P. Angot, C. Bruneau, and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numerische Mathematik, vol.81, issue.4, pp.497-520, 1999.
DOI : 10.1007/s002110050401

J. W. Barrett and E. Süli, Existence of Global Weak Solutions to Some Regularized Kinetic Models for Dilute Polymers, Multiscale Modeling & Simulation, vol.6, issue.2, pp.506-546, 2007.
DOI : 10.1137/060666810
URL : http://spiral.imperial.ac.uk/bitstream/10044/1/636/1/066681.pdf

M. Belzons, R. Blanc, J. L. Bouillot, and C. Camoin, Viscosité d'une suspension diluée et bidimensionnelle de sphères, C. R. Acad. Sci, Paris II, vol.292, pp.939-983, 1981.

H. Binous and R. J. Phillips, Dynamic simulation of one and two particles sedimenting in viscoelastic suspensions of FENE dumbbells, Journal of Non-Newtonian Fluid Mechanics, vol.83, issue.1-2, pp.93-130, 1999.
DOI : 10.1016/S0377-0257(98)00141-4

T. Bodnár and A. Sequeira, Numerical Study of the Significance of the Non-Newtonian Nature of Blood in Steady Flow Through a Stenosed Vessel, Advances in Mathematical Fluid Mechanics. Dedicated to Giovanni Paolo Galdi on the Occasion of his 60th Birthday, pp.83-104, 2010.
DOI : 10.1007/978-3-642-04068-9_6

G. Bossis and J. F. Brady, Dynamic simulation of sheared suspensions. I. General method, The Journal of Chemical Physics, vol.292, issue.10, pp.5141-5154, 1984.
DOI : 10.1051/jphys:01979004008078300
URL : https://authors.library.caltech.edu/10964/1/BOSjcp84.pdf

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

H. Brenner and M. E. , On the Stokes resistance of multiparticle systems in a linear shear field, Chemical Engineering Science, vol.27, issue.7, pp.1421-1439, 1972.
DOI : 10.1016/0009-2509(72)85029-2

F. P. Bretherton, The motion of rigid particles in a shear flow at low Reynolds number, Journal of Fluid Mechanics, vol.217, issue.02, pp.284-304, 1962.
DOI : 10.1007/BF01968851

Y. J. Choi, M. A. Hulsen, and H. E. Meijer, An extended finite element method for the simulation of particulate viscoelastic flows, Journal of Non-Newtonian Fluid Mechanics, vol.165, issue.11-12, pp.11-12607, 2010.
DOI : 10.1016/j.jnnfm.2010.02.021

L. Chupin and S. Martin, Stationary Oldroyd model with diffusive stress: Mathematical analysis of the model and vanishing diffusion process, Journal of Non-Newtonian Fluid Mechanics, vol.218, pp.27-39
DOI : 10.1016/j.jnnfm.2015.01.004
URL : https://hal.archives-ouvertes.fr/hal-00905096

P. Constantin and M. Kliegl, Note on Global Regularity for Two-Dimensional Oldroyd-B Fluids with Diffusive Stress, Archive for Rational Mechanics and Analysis, vol.19, issue.10???12, pp.725-740, 2012.
DOI : 10.1063/1.2783426
URL : http://arxiv.org/pdf/1204.3503

G. D. Avino and P. L. Maffettone, Particle dynamics in viscoelastic liquids, J. Non-Newtonian Fluid Mech, vol.215, pp.80-104, 2015.

G. D. Avino, P. L. Maffettone, F. Greco, and M. A. Hulsen, Viscoelasticity-induced migration of a rigid sphere in confined shear flow, J. Non-Newtonian Fluid Mech, vol.165, pp.9-10466, 2010.

E. Ding and C. K. Aidun, The dynamics and scaling law for particles suspended in shear flow with inertia, Journal of Fluid Mechanics, vol.423, pp.317-344, 2000.
DOI : 10.1017/S0022112000001932

J. Feng, P. Y. Huang, and D. 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
URL : http://www.math.ubc.ca/~jfeng/Publications/PDFs/96_JNNFM1.pdf

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.407-483, 1987.
DOI : 10.1017/S0022112066001721

R. Glowinski, T. Pan, T. I. Hesla, D. D. Joseph, and J. Periaux, A distributed Lagrange multiplier/fictitious domain method for the simulation of flow around moving rigid bodies: application to particulate flow, Computer Methods in Applied Mechanics and Engineering, vol.184, issue.2-4, pp.2-4241, 2000.
DOI : 10.1016/S0045-7825(99)00230-3

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

N. Goyal and J. J. Derksen, Direct simulations of spherical particles sedimenting in viscoelastic fluids, Journal of Non-Newtonian Fluid Mechanics, vol.183, issue.184, pp.183-1841, 2012.
DOI : 10.1016/j.jnnfm.2012.07.006

C. Guillopé and J. Saut, Existence results for the flow of viscoelastic fluids with a differential constitutive law. Nonlinear Anal, pp.849-869, 1990.

J. Hao, T. W. Pan, R. Glowinski, and D. D. Joseph, A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: A positive definiteness preserving approach, Journal of Non-Newtonian Fluid Mechanics, vol.156, issue.1-2, pp.95-111, 2009.
DOI : 10.1016/j.jnnfm.2008.07.006

J. Happel and H. Brenner, Low Reynolds number hydrodynamics, Martinus Nijho, vol.1, 1986.
DOI : 10.1007/978-94-009-8352-6

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

M. Hillairet, A. Lozinski, and M. Szopos, On discretization in time in simulations of particulate flows. Discrete Contin, Dyn. Syst. Ser. B, vol.15, issue.4, pp.935-956, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00631084

M. Hillairet and T. Takahashi, Collisions in Three-Dimensional Fluid Structure Interaction Problems, SIAM Journal on Mathematical Analysis, vol.40, issue.6, pp.2451-2477, 2009.
DOI : 10.1137/080716074

M. Hillairet and T. Takahashi, Blow up and grazing collision in viscous fluid solid interaction systems. Annales de l'Institut Henri Poincare (C) Non Linear Analysis, pp.291-313, 2010.
DOI : 10.1016/j.anihpc.2009.09.007
URL : https://hal.archives-ouvertes.fr/hal-00355684

H. 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, D. D. Joseph, and M. J. Crochet, Direct simulation of fluid particle motions, Theoretical and Computational Fluid Dynamics, vol.177, issue.5, pp.285-306, 1992.
DOI : 10.1007/BF00717645

P. Y. Huang, J. Feng, H. H. Hu, and D. D. Joseph, Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids, Journal of Fluid Mechanics, vol.343, pp.73-94, 1997.
DOI : 10.1017/S0022112097005764

P. Y. Huang, H. H. Hu, and D. D. Joseph, Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids, Journal of Fluid Mechanics, vol.362, pp.297-325, 1997.
DOI : 10.1017/S0022112098008672

W. R. Hwang, M. A. Hulsen, and H. E. Meijer, Direct simulation of particle suspensions in sliding bi-periodic frames, Journal of Computational Physics, vol.194, issue.2, pp.742-772, 2004.
DOI : 10.1016/j.jcp.2003.09.023

J. Janela, A. Lefebvre, and B. Maury, A penalty method for the simulation of fluid - rigid body interaction, CEMRACS 2004?mathematics and applications to biology and medicine, pp.115-123
DOI : 10.1051/proc:2005010
URL : https://hal.archives-ouvertes.fr/hal-00728372

G. B. Jeffery, The Motion of Ellipsoidal Particles Immersed in a Viscous Fluid, Proc. R. Soc. Lond. A, pp.161-179, 1922.
DOI : 10.1098/rspa.1922.0078

A. A. Johnson and T. E. Tezduyar, Simulation of multiple spheres falling in a liquid-filled tube, Computer Methods in Applied Mechanics and Engineering, vol.134, issue.3-4, pp.3-4351, 1996.
DOI : 10.1016/0045-7825(95)00988-4
URL : http://www.arc.umn.edu/~johnson/spaper.ps.gz

D. D. Joseph, Fluid Dynamics of Viscoelastic Liquids, Applied Mathematical Sciences, vol.84, issue.754, 1998.
DOI : 10.1007/978-1-4612-4462-2

D. D. Joseph, Y. J. Liu, M. Poletto, and J. Feng, Aggregation and dispersion of spheres falling in viscoelastic liquids, Journal of Non-Newtonian Fluid Mechanics, vol.54, pp.45-86, 1994.
DOI : 10.1016/0377-0257(94)80015-4

I. M. Krieger and T. J. Dougherty, A Mechanism for Non???Newtonian Flow in Suspensions of Rigid Spheres, Transactions of the Society of Rheology, vol.3, issue.1, pp.137-152, 1959.
DOI : 10.1122/1.548848

A. Lefebvre, Fluid-Particle simulations with FreeFem++, ESAIM: Proceedings, vol.18, pp.120-132, 2006.
DOI : 10.1051/proc:071810
URL : https://hal.archives-ouvertes.fr/hal-00728387

A. Lefebvre, Numerical simulation of gluey particles, ESAIM: Mathematical Modelling and Numerical Analysis, vol.51, issue.1, pp.53-80, 2009.
DOI : 10.1002/fld.1129
URL : https://hal.archives-ouvertes.fr/hal-00257510

G. Li, G. H. Mckinley, and A. M. Ardekani, Dynamics of particle migration in channel flow of viscoelastic fluids, Journal of Fluid Mechanics, vol.26, issue.12, pp.486-505
DOI : 10.1017/S0022112089001564
URL : http://dspace.mit.edu/bitstream/1721.1/107825/1/McKinley_Dynamics%20of%20particle.pdf

P. L. Lions and N. Masmoudi, Global solutions for some Oldroyd models of non-Newtonian flows. Chinese Ann, Math. Ser. B, vol.21, issue.2, pp.131-146, 2000.
DOI : 10.1007/bf02484187
URL : http://www.ceremade.dauphine.fr/CMD/preprints00/0004Glob._sol.ps

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

B. Maury, A time-stepping scheme for inelastic collisions, Numerische Mathematik, vol.102, issue.4, pp.649-679, 2006.
DOI : 10.1007/s00211-005-0666-6
URL : https://hal.archives-ouvertes.fr/hal-01473592

L. Molinet and R. Talhouk, On the global and periodic regular flows of viscoelastic fluids with a differential constitutive law, Nonlinear Differential Equations and Applications NoDEA, vol.11, issue.3, pp.349-359, 2004.
DOI : 10.1007/s00030-004-1073-x

N. A. Patankar and H. H. Hu, Rheology of a suspension of particles in viscoelastic fluids, Journal of Non-Newtonian Fluid Mechanics, vol.96, issue.3, pp.427-443, 2001.
DOI : 10.1016/S0377-0257(00)00154-3

N. A. Patankar, P. Singh, D. D. Joseph, R. Glowinski, and T. Pan, 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

T. N. Randrianarivelo, G. Pianet, S. Vincent, and J. P. Caltagirone, Numerical modelling of solid particle motion using a new penalty method, International Journal for Numerical Methods in Fluids, vol.34, issue.10-11, pp.10-111245, 2005.
DOI : 10.1002/fld.914

M. Renardy, Existence of Slow Steady Flows of Viscoelastic Fluids with Differential Constitutive Equations, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.245, issue.9, pp.449-451, 1985.
DOI : 10.1098/rspa.1958.0083
URL : http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA147240&Location=U2&doc=GetTRDoc.pdf

J. Saut, Lectures on the mathematical theory of viscoelastic fluids, Lect. Anal. Nonlinear Partial Differ. Equ, vol.3, pp.325-393, 2013.

H. M. Schaink, J. J. Slot, R. J. Jongschaap, and J. Mellema, The rheology of systems containing rigid spheres suspended in both viscous and viscoelastic media, studied by Stokesian dynamics simulations, Journal of Rheology, vol.44, issue.3, pp.473-498, 2000.
DOI : 10.1122/1.551097
URL : https://pure.tue.nl/ws/files/1820656/Metis214139.pdf

P. Singh, D. D. Joseph, T. I. Hesla, R. Glowinski, and T. Pan, A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows, Journal of Non-Newtonian Fluid Mechanics, vol.91, issue.2-3, pp.165-188, 2000.
DOI : 10.1016/S0377-0257(99)00104-4

Z. Yu and X. 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, A. Wachs, and Y. Peysson, Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method, Journal of Non-Newtonian Fluid Mechanics, vol.136, issue.2-3, pp.126-139, 2006.
DOI : 10.1016/j.jnnfm.2006.03.015