T. B. Anderson and R. Jackson, Fluid mechanical description of fluidized beds. equations of motion, Ind. and Eng. Chem. Fundamentals, vol.6, issue.4, pp.527-539, 1967.

G. B. Arfken, Mathematical methods for physicists, 2005.

R. C. Ball and J. R. Melrose, A simulation technique for many spheres in quasi-static motion under frameinvariant pair drag and brownian forces, Physica A : Stat. Mech. and Appl, vol.247, issue.1-4, pp.444-472, 1997.

L. Banz and A. Schröder, Biorthogonal basis functions in hp-adaptive fem for elliptic obstacle problems, Comp. and Math. with App, vol.70, issue.8, pp.1721-1742, 2015.

G. K. Batchelor, Brownian diffusion of particles with hydrodynamic interaction, J. of Fluid Mech, vol.74, issue.1, pp.1-29, 1976.

G. K. Batchelor and J. Green, The hydrodynamic interaction of two small freely-moving spheres in a linear flow field, J. of Fluid Mech, vol.56, issue.2, pp.375-400, 1972.

G. K. Batchelor and J. T. Green, The determination of the bulk stress in a suspension of spherical particles to order c 2, J. Fluid Mech, vol.56, issue.03, pp.401-427, 1972.

F. Berthelin, Existence and weak stability for a pressureless model with unilateral constraint, Math. Mod. and Meth. in App. Sci, vol.12, issue.02, pp.249-272, 2002.

F. Berthelin and F. Bouchut, Weak solutions for a hyperbolic system with unilateral constraint and mass loss, Annales de l'IHP (C) Non Linear Anal, vol.20, pp.975-997, 2003.

F. Berthelin and D. Broizat, A model for the evolution of traffic jams in multi-lane. Kinetic and Related Models, vol.5, pp.697-728, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00874398

F. Berthelin, P. Degond, M. Delitala, and M. Rascle, A model for the formation and evolution of traffic jams, Arch. for Rational Mech. and Anal, vol.187, issue.2, pp.185-220, 2008.

R. Bird, R. C. Armstrong, and O. Hassager, Dynamics of polymeric liquids, vol.1, 1987.

F. Blanc, Rhéologie et microstructure des suspensions concentrées non browniennes, 2011.

F. Blanc, F. Peters, and E. E. Lemaire, Local transient rheological behavior of concentrated suspensions, J. Rheol, vol.55, issue.4, pp.835-854, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00646078

F. Blanc, F. Peters, and E. E. Lemaire, Experimental signature of the pair trajectories of rough spheres in the shear-induced microstructure in noncolloidal suspensions, Phys. Rev. Lett, vol.107, issue.20, p.208302, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00645540

F. Blanc, E. Lemaire, A. Meunier, and F. Peters, Microstructure in sheared non-Brownian concentrated suspensions, J. Rheol, vol.57, issue.1, pp.273-292, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00781954

A. Bonami and J. Clerc, Sommes de cesaro et multiplicateurs des développements en harmoniques sphé-riques, Transactions of the American Mathematical Society, vol.183, pp.223-263, 1973.

G. Bossis and J. F. Brady, Dynamic simulation of sheared suspensions. i. general method. The J. of, Chem. Phys, vol.80, issue.10, pp.5141-5154, 1984.

C. Bost, G. Cottet, and E. E. Maitre, Convergence analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid, SIAM J. on Num. Anal, vol.48, issue.4, pp.1313-1337, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00352808

F. Bouchut and S. Boyaval, Unified derivation of thin-layer reduced models for shallow free-surface gravity flows of viscous fluids, E. J. of Mech.-B/Fluids, vol.55, pp.116-131, 2016.
URL : https://hal.archives-ouvertes.fr/hal-00833468

F. Bouchut, Y. Brenier, J. Cortes, and J. Ripoll, A hierarchy of models for two-phase flows, J. of NonLinear Sci, vol.10, issue.6, pp.639-660, 2000.

F. Bouchut, E. D. Fernandez-nieto, A. Mangeney, and G. Narbona-reina, A two-phase shallow debris flow model with energy balance, ESAIM : Math. Mod. and Num. Anal, vol.49, issue.1, pp.101-140, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00860871

F. Bouchut, E. D. Fernández-nieto, A. Mangeney, and G. Narbona-reina, A two-phase two-layer model for fluidized granular flows with dilatancy effects, J. of Fluid Mech, vol.801, pp.166-221, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01161930

F. Bouchut, E. D. Fernández-nieto, A. Mangeney, and G. Narbona-reina, A two-phase two-layer model for fluidized granular flows with dilatancy effects, J. of Fluid Mech, vol.801, pp.166-221, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01161930

S. Boyaval, T. Lelièvre, and C. Mangoubi, Free-energy-dissipative schemes for the oldroyd-b model, ESAIM : Math. Mod. and Num. Anal, vol.43, issue.3, pp.523-561, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00204620

F. Boyer, É. Guazzelli, and O. Pouliquen, Unifying suspension and granular rheology, Phys. Rev. Lett, vol.107, issue.18, p.188301, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01432411

F. Boyer, O. Pouliquen, and É. Guazzelli, Dense suspensions in rotating-rod flows : normal stresses and particle migration, J. Fluid Mech, vol.686, pp.5-25, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01432497

J. F. Brady and G. Bossis, The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation, J. of F. Mech, vol.155, pp.105-129, 1985.

J. F. Brady and G. Bossis, Stokesian dynamics, Ann. Rev. of Fluid Mech, vol.20, issue.1, pp.111-157, 1988.

J. F. Brady and J. F. Morris, Microstructure of strongly sheared suspensions and its impact on rheology and diffusion, J. Fluid Mech, vol.348, pp.103-139, 1997.

D. Bresch and M. Renardy, Development of congestion in compressible flow with singular pressure, Asymptotic Anal, vol.103, issue.1-2, pp.95-101, 2017.

D. Bresch, C. Perrin, and E. E. Zatorska, Singular limit of a navier-stokes system leading to a free/congested zones two-phase model, Comptes Rendus Mathematique, vol.352, issue.9, pp.685-690, 2014.

D. Bresch, S. Necasova, and C. Perrin, Compression effects in heterogeneous media, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01838014

H. Brezis, Functional analysis, Sobolev spaces and partial differential equations, 2011.

B. Cambou, M. Jean, and F. Radjai, Matériaux granulaires -Modélisation et simulation numérique, 2012.

R. N. Chacko, R. Mari, S. M. Fielding, and M. E. Cates, Shear reversal in dense suspensions : the challenge to fabric evolution models from simulation data, J. of Fluid Mech, vol.847, pp.700-734, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01954130

J. Chauchat and M. Médale, A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow, Comp. Meth. in App. Mech. and Eng, vol.199, pp.439-449, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00619372

A. W. Chow, J. H. Iwayima, S. W. Sinton, and D. T. Leighton, Particle migration of non-brownian, concentrated suspensions in a truncated cone-and-plate, In S. of Rheol. Meeting, vol.103, 1995.

E. Cossart, Des sources sédimentaires à l'exutoire : un problème de connectivité ? PhD thesis, 2014.

É. Couturier, F. Boyer, O. Pouliquen, and É. Guazzelli, Suspensions in a tilted trough : second normal stress difference, J. Fluid Mech, vol.686, pp.26-39, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01432501

P. A. Cundall and O. D. Strack, A discrete numerical model for granular assemblies, Geotechnique, vol.29, issue.1, pp.47-65, 1979.

S. Dagois-bohy, S. Hormozi, E. Guazzelli, and O. Pouliquen, Rheology of dense suspensions of non-colloidal spheres in yield-stress fluids, J. of Fluid Mech, vol.776, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01432397

F. Dai and K. Wang, Convergence rate of spherical harmonic expansions of smooth functions, J. of Math. Anal. and Appl, vol.348, issue.1, pp.28-33, 2008.

S. Dai and R. I. Tanner, Elongational flows of some non-colloidal suspensions, Rheol. Acta, vol.56, issue.1, pp.63-71, 2017.

S. Dai, E. Bertevas, F. Qi, and R. I. Tanner, Viscometric functions for noncolloidal sphere suspensions with Newtonian matrices, J. Rheol, vol.57, issue.2, pp.493-510, 2013.

T. Dbouk, A suspension balance direct-forcing immersed boundary model for wet granular flows over obstacles, J. Non-Newt. Fluid Mech, vol.230, pp.68-79, 2016.

T. Dbouk, E. Lemaire, L. Lobry, and F. Moukalled, Shear-induced particle migration : Predictions from experimental evaluation of the particle stress tensor, J. of Non-Newtonian Fluid Mech, vol.198, pp.78-95, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00824342

T. Dbouk, L. Lobry, and E. E. Lemaire, Normal stresses in concentrated non-Brownian suspensions, J. Fluid Mech, vol.715, pp.239-272, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00778723

A. Deboeuf, G. Gauthier, J. Martin, Y. Yurkovetsky, and J. F. Morris, Particle pressure in a sheared suspension : a bridge from osmosis to granular dilatancy, Phys. Rev. Lett, vol.102, issue.10, p.108301, 2009.

E. Degiuli, G. Düring, E. Lerner, and M. Wyart, Unified theory of inertial granular flows and non-brownian suspensions, Phys. Rev. E, vol.91, issue.6, p.62206, 2015.

P. Degond and M. Tang, All speed scheme for the low mach number limit of the isentropic euler equations, Comm. in Comp. Phy, vol.10, issue.1, pp.1-31, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00630995

P. Degond, S. Jin, and J. Yuming, Mach-number uniform asymptotic-preserving gauge schemes for compressible flows, Bulletin-Institute of Mathematics Academia Sinica, vol.2, issue.4, p.851, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00635618

P. Degond, J. Hua, and L. Navoret, Numerical simulations of the euler system with congestion constraint, J. of Comp. Phy, vol.230, issue.22, pp.8057-8088, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00996913

M. M. Denn and J. F. Morris, Rheology of non-brownian suspensions, Ann. Rev. Chem. Biomol. Eng, vol.5, pp.203-228, 2014.

G. Drazer, J. Koplik, B. Khusid, and A. Acrivos, Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions, J. Fluid Mech, vol.460, pp.307-335, 2002.

F. Dubois, V. Acary, and M. Jean, The Contact Dynamics method : A nonsmooth story, Comptes Rendus Mécanique, vol.346, pp.247-262, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01676287

G. Duvaut and J. Lions, Les inéquations en mécanique et en physique. Dunod, 1972.

J. W. Eaton, D. Bateman, and E. S. Hauberg, Octave : A high-level interactive language for numerical computations. Free software fundation, 2011.

A. Einstein, Eine neue bestimmung der moleküldimensionen, Ann. Phys. ser, vol.4, pp.289-306, 1906.

A. Einstein, Investigation on the theory of the Brownian movement, 1956.

Z. Fang, A. A. Mammoli, J. F. Brady, M. S. Ingber, L. A. Mondy et al., Flow-aligned tensor models for suspension flows, Int. J. of multiphase flow, vol.28, issue.1, pp.137-166, 2002.

S. Faure and B. Maury, Crowd motion from the granular standpoint, Math. Models and Meth. in App. Sci, vol.25, issue.03, pp.463-493, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01358423

E. D. Fernández-nieto, T. M. De-luna, G. Narbona-reina, and J. De-dieu-zabsonré, Formal deduction of the saint-venant-exner model including arbitrarily sloping sediment beds and associated energy, ESAIM : Math. Model. and Num. Anal, vol.51, issue.1, pp.115-145, 2017.

A. F. Fortes, D. D. Joseph, and T. S. Lundgren, Nonlinear mechanics of fluidization of beds of spherical particles, J. of Fluid Mech, vol.177, pp.467-483, 1987.

F. Gadala-maria and A. Acrivos, Shear-induced structure in a concentrated suspension of solid spheres, J. Rheol, vol.24, issue.6, pp.799-814, 1980.

S. Gallier, E. Lemaire, L. Lobry, and F. Peters, A fictitious domain approach for the simulation of dense suspensions, J. of Comp. Phys, vol.256, pp.367-387, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01026308

S. Gallier, E. Lemaire, F. Peters, and L. Lobry, Rheology of sheared suspensions of rough frictional particles, J of Fluid Mech, vol.757, pp.514-549, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01069828

S. Gallier, E. Lemaire, F. Peters, and L. Lobry, Rheology of sheared suspensions of rough frictional particles, J. Fluid Mech, vol.757, pp.514-549, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01069828

S. Gallier, E. Lemaire, L. Lobry, and F. Peters, Effect of confinement in wall-bounded non-colloidal suspensions, J. of Fluid Mech, vol.799, pp.100-127, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01347658

S. Gallier, F. Peters, and L. Lobry, Simulations of sheared dense noncolloidal suspensions : Evaluation of the role of long-range hydrodynamics, Phy. Rev. Fluids, vol.3, issue.4, p.42301, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01802715

R. Glowinski, T. Pan, T. I. Hesla, and D. D. Joseph, A distributed lagrange multiplier/fictitious domain method for particulate flows, Int. J. of Multiphase Flow, vol.25, issue.5, pp.755-794, 1999.

J. D. Goddard, Memory materials without characteristic time and their relation to the rheology of certain particle suspensions, Adv. Coll. Interf. Sci, vol.17, issue.1, pp.241-262, 1982.

J. D. Goddard, A dissipative anisotropic fluid model for non-colloidal particle dispersions, J. Fluid Mech, vol.568, pp.1-17, 2006.

A. J. Goldman, R. G. Cox, and H. Brenner, The slow motion of two identical arbitrarily oriented spheres through a viscous fluid, Chem. Eng. Sci, vol.21, issue.12, pp.1151-1170, 1966.

R. J. Gordon and W. R. Schowalter, Anisotropic fluid theory : a different approach to the dumbbell theory of dilute polymer solutions, J. Rheol, vol.16, pp.79-97, 1972.

E. Guazzelli and J. F. Morris, A physical introduction to suspension dynamics, 2012.

É. Guazzelli and O. Pouliquen, Rheology of dense granular suspensions, J. of Fluid Mech, vol.852, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01902053

H. Haddadi, S. Shojaei-zadeh, K. Connington, and J. F. Morris, Suspension flow past a cylinder : particle interactions with recirculating wakes, J. Fluid Mech, vol.760, p.2, 2014.

S. Haeri and J. Shrimpton, On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows, Int. J. of Multiphase Flow, vol.40, pp.38-55, 2012.

G. L. Hand, A theory of anisotropic fluids, J. Fluid Mech, vol.13, issue.1, pp.33-46, 1962.

E. J. Hinch and L. G. Leal, The effect of brownian motion on the rheological properties of a suspension of non-spherical particles, J. of Fluid Mech, vol.52, issue.4, pp.683-712, 1972.

H. H. Hu, Direct simulation of flows of solid-liquid mixtures, Int. J. of Multiphase Flow, vol.22, issue.2, pp.335-352, 1996.

H. H. Hu, D. D. Joseph, and M. J. Crochet, Direct simulation of fluid particle motions, Theo. and Comp. Fluid Dyn, vol.3, issue.5, pp.285-306, 1992.

M. A. Hulsen, A sufficient condition for a positive definite configuration tensor in differential models, J. Non-Newt. Fluid Mechanics, vol.38, issue.1, pp.93-100, 1990.

J. H. Irving and J. G. Kirkwood, The statistical mechanical theory of transport processes. iv. the equations of hydrodynamics, The J. of Chem. Phy, vol.18, issue.6, pp.817-829, 1950.

R. Jackson, Locally averaged equations of motion for a mixture of identical spherical particles and a Newtonian fluid, Chem. Eng. Sci, vol.52, issue.15, pp.2457-2469, 1997.

R. Jackson, The dynamics of fluidized particles, 2000.

A. A. Johnson and T. E. Tezduyar, Advanced mesh generation and update methods for 3d flow simulations, Comp. Mech, vol.23, issue.2, pp.130-143, 1999.

S. G. Johnson, Saddle-point integration of C ? "bump" functions. preprint, 2015.

E. Jones, T. Oliphant, and P. Peterson, Open source scientific tools for Python, 2001.

P. Jop, Y. Forterre, and O. Pouliquen, A constitutive law for dense granular flows, Nature, vol.441, issue.7094, p.727, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01432178

H. Kalf, On the expansion of a function in terms of spherical harmonics in arbitrary dimensions, Bulletin of the Belgian Mathematical Society Simon Stevin, vol.2, issue.4, pp.361-380, 1995.

V. G. Kolli, E. J. Pollauf, and F. Gadala-maria, Transient normal stress response in a concentrated suspension of spherical particles, J. Rheol, vol.46, issue.1, pp.321-334, 2002.

D. Kolymbas, An outline of hypoplasticity, Arch. Appl. Mech, vol.61, issue.3, pp.143-151, 1991.

I. M. Krieger, Rheology of monodisperse latices, Adv. in Coll. and Interface sci, vol.3, issue.2, pp.111-136, 1972.

M. Krieger and T. J. Dougherty, A mechanism for non-newtonian flow in suspensions of rigid spheres, Trans. Soc. Rheol, vol.3, issue.1, pp.137-152, 1959.

S. Labbé and E. Maitre, A free boundary model for korteweg fluids as a limit of barotropic compressible navier-stokes equations, Meth. and App. of Anal, vol.20, issue.2, pp.165-178, 2013.

L. G. Leal, Advanced transport phenomena : fluid mechanics and convective transport processes, 2007.

B. Lecampion and D. I. Garagash, Confined flow of suspensions modelled by a frictional rheology, J. Fluid Mech, vol.759, pp.197-235, 2014.

A. Lefebvre, Fluid-particle simulations with freefem++, Esaim : Proceedings, vol.18, pp.120-132, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00728387

A. Lefebvre, Modélisation numérique d'écoulements fluide/particules, 2007.

A. Lefebvre and B. Maury, Apparent viscosity of a mixture of a newtonian fluid and interacting particles, Comptes rendus mécanique, vol.333, issue.12, pp.923-933, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00728382

A. Lefebvre-lepot and B. Maury, Micro-macro modelling of an array of spheres interacting through lubrication forces, Adv. in Math. Sci. and App, vol.21, issue.2, pp.535-557, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00257250

D. Leighton and A. Acrivos, The shear-induced migration of particles in concentrated suspensions, J. of Fluid Mech, vol.181, pp.415-439, 1987.

D. Lhuillier, Migration of rigid particles in non-Brownian viscous suspensions, Phys. Fluids, vol.21, issue.2, p.23302, 2009.

C. Lin and K. Wang, Convergence rate of fourier-laplace series of l 2-functions, J. of Approx. Theory, vol.128, issue.2, pp.103-114, 2004.

R. A. Lionberger and W. B. Russel, A smoluchowski theory with simple approximations for hydrodynamic interactions in concentrated dispersions, J. of Rheol, vol.41, issue.2, pp.399-425, 1997.

P. Lions and N. Masmoudi, On a free boundary barotropic model, Annales de l'IHP (C) Non Linear Anal, vol.16, pp.373-410, 1999.

G. G. Lipscomb, M. M. Denn, D. U. Hur, and D. V. Boger, The flow of fiber suspensions in complex geometries, J. Non-Newt. Fluid Mech, vol.26, issue.3, pp.297-325, 1988.

S. Lomholt and M. R. Maxey, Force-coupling method for particulate two-phase flow : Stokes flow, J. of Comp. Phys, vol.184, issue.2, pp.381-405, 2003.

S. Luding, Cohesive, frictional powders : contact models for tension, Granular matter, vol.10, p.235, 2008.

M. K. Lyon and L. G. Leal, An experimental study of the motion of concentrated suspensions in twodimensional channel flow. part 1. monodisperse systems, J. of Fluid Mech, vol.363, pp.25-56, 1998.

R. Mari, R. Seto, J. F. Morris, and M. M. Denn, Shear thickening, frictionless and frictional rheologies in non-brownian suspensions, J. of Rheol, vol.58, issue.6, pp.1693-1724, 2014.

R. Mari, R. Seto, J. F. Morris, and M. M. Denn, Nonmonotonic flow curves of shear thickening suspensions, Phys. Rev. E, vol.91, issue.5, p.52302, 2015.

S. H. Maron and P. E. Pierce, Application of Ree-Eyring generalized flow theory to suspensions of spherical particles, J. Colloid Sci, vol.11, issue.1, pp.80-95, 1956.

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

B. Maury, A gluey particle model, ESAIM : Proceedings, vol.18, pp.133-142, 2007.

B. Maury and R. Glowinski, Fluid-particle flow : a symmetric formulation, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, vol.324, issue.9, pp.1079-1084, 1997.

B. Maury, A. Roudneff-chupin, and E. F. Santambrogio, A macroscopic crowd motion model of gradient flow type, Math. Models and Meth. in App. Sci, vol.20, issue.10, pp.1787-1821, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00418511

M. Maxey, Simulation methods for particulate flows and concentrated suspensions, Ann. Rev. of Fluid Mech, vol.49, pp.171-193, 2017.

M. R. Maxey and B. K. Patel, Localized force representations for particles sedimenting in stokes flow, Int. J. of multiphase flow, vol.27, issue.9, pp.1603-1626, 2001.

M. R. Maxey, B. K. Patel, E. J. Chang, and L. P. Wang, Simulations of dispersed turbulent multiphase flow, Fluid Dyn. Res, vol.20, issue.1-6, p.143, 1997.

B. Metzger and J. E. Butler, Irreversibility and chaos : role of long-range hydrodynamic interactions in sheared suspensions, Phys. Rev. E, vol.82, issue.5, p.51406, 2010.

M. Miller and J. F. Morris, Normal stress-driven migration and axial development in pressure-driven flow of concentrated suspensions, J. Non-Newt. Fluid Mech, vol.135, issue.2, pp.149-165, 2006.

R. M. Miller, J. P. Singh, and J. F. Morris, Suspension flow modeling for general geometries, Chem. Eng. Sci, vol.64, issue.22, pp.4597-4610, 2009.

P. Mills and P. Snabre, Rheology and structure of concentrated suspensions of hard spheres. shear induced particle migration, J. de Physique, vol.II, issue.10, pp.1597-1608, 1995.
URL : https://hal.archives-ouvertes.fr/jpa-00248257

J. J. Moré, B. S. Garbow, and K. E. Hillstrom, User guide for minpack-1, 1980.

J. Moreau, Standard inelastic shocks and the dynamics of unilateral constraints, Unilateral problems in structural analysis, pp.173-221, 1985.
URL : https://hal.archives-ouvertes.fr/hal-01544442

J. Moreau, Unilateral contact and dry friction in finite freedom dynamics, Nonsmooth mechanics and Applications, pp.1-82, 1988.
URL : https://hal.archives-ouvertes.fr/hal-01713847

J. Moreau, Sorne numerical methods in multibody dynamics : application to granular materials, Euro. J. of Mechanics-A/Solids, vol.13, issue.4-suppl, pp.93-114, 1993.
URL : https://hal.archives-ouvertes.fr/hal-01789082

J. F. Morris, A review of microstructure in concentrated suspensions and its implications for rheology and bulk flow, Rheol. Acta, vol.48, issue.8, pp.909-923, 2009.

J. F. Morris and F. Boulay, Curvilinear flows of noncolloidal suspensions : the role of normal stresses, J. Rheol, vol.43, issue.5, pp.1213-1237, 1999.

C. Müller, Spherical harmonics, vol.17, 1966.

A. Nadim and H. A. Stone, The motion of small particles and droplets in quadratic flows, Studies in app. math, vol.85, issue.1, pp.53-73, 1991.

T. Narumi, H. See, Y. Honma, T. Hasegawa, T. Takahashi et al., Transient response of concentrated suspensions after shear reversal, J. Rheol, vol.46, issue.1, pp.295-305, 2002.

M. Newville, T. Stensitzki, D. B. Allen, M. Rawlik, A. Ingargiola et al., Lmfit : non-linear least-square minimization and curve-fitting for python, Astrophysics Source Code Library, 2016.

P. R. Nott and J. F. Brady, Pressure-driven flow of suspensions : simulation and theory, J. Fluid Mech, vol.275, pp.157-199, 1994.

P. R. Nott, E. Guazzelli, and O. Pouliquen, The suspension balance model revisited, Phys. Fluids, vol.23, issue.4, p.43304, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01432494

R. W. O'brien, A method for the calculation of the effective transport properties of suspensions of interacting particles, J. of Fluid Mech, vol.91, issue.1, pp.17-39, 1979.

S. Oh, Y. Song, D. I. Garagash, B. Lecampion, and J. Desroches, Pressure-driven suspension flow near jamming, Phy. Rev. Let, vol.114, issue.8, p.88301, 2015.

J. G. Oldroyd, On the formulation of rheological equations of states, Proc. R. Soc. Lond. A, vol.200, pp.523-541, 1950.

M. Ouriemi, P. Aussillous, and E. E. Guazzelli, Sediment dynamics. part 1. bed-load transport by laminar shearing flows, J. of Fluid Mech, vol.636, pp.295-319, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01432009

G. Ovarlez, F. Bertrand, and E. S. Rodts, Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging, J. Rheol, vol.50, issue.3, pp.259-292, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00776443

G. Ovarlez, F. Mahaut, S. Deboeuf, N. Lenoir, S. Hormozi et al., Flows of suspensions of particles in yield stress fluids, J. of Rheol, vol.59, issue.6, pp.1449-1486, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01223726

O. Ozenda, P. Saramito, and G. Chambon, A new rate-independent tensorial model for suspensions of noncolloidal rigid particles in newtonian fluids, J. of Rheol, vol.62, issue.4, pp.889-903, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01528817

W. Pan, B. Caswell, and G. E. Karniadakis, Rheology, microstructure and migration in brownian colloidal suspensions, Langmuir, vol.26, issue.1, pp.133-142, 2009.

L. Paoli and M. Schatzman, Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales : cas avec perte d'énergie, ESAIM : Math. Model. and Num. Anal, vol.27, issue.6, pp.673-717, 1993.

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, Int. J. of Multiphase Flow, vol.26, issue.9, pp.1509-1524, 2000.

C. Perrin, Pressure-dependent viscosity model for granular media obtained from compressible navier-stokes equations, App. Math. Research eXpress, vol.2016, issue.2, pp.289-333, 2016.

C. Perrin and E. Zatorska, Free/congested two-phase model from weak solutions to multi-dimensional compressible navier-stokes equations, Comm. in PDE, vol.40, issue.8, pp.1558-1589, 2015.

F. Peters, G. Ghigliotti, S. Gallier, F. Blanc, E. Lemaire et al., Rheology of non-brownian suspensions of rough frictional particles under shear reversal : A numerical study, Journal of rheology, vol.60, issue.4, pp.715-732, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01347647

N. Phan-thien, Constitutive equation for concentrated suspensions in Newtonian liquids, J. Rheol, vol.39, issue.4, pp.679-695, 1995.

N. Phan-thien, X. Fan, and B. C. Khoo, A new constitutive model for monodispersed suspensions of spheres at high concentrations, Rheol. Acta, vol.38, issue.4, pp.297-304, 1999.

N. Phan-thien, X. Fan, and R. Zheng, A numerical simulation of suspension flow using a constitutive model based on anisotropic interparticle interactions, Rheol. Acta, vol.39, issue.2, pp.122-130, 2000.

R. J. Phillips, R. C. Armstrong, R. A. Brown, A. L. Graham, and J. R. Abbott, A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration, Phy. of Fluids A : Fluid Dyn, vol.4, issue.1, pp.30-40, 1992.

A. Prosperetti and G. Tryggvason, Computational methods for multiphase flow, 2007.

A. Prosperetti and G. Tryggvason, Computational methods for multiphase flow, 2009.

K. Radhakrishnan and A. C. Hindmarsh, Description and use of LSODE, the Livermore solver for ordinary differential equations, 1993.

A. Ramachandran and D. T. Leighton, The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions, J. of Fluid Mech, vol.603, pp.207-243, 2008.

I. Rampall, J. R. Smart, and D. T. Leighton, The influence of surface roughness on the particle-pair distribution function of dilute suspensions of non-colloidal spheres in simple shear flow, J. of Fluid Mech, vol.339, pp.1-24, 1997.

B. D. Reddy and G. P. Mitchell, Finite element analysis of fibre suspension flows, Comput. Meth. Appl. Mech. Eng, vol.190, issue.18, pp.2349-2367, 2001.

J. F. Richardson and W. N. Zaki, Sedimentation and fluidisation : Part i, Chem. Eng. Res. and Design, vol.75, pp.82-100, 1997.

P. Saramito, A new constitutive equation for elastoviscoplastic fluid flows, J. Non-Newt. Fluid Mech, vol.145, issue.1, pp.1-14, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00109101

P. Saramito, Complex fluids : modelling and algorithms, Gewerbestrasse, vol.11, 2016.

R. Seto and G. G. Giusteri, Normal stress differences in dense suspensions, J. of Fluid Mech, vol.857, pp.200-215, 2018.

R. Seto, G. G. Giusteri, and A. Martiniello, Microstructure and thickening of dense suspensions under extensional and shear flows, J. of Fluid Mech, vol.825, 2017.

A. Sierou and J. F. Brady, Accelerated stokesian dynamics simulations, J. of Fluid Mech, vol.448, pp.115-146, 2001.

A. Sierou and J. F. Brady, Rheology and microstructure in concentrated noncolloidal suspensions, J. of Rheol, vol.46, issue.5, pp.1031-1056, 2002.

A. Singh and P. R. Nott, Experimental measurements of the normal stresses in sheared stokesian suspensions, J. of Fluid Mech, vol.490, pp.293-320, 2003.

B. Snook, J. E. Butler, and E. Guazzelli, Dynamics of shear-induced migration of spherical particles in oscillatory pipe flow, J. of Fluid Mech, vol.786, pp.128-153, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01432419

D. E. Stewart, Rigid-body dynamics with friction and impact, SIAM review, vol.42, pp.3-39, 2000.
URL : https://hal.archives-ouvertes.fr/hal-01570533

J. J. Stickel and R. L. Powell, Fluid mechanics and rheology of dense suspensions, Ann. Rev. Fluid Mech, vol.37, pp.129-149, 2005.

J. J. Stickel, R. J. Phillips, and R. L. Powell, A constitutive model for microstructure and total stress in particulate suspensions, J. Rheol, vol.50, issue.4, pp.379-413, 2006.

J. J. Stickel, R. J. Phillips, and R. L. Powell, Application of a constitutive model for particulate suspensions : time-dependent viscometric flows, J. Rheol, vol.51, issue.6, pp.1271-1302, 2007.

J. W. Swan and J. F. Brady, Simulation of hydrodynamically interacting particles near a no-slip boundary, Phys. of Fluids, vol.19, issue.11, p.113306, 2007.

J. W. Swan and J. F. Brady, The hydrodynamics of confined dispersions, J. of Fluid Mech, vol.687, pp.254-299, 2011.

T. E. Tezduyar, M. Behr, S. Mittal, and 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, Comp. meth. in appl. mech. and eng, vol.94, issue.3, pp.353-371, 1992.

H. Troadec, F. Radjai, S. Roux, and J. C. Charmet, Model for granular texture with steric exclusion, Phys. Rev. E, vol.66, issue.4, p.41305, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00077973

N. Verdon, A. Lefebvre-lepot, P. Laure, and L. Lobry, Modified lees-edwards boundary conditions and viscous contact for numerical simulations of particles in a shear flow, Euro. J. of Comp. Mech, vol.21, pp.397-406, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00783667

P. Vigneaux, G. Chambon, A. Marly, L. Luu, and E. P. Philippe, Flow of a yield-stress fluid over a cavity : Experimental and numerical investigation of a viscoplastic boundary layer, J. of Non-Newt. Fluid Mech, vol.261, pp.38-49, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01857303

A. Wachs and I. A. Frigaard, Particle settling in yield stress fluids : limiting time, distance and applications, J. of Non-Newtonian Fluid Mech, vol.238, pp.189-204, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01455108

A. Wachs, A. Hammouti, G. Vinay, and M. Rahmani, Accuracy of finite volume/staggered grid distributed lagrange multiplier/fictitious domain simulations of particulate flows, Comp. and Fluids, vol.115, pp.154-172, 2015.

M. Wang and J. F. Brady, Spectral ewald acceleration of stokesian dynamics for polydisperse suspensions, J. of Comp Phy, vol.306, pp.443-477, 2016.

E. W. Weisstein, Spherical harmonic, from mathworld -a wolfram web resource, 2016.

T. Williams and C. Keley, gnuplot : an interactive program, 2010.

H. J. Wilson and R. H. Davis, The viscosity of a dilute suspension of rough spheres, J. of Fluid Mech, vol.421, pp.339-367, 2000.

M. Wyart and M. Cates, Discontinuous shear thickening without inertia in dense non-brownian suspensions, Physical review letters, vol.112, issue.9, p.98302, 2014.

K. Yapici, R. L. Powell, and R. J. Phillips, Particle migration and suspension structure in steady and oscillatory plane Poiseuille flow, Phys. Fluids, vol.21, issue.5, p.53302, 2009.

K. Yeo and M. R. Maxey, Dynamics of concentrated suspensions of non-colloidal particles in couette flow, Journal of Fluid Mechanics, vol.649, pp.205-231, 2010.

K. Yeo and M. R. Maxey, Simulation of concentrated suspensions using the force-coupling method, J. of Comput. Phys, vol.229, issue.6, pp.2401-2421, 2010.

K. Yeo and M. R. Maxey, Numerical simulations of concentrated suspensions of monodisperse particles in a poiseuille flow, J. of Fluid Mech, vol.682, pp.491-518, 2011.

I. E. Zarraga, D. A. Hill, and D. T. Leighton, The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids, J. Rheol, vol.44, issue.2, pp.185-220, 2000.

D. Zhang and A. Prosperetti, Averaged equations for inviscid disperse two-phase flow, Journal of Fluid Mechanics, vol.267, pp.185-219, 1994.