. Ph, C. Angot, P. Bruneau, and . Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math, vol.81, pp.497-520, 1999.

C. Bost, Méthodes Level-Set et pénalisation pour le calcul d'interactions fluide-structure Available for download at http, France, 2008.

F. Boyer and P. Fabrie, Eléments d'analyse pour l'´ etude de quelques modèles d'´ ecoulements de fluides visqueux incompressibles, Mathématiques & Applications, vol.52, 2006.
DOI : 10.1007/3-540-29819-3

H. Brezis, Analyse fonctionnelle, Théorie et applications, 1992.

C. Conca, H. J. San-martín, and M. Tucsnak, Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid, Comm. Partial Differential Equations, vol.25, pp.1019-1042, 2000.

M. Coquerelle and G. Cottet, A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies, Journal of Computational Physics, vol.227, issue.21, pp.9121-9137, 2008.
DOI : 10.1016/j.jcp.2008.03.041

URL : https://hal.archives-ouvertes.fr/hal-00297673

B. Desjardins and M. J. Esteban, Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid, Archive for Rational Mechanics and Analysis, vol.146, issue.1, pp.59-71, 1999.
DOI : 10.1007/s002050050136

R. J. Di-perna and P. , Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. math, pp.511-547, 1989.

H. Fujita and N. Sauer, On existence of weak solutions of the Navier-Stokes equations in regions with moving boundaries, 1A (became from 1993 Journal of mathematical sciences, pp.403-420, 1970.

R. Glowinski, T. W. Pan, T. I. Hesla, D. D. Joseph, and J. Périaux, A Fictitious Domain Approach to the Direct Numerical Simulation of Incompressible Viscous Flow past Moving Rigid Bodies: Application to Particulate Flow, Journal of Computational Physics, vol.169, issue.2, pp.363-426, 2001.
DOI : 10.1006/jcph.2000.6542

C. Grandmont and Y. Maday, Existence de solutions d'un probl??me de couplage fluide-structure bidimensionnel instationnaire, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.4, pp.525-530, 1998.
DOI : 10.1016/S0764-4442(97)89804-7

M. D. Gunzburger, H. Lee, and G. A. Seregin, Global Existence of Weak Solutions for Viscous Incompressible Flows around a Moving Rigid Body in Three Dimensions, Journal of Mathematical Fluid Mechanics, vol.2, issue.3, pp.219-266, 2000.
DOI : 10.1007/PL00000954

M. Hillairet, Lack of Collision Between Solid Bodies in a 2D Incompressible Viscous Flow, Communications in Partial Differential Equations, vol.336, issue.9, pp.1345-1371, 2007.
DOI : 10.1142/S0218202506001303

J. Janela, A. Lefebvre, and B. Maury, A penalty method for the simulation of fluid - rigid body interaction, ESAIM: Proceedings, pp.115-123, 2005.
DOI : 10.1051/proc:2005010

URL : https://hal.archives-ouvertes.fr/hal-00728372

J. Lions, Quelques méthodes de résolutions desprobì emes aux limites non linéaires, 1968.

B. Maury, Direct Simulations of 2D Fluid-Particle Flows in Biperiodic Domains, Journal of Computational Physics, vol.156, issue.2, pp.325-351, 1999.
DOI : 10.1006/jcph.1999.6365

N. A. Patankar, A formulation for fast computations of rigid particulate flows, Center Turbul. Res., Ann. Res. Briefs, pp.185-196, 2001.

J. San-martín, J. Scheid, T. Takahashi, and M. Tucsnak, Convergence of the Lagrange- Galerkin method for the equations modelling the motion of a fluid-rigid system, SIAM J. Numer. Anal, pp.43-1536, 2005.

J. A. San-martin, V. Starovoitov, and M. Tucsnak, Global Weak Solutions??for the Two-Dimensional Motion??of Several Rigid Bodies??in an Incompressible Viscous Fluid, Archive for Rational Mechanics and Analysis, vol.161, issue.2, pp.113-147, 2002.
DOI : 10.1007/s002050100172

A. Sarthou, S. Vincent, J. Caltagirone, . Ph, and . Angot, Eulerian???Lagrangian grid coupling and penalty methods for the simulation of multiphase flows interacting with complex objects, International Journal for Numerical Methods in Fluids, vol.191, issue.8, pp.1-6, 2007.
DOI : 10.1002/fld.1661

N. Sharma and N. A. Patankar, A fast computation technique for the direct numerical simulation of rigid particulate flows, Journal of Computational Physics, vol.205, issue.2, pp.439-457, 2005.
DOI : 10.1016/j.jcp.2004.11.012

R. Temam, Navier Stokes Equations: Theory and Numerical Analysis, Journal of Applied Mechanics, vol.45, issue.2, 1979.
DOI : 10.1115/1.3424338