Abstract
Stokes flow, discussed by G.G. Stokes in 1851, describes many microscopic biological flow phenomena, including cilia-driven transport and flagellar motility; the need to quantify and understand these flows has motivated decades of mathematical and computational research. Regularized stokeslet methods, which have been used and refined over the past 20 years, offer significant advantages in simplicity of implementation, with a recent modification based on nearest-neighbour interpolation providing significant improvements in efficiency and accuracy. Moreover this method can be implemented with the majority of the computation taking place through built-in linear algebra, entailing that state-of-the-art hardware and software developments in the latter, in particular multicore and GPU computing, can be exploited through minimal modifications (‘passive parallelism’) to existing Matlab computer code. Hence, and with widely available GPU hardware, significant improvements in the efficiency of the regularized stokeslet method can be obtained. The approach is demonstrated through computational experiments on three model biological flows: undulatory propulsion of multiple Caenorhabditis elegans, simulation of progression and transport by multiple sperm in a geometrically confined region, and left–right symmetry breaking particle transport in the ventral node of the mouse embryo. In general an order-of-magnitude improvement in efficiency is observed. This development further widens the complexity of biological flow systems that are accessible without the need for extensive code development or specialist facilities.This article is part of the theme issue ‘Stokes at 200 (part 2)’.
Highlights
Stokes flow describes the fluid mechanics of a vast range of microscopic life, for example the motility and generation of feeding currents by microorganisms, and organ cleansing, gamete/embryo transport and developmental patterning in higher organisms
We assess what effect this has on the computational cost of the method by benchmarking against previous work [31,32], as well as providing new simulations of multiple undulatory swimmers and investigating whether sperm-like swimmers are capable of driving particle transport through an enclosed channel
We conclude this review by presenting some experiments along these lines; it will be found that the use of a modest compute-graphical processing unit (GPU) in constructing and solving swimming-type problems can lead to a reduction in the required computational time that can be in excess of an order of magnitude when using the nearest-neighbour regularized stokeslet method
Summary
Stokes flow describes the fluid mechanics of a vast range of microscopic life, for example the motility and generation of feeding currents by microorganisms, and organ cleansing, gamete/embryo transport and developmental patterning in higher organisms. Flow and locomotion involve the action of individual or multiple slender organelles termed flagella and cilia, with the effects of cell surfaces, surrounding cavities and sometimes free surfaces playing crucial roles through hydrodynamic interaction. This biological relevance has motivated decades of research into what we refer to as the Stokes flow equations, originally studied (with the inclusion of an unsteady term) by Stokes [1], which describe Newtonian fluid dynamics in the inertialess regime associated with microscopic length scales. We assess what effect this has on the computational cost of the method by benchmarking against previous work [31,32], as well as providing new simulations of multiple undulatory swimmers and investigating whether sperm-like swimmers are capable of driving particle transport through an enclosed channel
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
