L. Littérature, Cette première étape nous a permis de valider le code (voir Chapitre 5)

G. Accary, Convection de Rayleigh Bénard dans les fluides supercritiques : mécanismes d'instabilité et transition vers la turbulence, thèse 3°cycle, 2005.

A. Alm06-]-d-'almeida and R. Prud-'homme, Comportement d'une poche fluide supercritique plongée dans un environnement à haute température, communication privé, 2006.

S. Amiroudine, Modélisation numérique des phénomènes de transport de chaleur et de masse dans les fluides supercritiques, thèse de l, 1995.

S. Amiroudine, J. Ouazzani, B. Zappoli, and P. Carlès, Numerical simulation of convective instabilities in near-critical pure fluids, Proc. 2 nd Europ. Symp. In Space, 1996.

S. Amiroudine, J. Ouazzani, B. Zappoli, and P. Carlès, Numerical solutions of 1D unsteady hypercompressible flows using finite volume methods, Europ. J. Mech., B/Fluids, vol.16, pp.5-665, 1997.

S. Amiroudine, P. Bontoux, P. Larroudé, B. Gilly, and B. Zappoli, Direct numerical simulation of instabilities in a two-dimensional near-critical fluid layer heated from below, Journal of Fluid Mechanics, vol.442, p.119, 2001.
DOI : 10.1017/S0022112001004967

URL : https://hal.archives-ouvertes.fr/hal-00259796

S. Amiroudine, K. Boutrouft, and B. Zappoli, The stabilizing effect of a

P. Bravais, B. Zappoli, and C. Mignon, Free convection in the vicinity of the critical point, 14 th IAF Congress, 1993.

W. H. Cabot and A. W. Cook, Reynolds number effects on Rayleigh-Taylor instability with possible implications for type-la supernovae, Nature Physics, vol.2, p.8, 2006.

P. Carlès, The effect of bulk viscosity on temperature relaxation near the critical point, Car98] Carlès P, p.2164, 1995.
DOI : 10.1063/1.869738

P. Carlès and B. Ugurtas, The onset of free convection near the liquid???vapour critical point Part I: Stationary initial state, Physica D: Nonlinear Phenomena, vol.126, issue.1-2, pp.69-82, 1999.
DOI : 10.1016/S0167-2789(98)00261-9

D. R. Chenoweth and S. Paolucci, Natural convection in an enclosed vertical air layer with large horizontal temperature differences, Journal of Fluid Mechanics, vol.83, issue.-1, p.173, 1986.
DOI : 10.1016/0021-9991(85)90043-9

Y. Chiwata and A. Onuki, Thermal oscillations plumes and convection in highly compressible fluids, Phy. Rev. Lett, vol.87, 2001.

D. Dahl and M. R. Moldover, Thermal Relaxation near the Critical Point, Physical Review A, vol.6, issue.5, 1972.
DOI : 10.1103/PhysRevA.6.1915

J. P. Dahlburg and J. H. Gardner, Ablative Rayleigh-Taylor instability in three dimensions, Physical Review A, vol.41, issue.10, pp.725-750, 1990.
DOI : 10.1103/PhysRevA.41.5695

R. E. Duff, F. H. Harlow, and H. C. , Effects of Diffusion on Interface Instability between Gases, Physics of Fluids, vol.5, issue.4, pp.417-425, 1962.
DOI : 10.1063/1.1706634

E. Khouri and L. , Hydrodynamique des fluides supercritiques et gravité, thèse de l, 2003.

J. Fröhlich, P. Laure, and R. Peyret, Large departures from Boussinesq approximation in the Rayleigh???B??nard problem, Physics of Fluids A: Fluid Dynamics, vol.4, issue.7, 1992.
DOI : 10.1063/1.858413

E. Fournier, S. Gauthier, and F. Renaud, 2D pseudo-spectral parallel Navier???Stokes simulations of compressible Rayleigh???Taylor instability, Computers & Fluids, vol.31, issue.4-7, pp.569-587, 2002.
DOI : 10.1016/S0045-7930(01)00065-2

B. Zappoli, Relaxation of a supercritical fluid after a heat pulse in the absence of gravity effects : theory and experiments, Phys. Rev. E, vol.57, issue.5, pp.5665-5681, 1998.

G. Z. Gershuni and E. M. Zhukhovitskii, Convective stability of incompressible fluids, Izdatel'stvo " Nauka, Moskva, translated from Russian, 1976.

M. S. Gitterman and V. A. Steinberg, Criteria for commencement of convection in a liquid close to the critical point, High Temp, vol.754, 1971.

M. S. Gitterman, Hydrodynamics of fluids near a critical point, Reviews of Modern Physics, vol.50, issue.1, p.85, 1978.
DOI : 10.1103/RevModPhys.50.85

J. Glim, X. L. Li, R. Menikoff, D. H. Sharp, and Q. Zhang, A numerical study of bubble interactions in Rayleigh???Taylor instability for compressible fluids, Physics of Fluids A: Fluid Dynamics, vol.2, issue.11, pp.2046-2054, 1990.
DOI : 10.1063/1.857679

S. W. Haan, Weakly nonlinear hydrodynamic instabilities in inertial fusion, Physics of Fluids B: Plasma Physics, vol.3, issue.8, pp.2349-2355, 1991.
DOI : 10.1063/1.859603

P. Haldenwang, C. Nicoli, and J. Daou, High pressure vaporization of LOX droplet crossing the critical conditions, Hin75] Hinze J.O., Turbulence, Mac-Graw Hill, pp.3453-64, 1975.
DOI : 10.1016/0017-9310(95)00396-7

C. Hirsch, Numerical computation of internal and external flows, 1988.

]. P. Hoh72, M. Hohenberg, and . Barmatz, Gravity effects near the gas-liquid critical point, Phys. Rev. A, vol.6, issue.1, pp.289-313, 1972.

D. Joseph, Fluid Dynamics of Two Miscible Liquids with Diffusion and Gradient Stresses, Eur. J. Mech., B/Fluids, vol.9, issue.6, pp.565-596, 1990.
DOI : 10.1007/978-1-4615-7061-5_6

A. Jounet, B. Zappoli, and A. Mojtabi, Simulation num??rique de l'Effet Piston avec prise en compte des ??changes thermiques pari??taux, Comptes Rendus de l'Acad??mie des Sciences - Series IIB - Mechanics-Physics-Astronomy, vol.327, issue.10, pp.991-996, 1999.
DOI : 10.1016/S1287-4620(00)87009-X

L. P. Kadanoff and J. Swift, Transport Coefficients near the Liquid-Gas Critical Point, Physical Review, vol.166, issue.1, p.89, 1968.
DOI : 10.1103/PhysRev.166.89

K. Kawasaki, Sound Attenuation and Dispersion near the Liquid-Gas Critical Point, Physical Review A, vol.1, issue.6, p.1750, 1970.
DOI : 10.1103/PhysRevA.1.1750

A. B. Kogan, Thermodynamics and hydrodynamics of a highly compressible fluid: He 3 near the liquid-vapor critical point, 2000.

A. B. Kogan and H. Meyer, near the critical point, Physical Review E, vol.63, issue.5, p.56310, 2001.
DOI : 10.1103/PhysRevE.63.056310

E. Kreyszig, Advanced engineering mathematics, 1993.

]. Kul91 and . H. Kull, Theory of Rayleigh-Taylor instability, Physics Reports (Review Section of Phys. Letters), vol.206, issue.5, pp.197-325, 1991.

P. Kurowski, C. Misbah, and S. Tchourkine, Gravitational Instability of a Fictitious Front During Mixing of Miscible Fluids, Europhysics Letters (EPL), vol.29, issue.4, pp.309-314, 1995.
DOI : 10.1209/0295-5075/29/4/007

L. D. Landau and E. M. Lifshitz, Physique théorique, tome 6 : Mécanique des Fluides, Librairie du Globe, Editions MIR, 1989.

B. K. Larkin, Heat flow to a confined fluid in zero gravity, Progress in Astronautics and Aeronautics, Themophysics of Spacecraft and Planetary Bodies, 1967.

E. E. Meshkov, Instability of the interface of two gases accelerated by a shock wave, Fluid Dynamics, vol.4, issue.no. 5/6, p.101, 1969.
DOI : 10.1007/BF01015969

H. Meyer and A. B. Kogan, Onset of convection in a very compressible fluid: The transient toward steady state, Physical Review E, vol.66, issue.5, 2002.
DOI : 10.1103/PhysRevE.66.056310

M. R. Moldover, J. V. Sengers, R. W. Gammon, and R. J. Hocken, Gravity effects in fluids near the gas-liquid critical point, Reviews of Modern Physics, vol.51, issue.1, pp.79-99, 1979.
DOI : 10.1103/RevModPhys.51.79

K. Nitsche and J. Straub, The critical " hump " of Cv under microgravity, result from the D-1 Spacelab experiment " Wärmekapazität, Proceeding of 6 th European Symposium on Material Science under Microgravity Conditions, 1987.

C. Normand, Y. Pomeau, and M. G. Velarde, Convective instability : a physicist's approach, Rev. of Modern Phys, p.3, 1977.

D. Ofer, D. Shvart, Z. Zinamon, and S. A. Orszag, Mode coupling in nonlinear Rayleigh???Taylor instability, Physics of Fluids B: Plasma Physics, vol.4, issue.11, pp.3549-3561, 1992.
DOI : 10.1063/1.860362

A. Onuki, H. Hong, and R. A. Ferrell, Fast adiabatic equilibration in a single-component fluid near the liquid-vapor critical point, Physical Review A, vol.41, issue.4, p.2256, 1990.
DOI : 10.1103/PhysRevA.41.2256

G. M. Pajonik, Sol-Gel Process Application, Proc. Int. Symp. Adv. Sol-Gel Process

S. Paolucci, On the filtering of sound from the Navier-Stokes equations, pp.82-8253, 1982.

S. V. Patankar and D. P. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, International Journal of Heat and Mass Transfer, vol.15, issue.10, pp.1787-1806, 1972.
DOI : 10.1016/0017-9310(72)90054-3

S. V. Patankar, Numerical heat transfer and fluid flow, 1980.

S. V. Patankar, A calculation procedure for two-dimensionnal elliptic situations, Numer. Heat Transfert, Part A, vol.14, issue.25, p.409, 1985.

P. Petitjeans and P. Kurowski, Fluides non miscibles/ Fluides miscibles : des similitudes intéressantes, pp.587-592, 1997.

R. Peyret and T. D. Taylor, Computational Methods for Fluid Flow, 1983.

C. Pittman, T. Doiron, and H. Meyer, mixture near their liquid-vapor critical point, Physical Review B, vol.20, issue.9, p.3678, 1979.
DOI : 10.1103/PhysRevB.20.3678

C. Pittman, L. Cohen, and H. Meyer, Transport properties of helium near the liquid-vapor critical point. I. Thermal conductivity of3He, Journal of Low Temperature Physics, vol.50, issue.1-2, p.115, 1982.
DOI : 10.1007/BF00655447

R. Prud-'homme, Combustion en micropesanteur, CRAS special, 2001.

S. Préau, R. Prud-'homme, J. Ouazzani, and B. Zappoli, Supercritical density relaxation as a new approach of droplet vaporization, Physics of Fluids, vol.16, issue.11, pp.4075-4087, 2004.
DOI : 10.1063/1.1790231

R. Prud-'homme and S. Préau, Echanges thermiques et phases fluides, ICTEA-HT3-06, 2004.

R. Prud-'homme and M. Habiballah, Instabilités liées au phénomène d'évaporation, 17 ème Congrès Français de Mécanique, 2005.

J. W. Rayleigh, Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density, Proc. London Math. Soc, 1883.
DOI : 10.1112/plms/s1-14.1.170

F. Renaud, Une méthode spectrale de décomposition de domaines dynamiques : application aux écoulements de Rayleigh-Bénard et de Kelvin-Helmoltz, Thèse 3° cycle, 1996.

F. Renaud and S. Gauthier, A Dynamical Pseudo-Spectral Domain Decomposition Technique: Application to Viscous Compressible Flows, Journal of Computational Physics, vol.131, issue.1, pp.89-108, 1997.
DOI : 10.1006/jcph.1996.5576

C. M. Rhie and W. L. Chow, Numerical study of turbulent flow past an airfoil with trailing edge separation, AIAA Journal, vol.21, issue.11, 1983.

R. D. Richtmyer, Taylor instability in shock acceleration of compressible fluids, Communications on Pure and Applied Mathematics, vol.13, issue.2, p.297, 1960.
DOI : 10.1002/cpa.3160130207

F. W. Sears, Thermodynamics , the kinetic theory of gases, and statistical mechanics, 1963.

J. Sengers, L. Sengers, and J. M. , Critical phenomena in classical fluids, in progress in liquid physics, 1978.

E. Serre and S. Gauthier, An Auto-Adaptative Multidomain Spectral Technique for Linear Stability Analysis: Application to Viscous Compressible Flows, J. of Scient. Comput, vol.17, pp.1-4, 2002.

D. B. Spalding, A novel finite difference formulation for differential expressions involving both first and second derivatives, International Journal for Numerical Methods in Engineering, vol.4, issue.4, p.551, 1972.
DOI : 10.1002/nme.1620040409

E. A. Spiegel and G. Veronis, On the Boussinesq Approximation for a Compressible Fluid., The Astrophysical Journal, vol.131, pp.1068-1090, 1960.
DOI : 10.1086/146849

E. A. Spiegel, Convective Instability in a Compressible Atmosphere., The Astrophysical Journal, vol.141, 1068.
DOI : 10.1086/148197

L. W. Spradley, S. V. Bougeois, C. Fan, and P. G. Grodzka, A numerical solution for thermoacoustic convection of fluids, 1973.

L. W. Spradley and S. W. Churchill, Pressure- and buoyancy-driven thermal convection in a rectangular enclosure, Journal of Fluid Mechanics, vol.8, issue.04, p.705, 1975.
DOI : 10.1121/1.1907288

H. E. Stanley, Introduction to Phase Transition and Critical Phenomena, 1971.
DOI : 10.1063/1.3127900

G. I. Taylor, The Instability of Liquid Surfaces when Accelerated in a Direction Perpendicular to their Planes. I, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.201, issue.1065, p.192, 1950.
DOI : 10.1098/rspa.1950.0052

G. D. Thiart, Finite difference scheme for the numerical solution of fluid flow and heat transfer problems on non-staggered grids, Part B, vol.17, pp.43-62, 1990.

G. Trayggvason and O. Unverdi, Computations of three-dimensional Rayleigh-Taylor instability, Phys. of Fluids A, pp.656-659, 1990.

J. D. Van-der-wals, Over de continuiteit van den gas en vloeistoftoestand

D. Youngs, Numerical simulation of turbulent mixing by Rayleigh-Taylor instability, Physica D: Nonlinear Phenomena, vol.12, issue.1-3, pp.32-44, 1984.
DOI : 10.1016/0167-2789(84)90512-8

D. Youngs, Three-dimensional numerical simulation of turbulent mixing by Rayleigh-Taylor instability, Phys. of Fluids A, pp.1312-1332, 1991.

B. Zappoli, D. Bailly, Y. Garrabos, L. Neindre, B. Guenoun et al., Anomalous heat transport by the piston effect in supercritical fluids under zero gravity, Physical Review A, vol.41, issue.4, pp.2264-2267, 1990.
DOI : 10.1103/PhysRevA.41.2264

B. Zappoli, The response of a nearly supercritical pure fluid to a thermal disturbance, Physics of Fluids A: Fluid Dynamics, vol.4, issue.5, pp.101-107, 1992.
DOI : 10.1063/1.858255

B. Zappoli and A. Durand-daubin, Heat and mass transport in a near supercritical fluid, Physics of Fluids, vol.6, issue.5, p.1924, 1994.
DOI : 10.1063/1.868249

B. Zappoli and P. Carlès, The thermo-acoustic nature of the critical speeding up, European J. Mech. B, vol.14, pp.41-65, 1995.

B. Zappoli, S. Amiroudine, P. Carlès, and J. Ouazzani, Thermoacoustic and buoyancy-driven transport in a square side-heated cavity filled with a near-critical fluid, Journal of Fluid Mechanics, vol.70, issue.-1, pp.53-72, 1996.
DOI : 10.1016/0017-9310(72)90054-3

B. Zappoli, S. Amiroudine, and S. Gauthier, Instabilit?? gravitationnelle dans un fluide supercritique pur, Comptes Rendus de l'Acad??mie des Sciences - Series IIB - Mechanics-Physics-Chemistry-Astronomy, vol.325, issue.1, 1997.
DOI : 10.1016/S1251-8069(97)83256-3

B. Zappoli, A. Jounet, S. A. Amiroudine, and A. Mojtabi, Thermoacoustic heating and cooling in near-critical fluids in the presence of a thermal plume, Journal of Fluid Mechanics, vol.388, pp.389-409, 1999.
DOI : 10.1017/S0022112099004802

J. Zierep and H. Oertel, Convective transport and instability phenomena, pp.3-24, 1982.

J. Zufiria, Vortex-in-cell simulation of bubble competition in a Rayleigh???Taylor instability, Physics of Fluids, vol.31, issue.11, pp.3199-3212, 1988.
DOI : 10.1063/1.866931