X. Nicolas, M. Medale, S. Glockner, and S. Gounand, Benchmark solution for a threedimensional mixed convection flow ? Part 1: reference solutions, Numerical Heat Transfer, Part B, vol.60, issue.5, pp.325-345, 2011.

X. Nicolas, S. Gounand, M. Medale, and S. Glockner, Benchmark solution for a threedimensional mixed convection flow ? Part 2: analysis of Richardson extrapolation in the presence of a singularity, Numerical Heat Transfer, Part B, vol.60, issue.5, pp.346-369, 2011.

X. Nicolas, A. Benzaoui, and S. Xin, Numerical simulation of thermoconvective flows and more uniform depositions in a cold wall rectangular APCVD reactor, Journal of Crystal Growth, vol.310, issue.1, pp.310-174, 2008.
DOI : 10.1016/j.jcrysgro.2007.10.016
URL : https://hal.archives-ouvertes.fr/hal-00353437

Q. H. Wang and Y. Jaluria, INSTABILITY AND HEAT TRANSFER IN MIXED-CONVECTION FLOW IN A HORIZONTAL DUCT WITH DISCRETE HEAT SOURCES, Numerical Heat Transfer, Part A: Applications, vol.33, issue.6, pp.42-445, 2002.
DOI : 10.1080/10407799308955881

X. Nicolas, Bibliographical review on the Poiseuille-Rayleigh-Bénard flows: the mixed convection flows in horizontal rectangular ducts heated from below, Int. J. Thermal Sc, pp.41-961, 2002.

K. C. Chiu and F. Rosenberger, Mixed convection between horizontal plates -1. Entrance effects, Int. J. Heat Mass Transfer, vol.30, pp.1645-1654, 1987.

M. T. Ouazzani, J. K. Platten, and A. Mojtabi, Etude expérimentale de la convection mixte entre deux plans horizontaux à températures différentes -2, Int. J. Heat Mass Transfer, pp.33-1417, 1990.

A. Benzaoui, X. Nicolas, and S. Xin, Efficient vectorized finite difference method to solve the incompressible Navier-Stokes equations for 3D mixed convection flows in high aspect ratio channels, Num. Heat Trans. B, pp.48-277, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00694583

M. Medale, X. Nicolas, . Call, and . Contributions, CALL FOR CONTRIBUTIONS: Towards numerical benchmark solutions for 3D mixed convection flows in rectangular channels heated from below, International Journal of Thermal Sciences, vol.45, issue.4, pp.45-331, 2006.
DOI : 10.1016/j.ijthermalsci.2005.12.004

H. Pabiou, S. Mergui, and C. Bénard, Wavy secondary instability of longitudinal rolls in RayleighPoiseuille flows, Journal of Fluid Mechanics, vol.542, issue.-1, pp.175-194, 2005.
DOI : 10.1017/S0022112005006154

X. Nicolas, J. M. Luijkx, and J. K. Platten, Linear stability of mixed convection flows in horizontal rectangular channels of finite transversal extension heated from below, International Journal of Heat and Mass Transfer, vol.43, issue.4, pp.43-589, 2000.
DOI : 10.1016/S0017-9310(99)00099-X
URL : https://hal.archives-ouvertes.fr/hal-00695287

K. Goda, A multistep technique with implicit difference schemes for calculating two- or three-dimensional cavity flows, Journal of Computational Physics, vol.30, issue.1, pp.76-95, 1979.
DOI : 10.1016/0021-9991(79)90088-3

J. L. Guermond and J. Shen, A new class of truly consistent splitting schemes for incompressible flows, Journal of Computational Physics, vol.192, issue.1, pp.192-262, 2003.
DOI : 10.1016/j.jcp.2003.07.009

S. A. Orszag, M. Israeli, and M. O. Deville, Boundary conditions for incompressible flows, Journal of Scientific Computing, vol.96, issue.1, pp.75-111, 1986.
DOI : 10.1007/BF01061454

G. E. Karniadakis, M. Israeli, and S. A. Orszag, High-order splitting methods for the incompressible Navier-Stokes equations, Journal of Computational Physics, vol.97, issue.2, pp.97-414, 1991.
DOI : 10.1016/0021-9991(91)90007-8

T. C. Papanastasiou, N. Malamataris, and K. Ellwood, A new outflow boundary condition, International Journal for Numerical Methods in Fluids, vol.30, issue.5, pp.14-587, 1992.
DOI : 10.1002/fld.1650140506

L. J. Timmermans, P. D. Minev, and F. N. , Van De Vosse, An approximate projection scheme for incompressible flow using spectral elements, Int. J. Num. Meth. Fluids, pp.22-673, 1996.

B. P. Leonard, A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering, vol.19, issue.1, pp.59-98, 1979.
DOI : 10.1016/0045-7825(79)90034-3

R. D. Falgout, J. E. Jones, and U. M. Yang, The Design and Implementation of Hypre, a Library of Parallel High Performance Preconditioners, chapter in Numerical Solution of Partial Differential Equations on Parallel Computers, pp.51-267, 2006.

A. Ern and J. L. Guermond, Eléments finis: théorie, applications, mise en oeuvre, 2002.

S. Turek, Efficent solvers for Incompressible Flow Problems -An Algorithmic and Computational Approach, Lecture Notes in Computational Science and Engineering, vol.6, 1999.

A. Quarteroni, F. Saleri, and A. Veneziani, Factorization methods for the numerical approximation of Navier???Stokes equations, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.1-3, pp.188-505, 2000.
DOI : 10.1016/S0045-7825(99)00192-9

Y. Saad, Iterative methods for sparse linear systems, SIAM, 2003.
DOI : 10.1137/1.9780898718003

Y. Notay, An aggregation-based algebraic multigrid method, Electronic Transactions on Numerical Analysis, vol.37, pp.123-146, 2010.

K. F. Alvin, W. L. Oberkampf, B. M. Rutherford, and K. V. Diegert, Methodology for characterizing modeling and discretization uncertainties in computational simulation, pp.2000-0515
DOI : 10.2172/752055

P. J. Roache, Perspective: A Method for Uniform Reporting of Grid Refinement Studies, Journal of Fluids Engineering, vol.116, issue.3, pp.405-413, 1994.
DOI : 10.1115/1.2910291

W. L. Oberkampf and T. Trucano, Verification and validation in computational fluid dynamics, Sandia Report, also in Progress in Aerospace Sciences, pp.2002-0529, 2002.

C. J. Roy, Review of code and solution verification procedures for computational simulation, Journal of Computational Physics, vol.205, issue.1, pp.131-156, 2005.
DOI : 10.1016/j.jcp.2004.10.036

G. Evans and S. Paolucci, The thermoconvective instability of plane poiseuille flow heated from below: A proposed benchmark solution for open boundary flows, International Journal for Numerical Methods in Fluids, vol.4, issue.7, pp.11-1001, 1990.
DOI : 10.1002/fld.1650110707

P. , L. Quéré, C. Weisman, H. Paillère, J. Vierendeels et al., Modelling of natural convection flows with large temperature differences: a benchmark problem for low Mach number solvers, pp.2-39, 2005.

O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Fourth Edition, 1994.

W. G. Strang and G. J. Fix, An analysis of the Finite Elements Method, first edition in Prentice-Hall Series in Automatic Computation (1973) and second edition in Wellesley, 2008.

W. Shyy, M. Garbey, A. Appukuttan, and J. Wu, EVALUATION OF RICHARDSON EXTRAPOLATION IN COMPUTATIONAL FLUID DYNAMICS, Numerical Heat Transfer, Part B: Fundamentals, vol.41, issue.2, pp.41-139, 2002.
DOI : 10.1016/0021-9991(82)90058-4

P. M. Gresho, R. L. Lee, R. L. Sani, M. K. Maslanik, and B. E. Eaton, The consistent Galerkin FEM for computing derived boundary quantities in thermal and or fluids problems, International Journal for Numerical Methods in Fluids, vol.2, issue.4, pp.7-1111, 1987.
DOI : 10.1002/fld.1650070406

T. J. Hughes, G. Engel, L. Mazzei, and M. G. Larson, The Continuous Galerkin Method Is Locally Conservative, Journal of Computational Physics, vol.163, issue.2, pp.163-467, 2000.
DOI : 10.1006/jcph.2000.6577

M. Garbey and W. Shyy, A least square extrapolation method for improving solution accuracy of PDE computations, Journal of Computational Physics, vol.186, issue.1, pp.186-187, 2003.
DOI : 10.1016/S0021-9991(02)00080-3