Issue |
ESAIM: ProcS
Volume 67, 2020
CEMRACS 2018 - Numerical and mathematical modeling for biological and medical applications: deterministic, probabilistic and statistical descriptions
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Page(s) | 46 - 60 | |
DOI | https://doi.org/10.1051/proc/202067004 | |
Published online | 09 June 2020 |
Swimming at low Reynolds number
1 Institut de Recherche Mathématique Avancée, Strasbourg, France
2 Université Côte d’Azur, Inria Sophia-Antipolis, France
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.
Résumé
Nous considérons le probléme de la nage à bas nombre de Reynolds. Ce régime, typique des micro-organismes nageurs, est décrit par les équations de Stokes. Nous couplons un solveur d’EDP des équations de Stokes, construit à l’aide de la librairie aux éléments finis Feel++, avec un solveur de corps rigide basé sur les quaternions. Nous validons les deux solveurs à l’aide d’une solution exacte en 2D pour le fluide et d’une solution exacte pour un corps rigide qui tourne. Nous les appliquons pour simuler la nage d’un micro-organisme qui obéit au théorème de la coquille de Saint-Jacques.
© EDP Sciences, SMAI 2020
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