C. Naturelle and E. , CONVECTION MIXTE Bibliographie [1] M. Abramowitz and I.A. Stegun. Handbook of Mathematical Functions, 1970.

F. Archambeau, N. Méchitoua, and M. Sakiz, Code Saturne : A finite volume code for the computation of turbulent incompressible flowsindustrial applications, Int. J. on Finite Volumes, 2004.

V. A. Baikov and N. H. Ibragimov, Continuation of approximate transformation groups via multiple time scales method, Nonlinear Dynamics, vol.22, issue.1, pp.3-13, 2000.
DOI : 10.1023/A:1008357023225

D. Baly, S. Mergui, and C. Niculae, Confined turbulent mixed convection in the presence of a horizontal buoyant wall jet, in : Fundamentals of mixed convection, ASME, vol.213, pp.65-72, 1992.

J. Bardina, J. H. Ferziger, and W. C. Reynolds, Improved subgrid-scale models for large-eddy simulation, 13th Fluid and PlasmaDynamics Conference, pp.80-1357, 1980.
DOI : 10.2514/6.1980-1357

J. Bardina, J. H. Ferziger, and W. C. Reynolds, Improved turbulence models based on for large eddy simulation of homogeneous, incompressible , turbulent flows, 1983.

Y. Benarafa, O. Cioni, F. Ducros, and P. Sagaut, Temperature wall modelling for large-eddy simulation in a heated turbulent plane channel flow, International Journal of Heat and Mass Transfer, vol.50, issue.21-22, pp.4360-4370, 2007.
DOI : 10.1016/j.ijheatmasstransfer.2006.12.038

L. C. Berselli, T. Iliescu, and W. J. Layton, Mathematics of Large Eddy Simulation of Turbulent Flows, 2006.

K. Brading and E. Castellani, Symmetries in Physics. Philosophical Reflections, 2003.

B. Cantwell, Introduction to Symmetry Analysis, Applied Mechanics Reviews, vol.57, issue.1, 2002.
DOI : 10.1115/1.1641778

R. Cheesewright, K. J. King, and S. Ziai, Experimental data for the validation of computer codes for the prediction of two-dimensionel buoyant cavity flows, ASME Winter Annual Meeting, p.155, 1986.

A. F. Cheviakov, GeM software package for computation of symmetries and conservation laws of differential equations, Computer Physics Communications, vol.176, issue.1, pp.48-61, 2007.
DOI : 10.1016/j.cpc.2006.08.001

M. Chhay and A. Hamdouni, Lie Symmetry Preservation by Finite Difference Schemes for the Burgers Equation, Symmetry, vol.2, issue.2, pp.868-883, 2010.
DOI : 10.3390/sym2020868
URL : https://hal.archives-ouvertes.fr/hal-00536622

M. Chhay and A. Hamdouni, A new construction for invariant numerical schemes using moving frames, Comptes Rendus M??canique, vol.338, issue.2, pp.97-101, 2010.
DOI : 10.1016/j.crme.2010.01.001
URL : https://hal.archives-ouvertes.fr/hal-00534605

M. Chhay and A. Hamdouni, On accuracy of invariant numerical schemes. Comm. Pure and Appli, Analysis, vol.10, issue.2, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00540188

D. H. Darryl, T. Schmah, and C. Stoica, Geometric Mechanics and Symmetry : From Finite to Infinite Dimensions, 2009.

T. Eidson, Numerical simulation of the turbulent Rayleigh???B??nard problem using subgrid modelling, Journal of Fluid Mechanics, vol.15, issue.-1, pp.245-268, 1985.
DOI : 10.1007/BF00156116

J. Taine and J. Petit, Transferts thermiques. Mécanique des fluides anisothermes : Cours et données de base, 1998.
URL : https://hal.archives-ouvertes.fr/hal-00262470

C. Fureby and G. Tabor, Mathematical and Physical Constraints on Large-Eddy Simulations, Theorical and Computational Fluid Dynamics, pp.85-102, 1997.
DOI : 10.1007/s001620050034

W. I. Fushchych, The symmetry and exact solutions of some multidimensional nonlinear equations of mathematical physics. Scientific, pp.175-179, 2001.

W. I. Fushchych, W. M. Shtelen, and S. L. Slavutsky, Reduction and exact solutions of the Navier-Stokes equations. Scientific, pp.306-319, 2002.

B. Galanti, J. D. Gibbon, and M. Heritage, Vorticity alignment results for the three-dimensional Euler and Navier - Stokes equations, Nonlinearity, vol.10, issue.6, pp.1675-1694, 1997.
DOI : 10.1088/0951-7715/10/6/013

P. Gamnitzer, V. Gravemeier, and W. A. Wall, Time-dependent subgrid scales in residual-based large eddy simulation of turbulent channel flow, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.13-16, pp.819-827, 2010.
DOI : 10.1016/j.cma.2009.07.009

W. George, M. Wosnik, and L. Castillo, Similarity analysis for forced convection thermal boundary layer, 10th International Symposium in Transport Phenomena in Thermal Science and Process Engineering, pp.239-244, 1997.

M. Germano, U. Piomelli, P. Moin, and W. Cabot, A dynamic subgrid???scale eddy viscosity model, Physics of Fluids A: Fluid Dynamics, vol.3, issue.7, pp.1760-1765, 1991.
DOI : 10.1063/1.857955

V. Grassi, R. Lea, G. Soliani, and P. Tempesta, Temperature behavior of vortices of a 3D thermoconducting viscous fluid

V. Grassi, R. Lea, G. Soliani, and P. Tempesta, Vortices and invariant surfaces generated by symmetries for the 3D Navier???Stokes equations, Physica A: Statistical Mechanics and its Applications, vol.286, issue.1-2, pp.79-108, 2000.
DOI : 10.1016/S0378-4371(00)00223-5

V. Grassi, R. Lea, G. Soliani, and P. Tempesta, A group analysis of the 2D Navier???Stokes???Fourier equations, Physica A: Statistical Mechanics and its Applications, vol.293, issue.3-4, pp.421-434, 2001.
DOI : 10.1016/S0378-4371(00)00628-2

N. H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, 1994.

T. Ishihara, T. Gotoh, and Y. Kaneda, Study of high-Reynolds number isotopic turbulence by direct numerical simulation, Annu. Rev

V. John and W. J. Layton, Analysis of Numerical Errors in Large Eddy Simulation, SIAM Journal on Numerical Analysis, vol.40, issue.3, pp.995-1020, 2002.
DOI : 10.1137/S0036142900375554

B. A. Kader, Temperature and concentration profiles in fully turbulent boundary layers, International Journal of Heat and Mass Transfer, vol.24, issue.9, pp.1541-1544, 1981.
DOI : 10.1016/0017-9310(81)90220-9

B. A. Kader, Heat and mass transfer in pressure-gradient boundary layers, International Journal of Heat and Mass Transfer, vol.34, issue.11, pp.2837-2857, 1991.
DOI : 10.1016/0017-9310(91)90245-A

G. Khujadze and M. Oberlack, DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow, Theoretical and Computational Fluid Dynamics, vol.18, issue.5, pp.391-411, 2004.
DOI : 10.1007/s00162-004-0149-x

G. Khujadze and M. Oberlack, DNS and Lie group analysis of turbulent boundarly layer flow, PAMM, vol.18, issue.1, pp.565-566, 2005.
DOI : 10.1002/pamm.200510259

M. Kinzel, M. Holzner, B. Lüthi, C. Tropea, W. Kinzelbach et al., Scaling laws of turbulent diffusion-an experimental va- BIBLIOGRAPHIE lidation, 14th Int Symp on Applications of Laser Techniques to Fluid Mechanics, pp.7-10, 2008.

A. N. Kolmogorov, Dissipation of Energy in the Locally Isotropic Turbulence, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.434, issue.1890, pp.301-305, 1941.
DOI : 10.1098/rspa.1991.0076

A. N. Kolmogorov, The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.434, issue.1890, pp.16-18, 1941.
DOI : 10.1098/rspa.1991.0075

A. Leonard, Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows, Adv. Geophys, A, vol.18, pp.237-248, 1974.
DOI : 10.1016/S0065-2687(08)60464-1

M. Lesieur, Turbulence in fluids. Fluid Mechanics and its Applications, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00261553

D. Lilly, A proposed modification of the Germano subgrid???scale closure method, Physics of Fluids A: Fluid Dynamics, vol.4, issue.3, pp.633-365, 1992.
DOI : 10.1063/1.858280

T. S. Lundgren, Strained spiral vortex model for turbulent fine structure, Physics of Fluids, vol.25, issue.12, p.2193, 1982.
DOI : 10.1063/1.863957

E. Lévêque, F. Toschi, L. Shao, and J. Bertoglio, Shear-Improved Smagorinsky model for large-eddy simulation od wall-bounded turbulent flows, J. Fluid Mech, 2008.

A. Majda and A. Bertozzi, Vorticity and Incompressible Flow, Cambridge Texts in Applied Mathematics, 2002.
DOI : 10.1017/CBO9780511613203

J. Meyers, B. J. Geurts, and P. Sagaut, A computational error-assessment of central finite-volume discretizations in large-eddy simulation using a Smagorinsky model, Journal of Computational Physics, vol.227, issue.1, pp.156-173, 2007.
DOI : 10.1016/j.jcp.2007.07.012

J. Meyers and P. Sagaut, Evaluation of Smagorinsky variants in large-eddy simulations of wall-resolved plane channel flows, Physics of Fluids, vol.19, issue.9, 2007.
DOI : 10.1063/1.2768944

O. Métais and M. Lesieur, Spectral large-eddy simulation of isotropic and stably stratified turbulence, Journal of Fluid Mechanics, vol.91, issue.-1, pp.157-194, 1992.
DOI : 10.1175/1520-0469(1976)033 2.0.CO;2

F. Nicoud and F. Ducros, Subgrid-scale stress modeling based on the square of the velocity gradient tensor. Flow, Turbulence and Combustion, pp.183-200, 1999.

M. Oberlack, Invariant modeling in large-eddy simulation of turbulence, Annual Research Briefs. Stanford University, 1997.

M. Oberlack, Symmetries, invariance and scaling-laws in homogeneous turbulent shear flows. Flow, Turbulence and Combustion, pp.111-135, 1999.

M. Oberlack, Symmetries of the Navier-Stokes equation and their applications for subgrid-models in large eddy simulation of turbulence

M. Oberlack, A unified approach for symmetries in plane parallel turbulent shear flows, Journal of Fluid Mechanics, vol.427, pp.299-328, 2001.
DOI : 10.1017/S0022112000002408

M. Oberlack and S. Guenther, Shear-free turbulent diffusion???classical and new scaling laws, Fluid Dynamics Research, vol.33, issue.5-6, pp.453-476, 2003.
DOI : 10.1016/j.fluiddyn.2003.08.004

P. Olver, Applications of Lie Groups to Differential Equations, Graduate Texts in Mathematics, 1993.

S. Pend and L. Davidson, Comparaison of subgrid-scale models in LES for turbulent convection flow with heat transfer, 2nd EF Conference in Turbulent Heat Transfer, pp.5-25, 1998.

S. Pend and L. Davidson, Numerical investigation of turbulent buoyant cavity flow using large eddy simulation, 3rd International Symposium on Turbulence, Heat and mass transfer, pp.737-744, 2000.

U. Piomelli, High Reynolds number calculations using the dynamic subgrid???scale stress model, Physics of Fluids A: Fluid Dynamics, vol.5, issue.6, pp.1484-1490, 1993.
DOI : 10.1063/1.858586

S. Pope, Turbulent Flows, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00338511

D. Razafindralandy, Contribution a l'étude mathématique et numérique de la simulation des grandes échelles, 2005.

D. Razafindralandy and A. Hamdouni, Analysis of subgrid models of heat convection by symmetry group theory, Comptes Rendus M??canique, vol.335, issue.4, pp.225-230, 2007.
DOI : 10.1016/j.crme.2007.03.004
URL : https://hal.archives-ouvertes.fr/hal-00312283

D. Razafindralandy, A. Hamdouni, and C. Béghein, A class of subgrid-scale models preserving the symmetry group of Navier???Stokes equations, Communications in Nonlinear Science and Numerical Simulation, vol.12, issue.3, pp.243-253, 2007.
DOI : 10.1016/j.cnsns.2005.02.006
URL : https://hal.archives-ouvertes.fr/hal-00312286

D. Razafindralandy, A. Hamdouni, and M. Oberlack, Analysis and development of subgrid turbulence models preserving the symmetry properties of the Navier???Stokes equations, European Journal of Mechanics - B/Fluids, vol.26, issue.4, pp.531-550, 2007.
DOI : 10.1016/j.euromechflu.2006.10.003
URL : https://hal.archives-ouvertes.fr/hal-00312287

D. Razafindralandy and A. Hamdouni, Consequences of Symmetries on the Analysis and Construction of Turbulence Models, Integrability and Geometry : Methods and Applications (SIGMA), 2006.
DOI : 10.3842/SIGMA.2006.052
URL : https://hal.archives-ouvertes.fr/hal-00312285

D. Razafindralandy, A. Hamdouni, and M. Chhay, Symmetry in turbulence simulation. in Numerical Simulation Research Progress, pp.161-207, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00542307

P. Sagaut, Introduction à la simulation des grandes échelles pour les écoulements de fluide incompresssible, Mathématiques et Applications, 1998.

P. Sagaut, Large Eddy Simulation for Incompressible Flows: An Introduction. Scientific Computation Series, Applied Mechanics Reviews, vol.55, issue.6, 2006.
DOI : 10.1115/1.1508154

V. Saveliev and M. Gorokhovski, Modèle de turbulence développée basé sur la théorie du groupe ; renormalisation des équations de Navier-Stokes. 18ème Congrès Français de Mécanique, 2007.

R. Schiestel, Les écoulements turbulents : Modélisation et simulation, 1998.

R. Schiestel, Méthodes de modélisation et de simulation des écoulements turbulents, 2006.

M. Tanaka and S. Kida, Characterization of vortex tubes and sheets, Physics of Fluids A: Fluid Dynamics, vol.5, issue.9, p.2079, 1983.
DOI : 10.1063/1.858546

L. Temmerman, M. A. Leschziner, C. P. Mellen, and J. Fröhlich, Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions, International Journal of Heat and Fluid Flow, vol.24, issue.2, pp.157-180, 2003.
DOI : 10.1016/S0142-727X(02)00222-9

E. Noether, Invariant Variationsprobleme, Kgl. Ges. Wiss., Nachr. Göttingen Math. Phys. K. l, pp.235-257, 1918.

H. K. Versteeg and W. Malalasekera, An introduction to computational fluid dynamics The finite volume method, Longman Scientific & Technical, 1995.

B. Wang, E. Yee, D. J. Bergstrom, and O. Iida, New dynamic subgrid-scale heat flux models for large-eddy simulation of thermal convection based on the general gradient diffusion hypothesis, Journal of Fluid Mechanics, vol.37
DOI : 10.2307/2371950

X. Wang and L. Castillo, Asymptotic solutions in forced convection turbulent boundary layers, Journal of Turbulence, vol.4, pp.1-18, 2003.
DOI : 10.1088/1468-5248/4/1/006

X. Wang, L. Castillo, and G. Araya, Temperature Scalings and Profiles in Forced Convection Turbulent Boundary Layers, Journal of Heat Transfer, vol.130, issue.2, 2008.
DOI : 10.1115/1.2813781

E. Wigner, Symmetries and Reflections, 1967.
DOI : 10.1063/1.3034986

Y. Zang, R. L. Street, and J. R. Koseff, A dynamic mixed subgrid???scale model and its application to turbulent recirculating flows, Physics of Fluids A: Fluid Dynamics, vol.5, issue.12, pp.3186-3196, 1993.
DOI : 10.1063/1.858675

W. Zhang and Q. Chen, Large eddy simulation of indoor airflow with a filtered dynamic subgrid scale model, International Journal of Heat and Mass Transfer, vol.43, issue.17, pp.3219-3231, 2000.
DOI : 10.1016/S0017-9310(99)00348-8