F. J. Alexander, S. Chen, and J. D. Sterling, Lattice Boltzmann thermohydrodynamics, Physical Review E, vol.47, issue.4, pp.2249-2252, 1993.
DOI : 10.1103/PhysRevE.47.R2249

P. L. Bhatnagar, E. P. Gross, and M. Krook, A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems, Physical Review, vol.94, issue.3, pp.511-525, 1954.
DOI : 10.1103/PhysRev.94.511

M. Bouzidi, M. Firdaouss, and P. Lallemand, Momentum transfer of a Boltzmann-lattice fluid with boundaries, Physics of Fluids, vol.13, issue.11, pp.3452-3459, 2001.
DOI : 10.1063/1.1399290

S. Chen and G. D. Doolen, LATTICE BOLTZMANN METHOD FOR FLUID FLOWS, Annual Review of Fluid Mechanics, vol.30, issue.1, pp.329-364, 1998.
DOI : 10.1146/annurev.fluid.30.1.329

M. A. Christon, P. M. Gresho, and S. B. Sutton, Computational predictability of time-dependent natural convection flows in enclosures (including a benchmark solution), International Journal for Numerical Methods in Fluids, vol.3, issue.2, pp.953-980, 2002.
DOI : 10.1002/fld.395

G. De-vahl and . Davis, Natural convection of air in a square cavity: A bench mark numerical solution, International Journal for Numerical Methods in Fluids, vol.12, issue.3, pp.249-264, 1983.
DOI : 10.1002/fld.1650030305

D. Dhumì-eres, I. Ginzburg, M. Krafczyk, P. Lallemand, and L. Luo, Multiple-relaxation-time lattice Boltzmann models in three dimensions, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.360, issue.1792, pp.437-451, 2002.
DOI : 10.1098/rsta.2001.0955

H. Dixit and V. Babu, Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, International Journal of Heat and Mass Transfer, vol.49, issue.3-4, pp.727-739, 2006.
DOI : 10.1016/j.ijheatmasstransfer.2005.07.046

A. D. Orazio, M. Coricone, and G. P. Celata, Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition, International Journal of Thermal Sciences, vol.43, issue.6, pp.575-586, 2004.
DOI : 10.1016/j.ijthermalsci.2003.11.002

A. D. Orazio and S. Succi, Computational Science ? ICC 2003, chapter Boundary Conditions for Thermal Lattice Boltzmann Simulations, pp.977-986, 2003.

U. Frisch, D. Dhumì-eres, B. Hasslacher, P. Lallemand, Y. Pomeau et al., Lattice gas hydrodynamics in two and three dimensions, Complex Syst, vol.1, pp.649-707, 1987.

I. Ginzburg, D. , and A. Kuzmin, Optimal Stability of Advection-Diffusion Lattice Boltzmann Models with Two Relaxation Times for??Positive/Negative Equilibrium, Journal of Statistical Physics, vol.38, issue.1/2, pp.1090-1143, 2010.
DOI : 10.1007/s10955-010-9969-9

I. Ginzburg, F. Verhaeghe, and D. Dhumì-eres, Two-relaxation-time lattice Boltzmann scheme: about parametrization, velocity, pressure and mixed boundary conditions, Commun. Comput. Phys, vol.3, pp.427-478, 2008.

I. Ginzburg and D. Dhumì-eres, Multireflection boundary conditions for lattice Boltzmann models, Physical Review E, vol.68, issue.6, p.66614, 2003.
DOI : 10.1103/PhysRevE.68.066614

Z. Guo, B. Shi, and C. Zheng, A coupled lattice BGK model for the Boussinesq equations, International Journal for Numerical Methods in Fluids, vol.27, issue.4, pp.325-342, 2002.
DOI : 10.1002/fld.337

M. S. Ashorynejad and A. A. Mohamad, Magnetic field effects on natural convection flow of a nanofluid in a horizontal cylindrical annulus using Lattice Boltzmann method, International Journal of Thermal Sciences, vol.64, 2013.
DOI : 10.1016/j.ijthermalsci.2012.08.006

X. He and L. Luo, Lattice Boltzmann Model for the Incompressible Navier???Stokes Equation, Journal of Statistical Physics, vol.88, issue.3/4, pp.927-944, 1997.
DOI : 10.1023/B:JOSS.0000015179.12689.e4

X. He, S. Chen, and G. D. Doolen, A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit, Journal of Computational Physics, vol.146, issue.1, pp.282-300, 1998.
DOI : 10.1006/jcph.1998.6057

X. He, L. Luo, and M. Dembo, Some Progress in Lattice Boltzmann Method. Part I. Nonuniform Mesh Grids, Journal of Computational Physics, vol.129, issue.2, pp.357-363, 1996.
DOI : 10.1006/jcph.1996.0255

H. Huang, X. Lu, and M. C. Sukop, Numerical study of lattice Boltzmann methods for a convection???diffusion equation coupled with Navier???Stokes equations, Journal of Physics A: Mathematical and Theoretical, vol.44, issue.5, p.55001, 2011.
DOI : 10.1088/1751-8113/44/5/055001

T. Inamuro, M. Yoshina, and F. Ogino, A non???slip boundary condition for lattice Boltzmann simulations, Physics of Fluids, vol.7, issue.12, pp.2928-2930, 1995.
DOI : 10.1063/1.868766

M. Jami, A. Mezrhab, M. Bouzidi, and P. Lallemand, Lattice Boltzmann method applied to the laminar natural convection in an enclosure with a heat-generating cylinder conducting body, International Journal of Thermal Sciences, vol.46, issue.1, pp.38-47, 2007.
DOI : 10.1016/j.ijthermalsci.2006.03.010

P. Lallemand and L. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Physical Review E, vol.61, issue.6, pp.6546-6562, 2000.
DOI : 10.1103/PhysRevE.61.6546

P. Lallemand and L. Luo, Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Physical Review E, vol.68, issue.3, p.36706, 2003.
DOI : 10.1103/PhysRevE.68.036706

J. Latt, Choice of units in lattice Boltzmann simulations, 2008.

J. Latt, B. Chopard, O. Malaspinas, M. Deville, and A. Michler, Straight velocity boundaries in the lattice Boltzmann method, Physical Review E, vol.77, issue.5, p.56703, 2008.
DOI : 10.1103/PhysRevE.77.056703

P. and L. Quéré, Accurate solutions to the square thermally driven cavity at high Rayleigh number, Computers & Fluids, vol.20, issue.1, pp.29-41, 1991.
DOI : 10.1016/0045-7930(91)90025-D

L. Luo, W. Lao, X. Chen, Y. Peng, and W. Zhang, Numerics of the lattice Boltzmann method: Effects of collision models on the lattice Boltzmann simulations, Physical Review E, vol.83, issue.5, p.56710, 2011.
DOI : 10.1103/PhysRevE.83.056710

G. R. Mcnamara and G. Zanetti, Use of the Boltzmann Equation to Simulate Lattice-Gas Automata, Physical Review Letters, vol.61, issue.20, pp.2332-2335, 1988.
DOI : 10.1103/PhysRevLett.61.2332

F. Meng, M. Wang, and Z. Li, Lattice Boltzmann simulations of conjugate heat transfer in high-frequency oscillating flows, International Journal of Heat and Fluid Flow, vol.29, issue.4, pp.1203-1210, 2008.
DOI : 10.1016/j.ijheatfluidflow.2008.03.001

A. Mezrhab, M. Bouzidi, and P. Lallemand, Hybrid lattice-Boltzmann finite-difference simulation of convective flows, Computers & Fluids, vol.33, issue.4, pp.623-641, 2004.
DOI : 10.1016/j.compfluid.2003.05.001

A. Mezrhab, M. A. Moussaoui, M. Jami, H. Naji, and M. Bouzidi, Double MRT thermal lattice Boltzmann method for simulating convective flows, Physics Letters A, vol.374, issue.34, pp.3743499-3507, 2010.
DOI : 10.1016/j.physleta.2010.06.059
URL : https://hal.archives-ouvertes.fr/hal-00512643

A. A. Mohamad, Lattice Boltzmann Methods, Fundamentals, Applications, with Computer Codes, 2011.

A. Mohamad and A. Kuzmin, A critical evaluation of force term in lattice Boltzmann method, natural convection problem, International Journal of Heat and Mass Transfer, vol.53, issue.5-6, pp.990-996, 2010.
DOI : 10.1016/j.ijheatmasstransfer.2009.11.014

M. Moussaoui, A. Mezrhab, and H. Naji, A computation of flow and heat transfer past three heated cylinders in a vee shape by a double distribution MRT thermal lattice Boltzmann model, International Journal of Thermal Sciences, vol.50, issue.8, pp.1532-1542, 2011.
DOI : 10.1016/j.ijthermalsci.2011.03.011
URL : https://hal.archives-ouvertes.fr/hal-00602433

X. Nicolas, S. Gounand, M. Médale, and S. Glockner, Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 2: Analysis of Richardson Extrapolation in the Presence of a Singularity, Numerical Heat Transfer, Part B: Fundamentals, vol.186, issue.5, pp.346-369, 2011.
DOI : 10.1080/10407790.2011.616761
URL : https://hal.archives-ouvertes.fr/hal-00692094

Y. Peng, C. Shu, and Y. Chew, Simplified thermal lattice Boltzmann model for incompressible thermal flows, Physical Review E, vol.68, issue.2, p.26701, 2003.
DOI : 10.1103/PhysRevE.68.026701

C. Shu, Y. Peng, and Y. Chew, SIMULATION OF NATURAL CONVECTION IN A SQUARE CAVITY BY TAYLOR SERIES EXPANSION- AND LEAST SQUARES-BASED LATTICE BOLTZMANN METHOD, International Journal of Modern Physics C, vol.13, issue.10, pp.1399-1414, 2002.
DOI : 10.1142/S0129183102003966

G. Silva, Corner boundary conditions in lattice Boltzmann method. Lecture note, 2011.

S. Suga, NUMERICAL SCHEMES OBTAINED FROM LATTICE BOLTZMANN EQUATIONS FOR ADVECTION DIFFUSION EQUATIONS, International Journal of Modern Physics C, vol.17, issue.11, p.1563, 2006.
DOI : 10.1142/S0129183106010030

J. Wang, D. Wang, P. Lallemand, and L. Luo, Lattice Boltzmann simulations of thermal convective flows in two dimensions, Computers & Mathematics with Applications, vol.65, issue.2, pp.262-286, 2013.
DOI : 10.1016/j.camwa.2012.07.001

J. Wang, M. Wang, and Z. Li, A lattice Boltzmann algorithm for fluid???solid conjugate heat transfer, International Journal of Thermal Sciences, vol.46, issue.3, pp.228-234, 2007.
DOI : 10.1016/j.ijthermalsci.2006.04.012

S. Xin and P. L. Quéré, An extended Chebyshev pseudo-spectral benchmark for the 8:1 differentially heated cavity, International Journal for Numerical Methods in Fluids, vol.322, issue.4, pp.981-998, 2002.
DOI : 10.1002/fld.399

Y. Yan and Y. Zu, Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder ??? A LBM approach, International Journal of Heat and Mass Transfer, vol.51, issue.9-10, pp.2519-2536, 2008.
DOI : 10.1016/j.ijheatmasstransfer.2007.07.053

Q. Zou and X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Physics of Fluids, vol.9, issue.6, pp.1591-1598, 1997.
DOI : 10.1063/1.869307