Numerical analysis, Partial differential equations
Modelling and finite element simulation of multi-sphere swimmers
Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1119-1127.

We propose a numerical method for the finite element simulation of micro-swimmers composed of several rigid bodies moving relatively to each other. Three distinct formulations are proposed to impose the relative velocities between the rigid bodies. We validate our model on the three-sphere swimmer, for which analytical results are available.

Dans cet article nous proposons une méthode numérique pour la simulation aux éléments finis d’une classe de micro-nageurs. Ces nageurs sont composés par différents corps rigides qui peuvent bouger les uns par rapport aux autres. Nous appliquons notre méthode sur un exemple de micro-nageur connu sous le nom de Three-sphere swimmer.

Published online:
DOI: 10.5802/crmath.234
Classification: 65M60, 74F10, 76D07, 76M10
Berti, Luca 1; Chabannes, Vincent 1; Giraldi, Laetitia 2; Prud’homme, Christophe 1

1 Cemosis, IRMA UMR 7501, CNRS, Université de Strasbourg, France
2 CALISTO team, INRIA, Université Côte d’Azur, France
     author = {Berti, Luca and Chabannes, Vincent and Giraldi, Laetitia and Prud{\textquoteright}homme, Christophe},
     title = {Modelling and finite element simulation of multi-sphere swimmers},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1119--1127},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {9},
     year = {2021},
     doi = {10.5802/crmath.234},
     language = {en},
     url = {}
AU  - Berti, Luca
AU  - Chabannes, Vincent
AU  - Giraldi, Laetitia
AU  - Prud’homme, Christophe
TI  - Modelling and finite element simulation of multi-sphere swimmers
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 1119
EP  - 1127
VL  - 359
IS  - 9
PB  - Académie des sciences, Paris
UR  -
DO  - 10.5802/crmath.234
LA  - en
ID  - CRMATH_2021__359_9_1119_0
ER  - 
%0 Journal Article
%A Berti, Luca
%A Chabannes, Vincent
%A Giraldi, Laetitia
%A Prud’homme, Christophe
%T Modelling and finite element simulation of multi-sphere swimmers
%J Comptes Rendus. Mathématique
%D 2021
%P 1119-1127
%V 359
%N 9
%I Académie des sciences, Paris
%R 10.5802/crmath.234
%G en
%F CRMATH_2021__359_9_1119_0
Berti, Luca; Chabannes, Vincent; Giraldi, Laetitia; Prud’homme, Christophe. Modelling and finite element simulation of multi-sphere swimmers. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1119-1127. doi : 10.5802/crmath.234.

[1] Alouges, François; DeSimone, Antonio; Giraldi, L.; Zoppello, Marta Self-propulsion of slender micro-swimmers by curvature control: N-link swimmers, Int. J. Non-Linear Mech., Volume 56 (2013), pp. 132-141 | DOI

[2] Alouges, François; DeSimone, Antonio; Heltai, Luca; Lefebvre-Lepot, Aline; Merlet, Benoît Optimally swimming stokesian robots, Discrete Contin. Dyn. Syst., Ser. B, Volume 18 (2013) no. 5, pp. 1189-1215 | DOI | MR | Zbl

[3] Chabannes, Vincent; Pena, Gonçalo; Prud’homme, Christophe High-order fluid-structure interaction in 2D and 3D application to blood flow in arteries, J. Comput. Appl. Math., Volume 246 (2013), pp. 1-9 Fifth International Conference on Advanced COmputational Methods in ENgineering (ACOMEN 2011) | DOI | MR | Zbl

[4] Chabannes, Vincent; Prud’homme, Christophe Github Feel++ repository

[5] Elman, Howard C.; Silvester, David J.; Wathen, Andrew J. Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics, Numerical Mathematics and Scientific Computation, Oxford University Press, 2014 | Zbl

[6] Glowinski, Roland; Pan, Tsorng-Whay; Hesla, Todd I.; Joseph, Daniel D. A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, Volume 25 (1999) no. 5, pp. 755-794 | DOI | MR

[7] Happel, John; Brenner, Howard Low Reynolds number hydrodynamics, Mechanics of Fluids and Transport Processes, Springer, 1983 | DOI | Zbl

[8] Kanchi, Harish; Masud, Arif A 3D adaptive mesh moving scheme, Int. J. Numer. Methods Fluids, Volume 54 (2007) no. 6-8, pp. 923-944 | DOI | MR | Zbl

[9] Kim, S.; Karrila, S. J. Microhydrodynamics: Principles and Selected Applications, Butterworth–Heinemann series in chemical engineering, Dover Publications, 2005

[10] Lefebvre-Lepot, Aline; Merlet, Benoît A stokesian submarine, ESAIM, Proc., Volume 28 (2009), pp. 150-161 | DOI | MR | Zbl

[11] Maury, Bertrand Direct simulations of 2D fluid-particle flows in biperiodic domains, J. Comput. Phys., Volume 156 (1999) no. 2, pp. 325-351 | DOI | Zbl

[12] Najafi, Ali; Golestanian, Ramin Simple swimmer at low Reynolds number: Three linked spheres, Phys. Rev. E, Volume 69 (2004), p. 062901 | DOI

[13] Rorai, C.; Zaitsev, M.; Karabasov, Sergey On the limitations of some popular numerical models of flagellated microswimmers: importance of long-range forces and flagellum waveform, R. Soc. open sci., Volume 6 (2019) no. 1, p. 180745 (Accessed 2021-03-02) | DOI | MR

[14] Tsang, Alan Cheng Hou; Tong, Pun Wai; Nallan, Shreyes; Pak, On Shun Self-learning how to swim at low Reynolds number, Phys. Rev. Fluids, Volume 5 (2020) no. 7, p. 074101 (Accessed 2021-02-25) | DOI

[15] Vladimirov, V. A. On the self-propulsion of an N -sphere micro-robot, J. Fluid Mech., Volume 716 (2013), R1, 11 pages | DOI | MR | Zbl

[16] Walker, Benjamin J.; Wheeler, Richard J.; Ishimoto, Kenta; Gaffney, Eamonn A. Boundary behaviours of Leishmania mexicana: A hydrodynamic simulation study, J. Theor. Biol., Volume 462 (2019), pp. 311-320 | DOI | Zbl

Cited by Sources: