Comptes Rendus
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

Luca Berti 1; Vincent Chabannes 1; Laetitia Giraldi 2; Christophe Prud’homme 1

1 Cemosis, IRMA UMR 7501, CNRS, Université de Strasbourg, France
2 CALISTO team, INRIA, Université Côte d’Azur, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Luca Berti and Vincent Chabannes and Laetitia Giraldi and Christophe Prud{\textquoteright}homme},
     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},
AU  - Luca Berti
AU  - Vincent Chabannes
AU  - Laetitia Giraldi
AU  - Christophe Prud’homme
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
DO  - 10.5802/crmath.234
LA  - en
ID  - CRMATH_2021__359_9_1119_0
ER  - 
%0 Journal Article
%A Luca Berti
%A Vincent Chabannes
%A Laetitia Giraldi
%A Christophe Prud’homme
%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
Luca Berti; Vincent Chabannes; Laetitia Giraldi; Christophe Prud’homme. 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] François Alouges; Antonio DeSimone; L. Giraldi; Marta Zoppello 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] François Alouges; Antonio DeSimone; Luca Heltai; Aline Lefebvre-Lepot; Benoît Merlet Optimally swimming stokesian robots, Discrete Contin. Dyn. Syst., Ser. B, Volume 18 (2013) no. 5, pp. 1189-1215 | DOI | MR | Zbl

[3] Vincent Chabannes; Gonçalo Pena; Christophe Prud’homme 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] Vincent Chabannes; Christophe Prud’homme Github Feel++ repository

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

[6] Roland Glowinski; Tsorng-Whay Pan; Todd I. Hesla; Daniel D. Joseph 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] John Happel; Howard Brenner Low Reynolds number hydrodynamics, Mechanics of Fluids and Transport Processes, Springer, 1983 | DOI | Zbl

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

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

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

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

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

[13] C. Rorai; M. Zaitsev; Sergey Karabasov 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 | DOI | MR

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

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

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

Cited by Sources:

Comments - Policy