Method of regularized stokeslets: flow analysis and improvement of convergence

Boan Zhao, Eric Lauga, Lyndon Koens*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)
    25 Downloads (Pure)

    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.

    Original languageEnglish
    Article number084104
    Pages (from-to)1-21
    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.

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