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Method of regularized stokeslets: Flow analysis and improvement of convergence

Boan Zhao1, Eric Lauga1, and Lyndon Koens1,2,*

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
  • 2Department of Mathematics and Statistics, Macquarie University, 192 Balaclava Rd, Macquarie Park, NSW 2113, Australia

  • *lyndon.koens@mq.edu.au
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Phys. Rev. Fluids 4, 084104 – Published 27 August, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.084104

Abstract

Since their development in 2001, regularized stokeslets have become a popular numerical 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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Phys. Rev. Fluids 4, 084104– Published 27 August, 2019
  • Received 17 June 2019
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