regularized stokeslet is first derived, which is shown to simplify for spherically symmetric blobs. Far from the center of any regularized stokeslet we show that the flow can be written in terms of an infinite number of singularity solutions provided the blob decays sufficiently rapidly. This infinite number of singularities reduces to a point force and source dipole for spherically symmetric blobs. Slowly decaying blobs induce additional flow resulting from the nonzero body forces acting on the fluid. We also show that near the center of spherically symmetric regularized stokeslets the flow becomes isotropic, which contrasts with the flow anisotropy fundamental to viscous systems. The concepts developed are used to identify blobs that reduce regularization errors. These blobs contain regions of negative force in order to counter the flows produced in the regularization process but still retain a form convenient for computations.",
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Method of regularized stokeslets : flow analysis and improvement of convergence. / Zhao, Boan; Lauga, Eric; Koens, Lyndon.

In: Physical Review Fluids, Vol. 4, No. 8, 084104, 08.2019, p. 1-21.

Research output: Contribution to journalArticleResearchpeer-review

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