Modelling and simulation of 2D stokesian Squirmers
ESAIM. Proceedings, Tome 38 (2012), pp. 36-53
Cet article a éte moissonné depuis la source EDP Sciences
Direct numerical simulations of the individual and collective dynamics of neutral squirmers are presented. “Squirmer” refers to a class of swimmers driven by prescribed tangential deformations at their surface, and “cneutral” means that the swimmer does not apply a force dipole on the fluid. The squirmer model is used in this article to describe self-propelled liquid droplets. Each swimmer is a fluid sphere in Stokes flow without radial velocity and with a prescribed tangential velocity, which is constant in time in the swimmer frame. The interaction between two or more swimmers is taken into account through the relaxation of their translational and angular velocities. The algorithm presented for solving the fluid flow and the motion of the liquid particles is based on a variational formulation written on the whole domain (including the external fluid and the liquid particles) and on a fictitious domain approach. The constraint on the tangential velocity of swimmers can be enforced using two different methods: penalty approach of the strain rate tensor on the particles domain, or a saddle-point formulation involving a Lagrange multiplier associated to the constraint. This leads to a minimization problem over unconstrained functional spaces that can be implemented straightforwardly in a finiteelement multi-purpose solver. In order to ensure robustness, a projection algorithm is used to deal with contacts between particles. Two-dimensional numerical simulations implemented with FreeFem++ are presented.
Affiliations des auteurs :
Nina Aguillon 1 ; Astrid Decoene 1 ; Benoît Fabrèges 1 ; Bertrand Maury 1 ; Benôit Semin 2
@article{EP_2012_38_a2,
author = {Nina Aguillon and Astrid Decoene and Beno{\^\i}t Fabr\`eges and Bertrand Maury and Ben\^oit Semin},
title = {Modelling and simulation of {2D} stokesian {Squirmers}},
journal = {ESAIM. Proceedings},
pages = {36--53},
year = {2012},
volume = {38},
doi = {10.1051/proc/201238003},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201238003/}
}
TY - JOUR AU - Nina Aguillon AU - Astrid Decoene AU - Benoît Fabrèges AU - Bertrand Maury AU - Benôit Semin TI - Modelling and simulation of 2D stokesian Squirmers JO - ESAIM. Proceedings PY - 2012 SP - 36 EP - 53 VL - 38 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201238003/ DO - 10.1051/proc/201238003 LA - en ID - EP_2012_38_a2 ER -
%0 Journal Article %A Nina Aguillon %A Astrid Decoene %A Benoît Fabrèges %A Bertrand Maury %A Benôit Semin %T Modelling and simulation of 2D stokesian Squirmers %J ESAIM. Proceedings %D 2012 %P 36-53 %V 38 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/201238003/ %R 10.1051/proc/201238003 %G en %F EP_2012_38_a2
Nina Aguillon; Astrid Decoene; Benoît Fabrèges; Bertrand Maury; Benôit Semin. Modelling and simulation of 2D stokesian Squirmers. ESAIM. Proceedings, Tome 38 (2012), pp. 36-53. doi: 10.1051/proc/201238003
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