Swimming at Low Reynolds Number

TL;DR

This paper develops a numerical framework combining PDE and rigid-body solvers to simulate micro-swimmer motion at low Reynolds number, validating results and applying to a scallop theorem-compliant swimmer.

Contribution

It introduces a coupled PDE and quaternion-based rigid-body simulation approach for low Reynolds number swimming, validated against exact solutions.

Findings

Validated numerical results with exact solutions

Successfully simulated a scallop theorem-compliant swimmer

Demonstrated effectiveness of the coupled solver

Abstract

We address the swimming problem at low Reynolds number. This regime, which is typically used for micro-swimmers, is described by Stokes equations. We couple a PDE solver of Stokes equations, derived from the Feel++ finite elements library, to a quaternion-based rigid-body solver. We validate our numerical results both on a 2D exact solution and on an exact solution for a rotating rigid body respectively. Finally, we apply them to simulate the motion of a one-hinged swimmer, which obeys to the scallop theorem.