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Meshfree and efficient modeling of swimming cells

Meurig T. Gallagher* and David J. Smith†

  • School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom

  • *m.t.gallagher@bham.ac.uk
  • †d.j.smith@bham.ac.uk
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Phys. Rev. Fluids 3, 053101 – Published 31 May, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.053101

Abstract

Locomotion in Stokes flow is an intensively studied problem because it describes important biological phenomena such as the motility of many species' sperm, bacteria, algae, and protozoa. Numerical computations can be challenging, particularly in three dimensions, due to the presence of moving boundaries and complex geometries; methods which combine ease of implementation and computational efficiency are therefore needed. A recently proposed method to discretize the regularized Stokeslet boundary integral equation without the need for a connected mesh is applied to the inertialess locomotion problem in Stokes flow. The mathematical formulation and key aspects of the computational implementation in matlab or GNU Octave are described, followed by numerical experiments with biflagellate algae and multiple uniflagellate sperm swimming between no-slip surfaces, for which both swimming trajectories and flow fields are calculated. These computational experiments required minutes of time on modest hardware; an extensible implementation is provided in a GitHub repository. The nearest-neighbor discretization dramatically improves convergence and robustness, a key challenge in extending the regularized Stokeslet method to complicated three-dimensional biological fluid problems.

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Phys. Rev. Fluids 3, 053101– Published 31 May, 2018
  • Received 23 February 2018
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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