V. La-figure, ) pour un poids adimensionnel F = 402.1, ainsi que son spectre de puissance du signal Y 1 (t) La trajectoire est périodique de fréquence f 1 ? 0.369Hz. En augmentant F (F ? 420), la trajectoire reste périodique et les premiers harmoniques de f 1 apparaissent (Cf. figure V.12)

. La-dynamique-périodique-perdure-jusqu-'à-f-?-486, A partir de cette valeur, la dynamique des particules devient quasi-périodique à deux fréquences, f 1 et f 2 Un exemple est donné sur la figure V.13, ce cas, les positions des différents pics du spectre de puissance du signal Y 1 (t) sont des combinaisons linéaires des fréquences f 1 et f 2 commme nous le montrons sur la figure V.14

F. Enfin-lorsque, le spectre de puissance du signal Y 1 (t) devient complètement bruité, caractéristique d'une dynamique chaotique (Cf

C. K. Aidun, E. Et, and . Ding, Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state, Physics of Fluids, vol.55, issue.6, pp.1612-1626, 2003.
DOI : 10.1103/PhysRevE.55.2397

L. O. Amoudry, A. J. Et, and . Souza, DETERMINISTIC COASTAL MORPHOLOGICAL AND SEDIMENT TRANSPORT MODELING: A REVIEW AND DISCUSSION, Reviews of Geophysics, vol.120, issue.9, 2011.
DOI : 10.1061/(ASCE)0733-9429(1994)120:9(1021)

M. Andrews, P. Et, and . O-'rourke, The multiphase particle-in-cell (MP-PIC) method for dense particulate flows, International Journal of Multiphase Flow, vol.22, issue.2, pp.379-402, 1996.
DOI : 10.1016/0301-9322(95)00072-0

J. F. Brady, G. Et, and . Bossis, Stokesian Dynamics, Annual Review of Fluid Mechanics, vol.20, issue.1, pp.111-157, 1988.
DOI : 10.1146/annurev.fl.20.010188.000551

S. Champmartin, Matrice de résistance et description du mouvement d'une particule en interaction hydrodynamique et conséquences du confinement asymétrique sur les phénomènes de transfert, pp.79-82, 2006.

J. Chauchat, Contribution à la modélisation diphasique du transport sédimentaire en milieu côtier et estuarien, 2007.

A. J. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

N. De-mestre and W. Et, Low-Reynolds-number translation of a slender cylinder near a plane wall, Journal of Engineering Mathematics, vol.1, issue.2, pp.81-91, 1975.
DOI : 10.1007/BF01535390

B. Dvinsky, A. Et, and A. Popel, Motion of a rigid cylinder between parallel plates in stokes flow, Computers & Fluids, vol.15, issue.4, p.391, 1987.
DOI : 10.1016/0045-7930(87)90031-4

J. Feng, H. H. Hu, and D. D. Joseph, Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation, Journal of Fluid Mechanics, vol.141, issue.-1, pp.95-134, 1994.
DOI : 10.1017/S0022112092001368

J. Feng, P. Huang, and E. D. Joseph, Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid, Journal of Non-Newtonian Fluid Mechanics, vol.63, issue.1, pp.63-88, 1996.
DOI : 10.1016/0377-0257(95)01412-8

Z. Feng, E. E. Et, and . Michaelides, The immersed boundary-lattice Boltzmann method for solving fluid???particles interaction problems, Journal of Computational Physics, vol.195, issue.2, pp.602-628, 2004.
DOI : 10.1016/j.jcp.2003.10.013

A. F. Fortes, D. D. Joseph, and T. S. Lundgren, Nonlinear mechanics of fluidization of beds of spherical particles, Journal of Fluid Mechanics, vol.18, issue.-1, pp.467-83, 1987.
DOI : 10.1017/S0022112066001721

R. Glowinski, T. Pan, T. Hesla, and E. D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows, International Journal of Multiphase Flow, vol.25, issue.5, pp.755-794, 1999.
DOI : 10.1016/S0301-9322(98)00048-2

R. Glowinski, T. Pan, T. Hesla, D. Joseph, and E. 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

E. Guazzelli, J. Morris, and E. S. Pic, A Physical Introduction to Suspension Dynamics, Cambridge Texts in Applied Mathematics, vol.256, p.101, 2011.
DOI : 10.1017/CBO9780511894671

S. Guillou, R. Et, and . Makhloufi, Effect of a shear-thickening rheological behaviour on the friction coefficient in a plane channel flow: A study by Direct Numerical Simulation, Journal of Non-Newtonian Fluid Mechanics, vol.144, issue.2-3, pp.73-86, 2007.
DOI : 10.1016/j.jnnfm.2007.03.008

S. Guillou, J. Thiébot, J. Chauchat, R. Verjus, A. Besq et al., The Filling Dynamics of an Estuary: From the Process to the Modelling, pp.125-146, 2011.
DOI : 10.5772/19933

URL : https://hal.archives-ouvertes.fr/hal-00696510

S. Haeri, J. Et, and . Shrimpton, On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows, International Journal of Multiphase Flow, vol.40, issue.0, pp.38-55, 2012.
DOI : 10.1016/j.ijmultiphaseflow.2011.12.002

E. Y. Harper, I. Et, and . Chang, Drag on a Cylinder between Parallel Walls in Stokes' Flow, Physics of Fluids, vol.10, issue.1, pp.83-88, 1958.
DOI : 10.1063/1.1761999

K. Höfler, S. Et, and . Schwarzer, Navier-Stokes simulation with constraint forces: Finite-difference method for particle-laden flows and complex geometries, Physical Review E, vol.283, issue.6, pp.7146-7160, 2000.
DOI : 10.1017/S0022112095002217

H. Hu, Direct simulation of flows of solid-liquid mixtures, International Journal of Multiphase Flow, vol.22, issue.2, pp.335-352, 1996.
DOI : 10.1016/0301-9322(95)00068-2

H. H. Hu, Motion of a circular cylinder in a viscous liquid between parallel plates, Theoretical and Computational Fluid Dynamics, pp.441-455, 1995.

H. H. Hu, D. D. Joseph, and M. J. Crochet, Direct simulation of fluid particle motions, Theoretical and Computational Fluid Dynamics, pp.285-306, 1007.

H. H. Hu, N. Patankar, and E. M. Zhu, Direct Numerical Simulations of Fluid???Solid Systems Using the Arbitrary Lagrangian???Eulerian Technique, Journal of Computational Physics, vol.169, issue.2, pp.427-462, 2001.
DOI : 10.1006/jcph.2000.6592

K. Jayaweera, B. Mason, and E. G. Slack, The behaviour of clusters of spheres falling in a viscous fluid Part 1. Experiment, Journal of Fluid Mechanics, vol.5, issue.01, pp.121-128, 1964.
DOI : 10.1088/0508-3443/11/2/111

K. O. Jayaweera, B. J. Et, and . Mason, The behaviour of freely falling cylinders and cones in a viscous fluid, Journal of Fluid Mechanics, vol.16, issue.04, pp.709-720, 1965.
DOI : 10.1063/1.1721373

B. Joseph and D. D. , Interrogations of direct numerical simulation of solid-liquid flow, Web based book, p.133, 2002.

G. Joseph, Collisional dynamics of macroscopic particles in a viscous fluid, p.11, 2003.

S. Kim, S. Et, and . Karrila, Microhydrodynamics : Principles And Selected Applications, Dover Civil and Mechanical Engineering Series, p.12, 1991.

A. J. Ladd, Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation, Journal of Fluid Mechanics, vol.21, issue.8, pp.285-309, 1994.
DOI : 10.1063/1.454658

M. Lai, C. S. Et, and . Peskin, An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity, Journal of Computational Physics, vol.160, issue.2, pp.705-719, 2000.
DOI : 10.1006/jcph.2000.6483

J. Lee, J. Kim, H. Choi, and K. Yang, Sources of spurious force oscillations from an immersed boundary method for moving-body problems, Journal of Computational Physics, vol.230, issue.7, pp.2677-2695, 2011.
DOI : 10.1016/j.jcp.2011.01.004

C. Liu, X. Zheng, and E. C. Sung, Preconditioned Multigrid Methods for Unsteady Incompressible Flows, Journal of Computational Physics, vol.139, issue.1, pp.35-57, 1998.
DOI : 10.1006/jcph.1997.5859

Y. Liu, J. Nelson, J. Feng, and E. D. Joseph, Anomalous rolling of spheres down an inclined plane, Journal of Non-Newtonian Fluid Mechanics, vol.50, issue.2-3, pp.305-329, 1993.
DOI : 10.1016/0377-0257(93)80036-B

R. Mittal, G. Et, and . Iaccarino, IMMERSED BOUNDARY METHODS, Annual Review of Fluid Mechanics, vol.37, issue.1, pp.239-261, 2005.
DOI : 10.1146/annurev.fluid.37.061903.175743

T. Pan, R. Et, and . Glowinski, Direct Simulation of the Motion of Neutrally Buoyant Circular Cylinders in Plane Poiseuille Flow, Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160, pp.260-279, 1998.
DOI : 10.1006/jcph.2002.7123

N. Patankar and H. Hu, A Numerical Investigation of the Detachment of the Trailing Particle From a Chain Sedimenting in Newtonian and Viscoelastic Fluids, Journal of Fluids Engineering, vol.22, issue.3, pp.517-521, 2000.
DOI : 10.1016/0301-9322(95)00068-2

N. Patankar, D. Et, and . Joseph, Modeling and numerical simulation of particulate flows by the Eulerian???Lagrangian approach, International Journal of Multiphase Flow, vol.27, issue.10, pp.1659-1684, 2001.
DOI : 10.1016/S0301-9322(01)00021-0

N. Patankar, P. Singh, D. Joseph, and R. Glowinski, A new formulation of the distributed Lagrange multiplier/fictitious domain method for particulate flows, International Journal of Multiphase Flow, vol.26, issue.9, pp.1509-1524, 2000.
DOI : 10.1016/S0301-9322(99)00100-7

S. M. Peker, S. Et, and . Helvaci, 4 -motion of particles in fluids, in Solid-Liquid Two Phase Flow, pp.245-289, 2007.

C. S. Peskin, Numerical analysis of blood flow in the heart, Journal of Computational Physics, vol.25, issue.3, pp.220-252, 1977.
DOI : 10.1016/0021-9991(77)90100-0

C. S. Peskin, The immersed boundary method, Acta Numerica, vol.11, pp.479-517, 2002.

A. Prosperetti, G. Et, and . Tryggvason, Computational Methods For Multiphase Flow, Cambridge books online, 470 pp, p.133, 2007.

J. Richardson, W. Et, and . Zaki, Sedimentation and fluidisation: Part I, Chemical Engineering Research and Design, vol.75, issue.119, pp.35-53, 1954.
DOI : 10.1016/S0263-8762(97)80006-8

A. B. Richou, A. Ambari, M. Lebey, and E. J. Naciri, Drag force on a circular cylinder midway between two parallel plates at Part 2: moving uniformly (numerical and experimental), Chemical Engineering Science, vol.60, issue.10, pp.2535-2543, 2005.
DOI : 10.1016/j.ces.2004.08.050

A. M. Bibliographie-roma, C. S. Peskin, M. J. Berger????????@bullet?, ?. ??, and . ?????????, An Adaptive Version of the Immersed Boundary Method, Journal of Computational Physics, vol.153, issue.2, pp.509-534, 1999.
DOI : 10.1006/jcph.1999.6293

D. Ruelle, F. Et, and . Takens, On the nature of turbulence, Communications in Mathematical Physics, vol.169, issue.3, pp.167-192, 1971.
DOI : 10.1007/BF01646553

M. Sahin, R. G. Et, and . Owens, A numerical investigation of wall effects up to high blockage ratios on two-dimensional flow past a confined circular cylinder, Physics of Fluids, vol.187, issue.5, pp.16-1305, 1994.
DOI : 10.1016/S0377-0257(97)00067-0

N. Sharma, N. A. Et, and . 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

A. Sierou, J. F. Et, and . Brady, Accelerated Stokesian Dynamics simulations, Journal of Fluid Mechanics, vol.448, pp.115-146, 2001.
DOI : 10.1017/S0022112001005912

A. L. Silva, A. Silveira-neto, and E. J. Damasceno, Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method, Journal of Computational Physics, vol.189, issue.2, pp.351-370, 2003.
DOI : 10.1016/S0021-9991(03)00214-6

S. Singha, K. Et, and . Sinhamahapatra, Flow past a circular cylinder between parallel walls at low Reynolds numbers, Ocean Engineering, pp.757-769, 2010.

G. Stokes, the Effect of the Internal Friction of Fluids on the Motion of Pendulums, Transactions of the Cambridge Philosophical Society, p.12, 1851.

R. Temam, Sur l'approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires (I), Archive for Rational Mechanics and Analysis, pp.135-153, 1969.

T. Tezduyar, M. Behr, S. Mittal, and E. J. Liou, A new strategy for finite element computations involving moving boundaries and interfaces???The deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders, Computer Methods in Applied Mechanics and Engineering, vol.94, issue.3, pp.94-353, 1992.
DOI : 10.1016/0045-7825(92)90060-W

V. Topin, F. Dubois, Y. Monerie, F. Perales, and E. A. Wachs, Micro-rheology of dense particulate flows: Application to immersed avalanches, Journal of Non-Newtonian Fluid Mechanics, vol.166, issue.1-2, pp.63-72, 2011.
DOI : 10.1016/j.jnnfm.2010.10.006

URL : https://hal.archives-ouvertes.fr/hal-00806645

M. Uhlmann, New results on the simulation of particulate flows, p.31, 2004.

M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, Journal of Computational Physics, vol.209, issue.2, pp.448-476, 2005.
DOI : 10.1016/j.jcp.2005.03.017

M. Van-dyke, An album of fluid motion, An Album of Fluid Motion, p.133, 1982.

C. Veeramani, P. Minev, and E. K. Nandakumar, A fictitious domain formulation for flows with rigid particles: A non-Lagrange multiplier version, Journal of Computational Physics, vol.224, issue.2, pp.867-879, 2007.
DOI : 10.1016/j.jcp.2006.10.028

R. Verjus, S. Et, and . Guilou, Study of polydisperse particulate systems with a "Direct- Forcing/Fictitious Domain" method, in proceedings THESIS2013, pp.4-124, 2013.

B. Wachmann, W. Kalthoff, S. Schwarzer, and H. J. Herrmann, Collective drag and sedimentation: comparison of simulation and experiment in two and three dimensions, Granular Matter, vol.1, issue.2, pp.75-82, 1998.
DOI : 10.1007/s100350050012

A. Wachs, A DEM-DLM/FD method for direct numerical simulation of particulate flows: Sedimentation of polygonal isometric particles in a Newtonian fluid with collisions, Computers & Fluids, vol.38, issue.8, pp.1608-1628, 2009.
DOI : 10.1016/j.compfluid.2009.01.005

J. C. Winterwerp, W. G. Et, and . Van-kesteren, Introduction to the Physics of Cohesive Sediment Dynamics in the Marine Environment, Developments in Sedimentology, p.116, 2004.

X. Yang, X. Zhang, Z. Li, and G. He, A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations, Jour- BIBLIOGRAPHIE nal of Computational Physics, pp.7821-7836, 2009.

T. Ye, R. Mittal, H. Udaykumar, and E. W. Shyy, An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries, Journal of Computational Physics, vol.156, issue.2, pp.209-240, 1999.
DOI : 10.1006/jcph.1999.6356

Z. Yu, X. Et, and . Shao, A direct-forcing fictitious domain method for particulate flows, Journal of Computational Physics, vol.227, issue.1, pp.292-314, 2007.
DOI : 10.1016/j.jcp.2007.07.027

Z. Yu, N. Phan-thien, Y. Fan, and R. I. Tanner, Viscoelastic mobility problem of a system of particles, Journal of Non-Newtonian Fluid Mechanics, vol.104, issue.2-3, pp.87-124, 2002.
DOI : 10.1016/S0377-0257(02)00014-9

H. Zhu, Z. Zhou, R. Yang, and E. A. Yu, Discrete particle simulation of particulate systems: Theoretical developments, Chemical Engineering Science, vol.62, issue.13, pp.3378-3396, 2007.
DOI : 10.1016/j.ces.2006.12.089

H. Zhu, Z. Zhou, R. Yang, and E. A. Yu, Discrete particle simulation of particulate systems: A review of major applications and findings, Chemical Engineering Science, vol.63, issue.23, pp.5728-5770, 2008.
DOI : 10.1016/j.ces.2008.08.006

T. Des and F. , 1 Représentation schématique de la sédimentation d'une particule en milieu confiné. W est la largeur du canal, Y est l'excentrement (nous utiliserons aussi e = 2Y /W comme excentrement adimensionné), p.76

C. Harper, La fonction ?K(e) apparaissant dans l'expression de la traînée d, p.78, 1967.

C. Harper, W. De, R. Ep-jusqu-'à-disparaitre-complètement, and .. , La survitesse peut atteindre 25% à petit Reynolds et fort confinement 83 TABLE DES FIGURES V.4 Fort confinement W/D = 4 et Reynolds de l'ordre de l'unité : évolution temporelle des positions transversales du doublets de particules pour F = 136.77. Deux structures coexistent pour ce même F qui apparaissent selon la position initiales des particules : la structure oblique stable et la structure oblique oscillante, p.102, 1967.

D. Attracteur-Étrange, ) et phénomène pour F = 197.68.(b) DKT pour des régimes d'écoulements plus important pour F = 241, p.105

L. Des-tableaux-iv-la-survitesse and .. , 1 Sédimentation d'une particule excentrée à R ep = 0.1 : résultats de la survitesse comparés avec la formule (IV.7) de Champmartin (2006) (obtenue pour une particule qui ne tourne pas) pour différents confinements. Les résultats sont en bon accord. La rotation de la particule ne semble avoir aucun effet sur l'amplitude, p.84

. Dans-cette-thèse, nous avons développé un code de simulation numérique directe particulièrement bien adapté à l'étude des écoulements à phase dispersée