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For a sperm cell-like flagellated swimmer in an unbounded domain, severalnumerical models of different fidelity are considered based on the Stokes flowapproximation. The models include a Regularised Stokeslet Method and a 3DFinite Element Method, which serve as the benchmark solutions for severalapproximate models considered. The latter include the Resistive Force Theoryversions of Lighthill and Gray and Hancock as well as a simplifiedapproximation based on computing the hydrodynamic forces exerted on the headand the flagellum separately. It is shown how none of the simplified models isrobust enough with regards to predicting the effect of the swimmer head shapechange on the swimmer dynamics. For a range of swimmer motions considered, theresulting solutions for the swimmer force and velocities are analysed and theapplicability of the Stokes model for the swimmers in question is probed.

On the limitations of some popular numerical models of flagellated microswimmers: importance of long-range forces and flagellum waveform