A. Aguilar-corona, Agitation of particles in a liquid fluidize bed: Experimental study, 2008.

A. Aguilar-corona, R. Zenit, and O. Masbernat, Collisions in a liquid fluidized bed, International Journal of Multiphase Flow, vol.37, issue.7, pp.695-705, 2011.
DOI : 10.1016/j.ijmultiphaseflow.2011.02.004

A. Chouippe and M. Uhlmann, Forcing homogeneous turbulence in direct numerical simulation of particulate flow with interface resolution and gravity, Physics of Fluids, vol.27, issue.12, 2015.
DOI : 10.1063/1.4936274

C. Corre, J. L. Estivalezes, S. Vincent, and O. Simonin, Direct numerical simulation of a liquid-solid fluidized bed computational techniques for multiphase flows, 7th International Conference on Multiphase Flow -ICMF 2010 Proceedings, 2010.

J. Derksen, Simulations of scalar dispersion in fluidized solid-liquid suspensions, AIChE Journal, vol.29, issue.14, pp.1880-1890, 2014.
DOI : 10.1002/aic.14372

J. J. Derksen and S. Sundaresan, Direct numerical simulations of dense suspensions: wave instabilities in liquid-fluidized beds, Journal of Fluid Mechanics, vol.258, pp.303-336, 2007.
DOI : 10.1016/S0032-5910(00)00395-8

E. Deutsch and O. Simonin, Large eddy simulation applied to the motion of particles in stationary homogeneous fluid turbulence, in: Turbulence Modification in Multiphase Flows, ASME FED, pp.35-42, 1991.

D. Felice, R. Kehlenbeck, and R. , Sedimentation Velocity of Solids in Finite Size Vessels, Chemical Engineering & Technology, vol.85, issue.12, pp.1123-1126, 2000.
DOI : 10.1002/1521-4125(200012)23:12<1123::AID-CEAT1123>3.0.CO;2-2

P. Duru and ´. E. Guazzelli, Experimental investigation on the secondary instability of liquid-fluidized beds and the formation of bubbles, Journal of Fluid Mechanics, vol.470, pp.359-382, 2002.
DOI : 10.1017/S0022112002002100

P. Février, O. Simonin, and K. Squires, Partitioning of particle velocities in gassolid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study, Journal of Fluid Mechanics, vol.533, pp.1-46, 2005.

R. Fox, On multiphase turbulence models for collisional fluidparticle flows, Journal of Fluid Mechanics, vol.742, p.368424, 2014.
DOI : 10.1017/jfm.2014.21

F. Gevrin, O. Masbernat, and O. Simonin, Granular pressure and particle velocity fluctuations prediction in liquid fluidized beds, Chemical Engineering Science, vol.63, issue.9, pp.2450-2464, 2008.
DOI : 10.1016/j.ces.2008.01.031

K. Khadra, P. Angot, S. Parneix, and J. P. Caltagirone, Fictitious domain approach for numerical modelling of Navier-Stokes equations, International Journal for Numerical Methods in Fluids, vol.16, issue.8, pp.651-684, 2000.
DOI : 10.1002/1097-0363(20001230)34:8<651::AID-FLD61>3.0.CO;2-D

D. Legendre, R. Zenit, C. Daniel, and P. Guiraud, A note on the modelling of the bouncing of spherical drops or solid spheres on a wall in viscous fluid, Chemical Engineering Science, vol.61, issue.11, pp.3543-3549, 2006.
DOI : 10.1016/j.ces.2005.12.028

J. C. Brändle-de-motta, W. P. Breugem, B. Gazanion, J. L. Estivalezes, S. Vincent et al., Numerical modelling of finite-size particle collisions in a viscous fluid, Physics of Fluids, vol.25, issue.8, p.83302, 2013.
DOI : 10.1063/1.4817382

H. Nicolai, B. Herzhaft, E. Hinch, L. Oger, and E. Guazzelli, Particle velocity fluctuations and hydrodynamic self???diffusion of sedimenting non???Brownian spheres, Physics of Fluids, vol.7, issue.1, pp.3936-3944, 1995.
DOI : 10.1063/1.868733

T. W. Pan, D. D. Joseph, R. Bai, R. Glowinski, and V. Sarin, Fluidization of 1204 spheres: simulation and experiment, Journal of Fluid Mechanics, vol.451, pp.169-191, 2002.
DOI : 10.1017/S0022112001006474

J. Richardson and W. Zaki, The sedimentation of a suspension of uniform spheres under conditions of viscous flow, Chemical Engineering Science, vol.3, issue.2, pp.65-73, 1954.
DOI : 10.1016/0009-2509(54)85015-9

C. Tchen, Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid, 1947.

S. Tenetti and S. Subramanian, Particle-Resolved Direct Numerical Simulation for Gas-Solid Flow Model Development, Annual Review of Fluid Mechanics, vol.46, issue.1, pp.199-230, 2014.
DOI : 10.1146/annurev-fluid-010313-141344

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. Uhlmann and J. Du?ek, The motion of a single heavy sphere in ambient fluid: A benchmark for interface-resolved particulate flow simulations with significant relative velocities, International Journal of Multiphase Flow, vol.59, pp.221-243, 2014.
DOI : 10.1016/j.ijmultiphaseflow.2013.10.010

S. Vincent, J. C. Brändle-de-motta, A. Sarthou, J. L. Estivalezes, O. Simonin et al., A Lagrangian VOF tensorial penalty method for the DNS of resolved particle-laden flows, Journal of Computational Physics, vol.256, pp.582-614, 2014.
DOI : 10.1016/j.jcp.2013.08.023

URL : https://hal.archives-ouvertes.fr/hal-01078245

K. Zhang, Y. Guan, X. Yao, Y. Li, X. Fan et al., Two- and three-dimensional computational studies of liquid???solid fluidization, Powder Technology, vol.235, pp.180-191, 2013.
DOI : 10.1016/j.powtec.2012.09.046

Z. Zhang, L. Botto, and A. Prosperetti, Microstructural effects in a fullyresolved simulation of 1,024 sedimenting spheres, IUTAM Symposium on Computational Approaches to Multiphase Flow. Springer Netherlands. number 81 in Fluid Mechanics and Its Applications, pp.197-206, 2006.

Z. Zhang and A. Prosperetti, A second-order method for three-dimensional particle simulation, Journal of Computational Physics, vol.210, issue.1, pp.292-324, 2005.
DOI : 10.1016/j.jcp.2005.04.009