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A boundary element implementation of the regularised Stokeslet method ofCortez is applied to cilia and flagella-driven flows in biology.Previously-published approaches implicitly combine the force discretisation andthe numerical quadrature used to evaluate boundary integrals. By contrast, aboundary element method can be implemented by discretising the force usingbasis functions, and calculating integrals using accurate numerical or analyticintegration. This substantially weakens the coupling of the mesh size for theforce and the regularisation parameter, and greatly reduces the number ofdegrees of freedom required. When modelling a cilium or flagellum as aone-dimensional filament, the regularisation parameter can be considered aproxy for the body radius, as opposed to being a parameter used to minimisenumerical errors. Modelling a patch of cilia, it is found that: (1) For a fixednumber of cilia, reducing cilia spacing reduces transport. (2) For fixed patchdimension, increasing cilia number increases the transport, up to a plateau at$9\times 9$ cilia. Modelling a choanoflagellate cell it is found that thepresence of a lorica structure significantly affects transport and flow outsidethe lorica, but does not significantly alter the force experienced by theflagellum.

A boundary element regularised Stokeslet method applied to cilia and flagella-driven flow