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

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 co...

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Bibliographic Details
Published in:Royal Society open science 2021-05, Vol.8 (5), p.210108-210108
Main Authors: Gallagher, M. T., Smith, D. J.
Format: Article
Language:English
Subjects:
Biological Fluid Dynamics
Mathematics
Stokes Flow
Stokeslets
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Summary: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.
ISSN:2054-5703
2054-5703
DOI:10.1098/rsos.210108