The art of coarse Stokes: Richardson extrapolation improves the accuracy and efficiency of the method of regularized stokeslets

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Abstract

The method of regularized stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly varying regularized stokeslet kernel. Here, we show how Richardson extrapolation with coarse values of the regularization parameter is ideally suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency.

Original languageEnglish
Article number210108
JournalRoyal Society Open Science
Volume8
Issue number5
DOIs
Publication statusPublished - 26 May 2021

Bibliographical note

Funding Information:
Data accessibility. Data and relevant code for this research work are stored in GitLab: https://gitlab.com/ meuriggallagher/the-art-of-coarse-stokes (MATLAB code for Nyström and Richardson extrapolation) and https:// gitlab.com/meuriggallagher/NEAREST (MATLAB code for NEAREST and other dependencies); and have been archived within the Zenodo repository: https://doi.org/10.5281/zenodo.4632956. Competing interests. We declare we have no competing interests. Funding. This work was supported by Engineering and Physical Sciences Research Council (EPSRC) award no. EP/N021096/1. M.T.G. acknowledges support from EPSRC Centre grant no. EP/N014391/2. Acknowledgements. We thank Eamonn Gaffney and Kenta Ishimoto for valuable discussion.

Publisher Copyright:
© 2021 The Authors.

Keywords

  • regularized stokeslets
  • richardson extrapolation
  • Stokes flow

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation

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