M. E. White, J. P. Drumniond, and . Kumar, Evolution and application of CFD techniques for scramjet engine analysis, Journal of Propulsion and Power, vol.3, issue.5, pp.423-439, 1987.
DOI : 10.2514/3.23007

M. Barreré, La combustion supersonique : problèmes posés pour son développement, L'aéronautique et l'astronautique, pp.43-55, 1988.

P. Gastebois, Contribution à l'étude des combustions stabilisées sur ondes de chocs, 1969.

M. Barreré and &. A. Mestré, Stabilisation de la flamme en combustion supersonique, La Recherche Aérospatiale, vol.1, pp.1-13, 1988.

R. J. Kee, J. A. Miller, and &. H. Jefferson, CHEMKIN: a general purpose, problemindependent , transportable, FORTRAN chemical kinetics code package, 1983.

P. Deufihard, E. Hairer, and &. J. Zugck, One-step and extrapolation methods for differential-algebraic systems, Numerische Mathematik, vol.26, issue.5, pp.501-516, 1987.
DOI : 10.1007/BF01400352

P. Deufihard, Recent Progress in Extrapolation Methods for Ordinary Differential Equations , SIAM review, pp.505-540, 1985.

Y. D. Angelo and &. B. Larrouturou, Comparison and analysis of some numerical schemes for stiff complex chemistry problems, Math. Mod. Num. Anal, 1993.

R. Courant and &. K. Friedrichs, Supersonic Flow and Shock Waves, 1948.
DOI : 10.1007/978-1-4684-9364-1

R. D. Mccarty, K. E. Cox, and K. Willamson, Hydrogen: its technology and implications, 1975.

D. Thévenin, Dynamique de l'allumage des flammes de diffusion dans des écoulements cisaillés, Thèse de l'Ecole Centrale de Paris, p.143, 1992.

P. Deuflhard, Recent Progress in Extrapolation Methods for Ordinary Differential Equations , SIAM review, pp.505-540, 1985.

R. S. Varga, Matrix iterative analysis, 1962.

F. M. White, Viscous fluid flow, 1991.

]. Y. Bibliographie1 and . Larrouturou, Numerical Simulation of Supersonic Combustion with Complex Chemistry, 5th Int. Cong, on Numerical Combustion, 1993.

Y. D. Angelo, A. Ern-&-b, and . Larrouturou, Numerical Simulations of Twodimensional combustive flows with detailed chemistry, 6th joint EPS-APS Int. Conf. on Pliys. Comp, 1994.

B. Larrouturou-&-l and . Fezoui, On the equations of multi-component perfect or real gas inviscid flowNon linear hyperbolic problems, Carasso Charrier Hanouzet &

H. C. Yee, Upwind and symmetric shock capturing schemes, 1987.

P. K. Sweeby, High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws, SIAM Journal on Numerical Analysis, vol.21, issue.5, pp.995-1011, 1984.
DOI : 10.1137/0721062

B. Van and . Leer, Towards the ultimate conservative difference scheme IT -Monotonicity and conservation combined in a second-order scheme, J. Comp. Phys, vol.14, pp.361-370, 1974.

G. Melhlman, Etude de quelques problèmes liés aux écoulements en déséquilibre chimique et thermique, 1991.

J. A. Desideri, N. Glinsky-&-e, and . Hettena, Hypersonic reactive flow computations, Computers & Fluids, vol.18, issue.2, pp.151-182, 1990.
DOI : 10.1016/0045-7930(90)90017-R

J. A. Desideri, N. Glinsky-&-l, and . Fezoui, Numerical computation of the chemical dissociation and relaxation phenomena behind a detached strong shock, 1987.
URL : https://hal.archives-ouvertes.fr/inria-00075778

H. Steve, Schemas implicites linéarisés décentrés pour la résolution des équations d'Euler en plusieurs dimensions, 1988.

P. Arminjon, A. Dervieux, L. Fezoui, B. Stoufflet-&-h, and . Steve, Non-Oscillatory Schemes for Multidimensional Euler Calculations with Unstructured Grids, Second Conf. in Hyperbolic Problems, 1988.
DOI : 10.1007/978-3-322-87869-4_1

S. K. Godunov, A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics, Math. Sbornik, vol.47, pp.271-306, 1959.

Y. D. Angelo, Analyse de l'allumage d'un mélange air-hydrogène à l'aval d'un système stationnaire d'oncle de chocs

M. S. Liou, B. J. Van, and . Shuen, Splitting of mviscid fluxes for real gases, 1988.

T. P. Liu, The Riemann problem for general systems of conservation laws, Journal of Differential Equations, vol.18, issue.1, pp.218-252, 1975.
DOI : 10.1016/0022-0396(75)90091-1

P. and C. &. Glaz, Efficient Solution Algorithms for the Riemann Problem for Real Gases, J. Comp. Phys, vol.59, pp.264-89, 1985.

R. G. Smith, The Riemann problem in gas dynamics, Transactions of the American Mathematical Society, vol.249, issue.1, pp.1-50, 1979.
DOI : 10.1090/S0002-9947-1979-0526309-2

J. A. Smoller, Shock Waves and Reaction-Diffusion Equations, 1983.

J. Miller, R. E. Mitchell, M. D. Smooke-&-r, and . Kee, Toward a comprehensive chemical kinetic mechanism for the oxidation of acetylene: Comparison of model predictions with results from flame and shock tube experiments, 19th International Symposium on combustion, pp.181-96, 1982.
DOI : 10.1016/S0082-0784(82)80189-6

N. Maman and B. Larrouturou, On the use of dynamical finite-element mesh adaptation for 2D Simulation of unsteady flame propagation, 12th international conference on numerical methods in fluid dynamics, pp.534-539, 1990.
DOI : 10.1007/3-540-53619-1_258

B. Larrouturou, How to preserve the mass fractions positivity when computing compressible multi-component flows, Journal of Computational Physics, vol.95, issue.1, pp.59-84, 1991.
DOI : 10.1016/0021-9991(91)90253-H

URL : https://hal.archives-ouvertes.fr/inria-00075479

A. and C. Hindmarsh, ODEPACK, a systematized collection of ODE solvers, IMACS Trans, on Sc, Comp, pp.55-64, 1983.

R. J. Kee, J. A. Miller-&-t, and . Jefferson, CHEMKIN : a general purpose, problem-independent, transportable, FORTRAN chemical kinetics code package

R. Abgrall, Preliminary results on the extension of Roe's scheme to a class of real gas mixtures, 1989.

P. Deuflhard, E. Hairer, and J. Zugck, One-step and extrapolation methods for differential-algebraic systems, Numerische Mathematik, vol.26, issue.5, pp.501-516, 1987.
DOI : 10.1007/BF01400352

URL : https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/2075

R. L. Abgrall-&-j and . Montagne, Generalisation du schéma d'Osber pour le calcul d'écoulements de mélanges de gaz à concentrations variables et de gaz réels, La Recherche Aérospatiale, vol.4, pp.1-13, 1989.

R. Abgrall, L. Fezoui, and J. Talandier, An extension of Osher's Riemann solver for chemical and vibrational non-equilibrium gas flows, International Journal for Numerical Methods in Fluids, vol.1402, issue.8, p.1221, 1990.
DOI : 10.1002/fld.1650140805

A. Harten, P. D. Lax, B. Van, and . Leer, On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws, SIAM Review, vol.25, issue.1, pp.35-61, 1983.
DOI : 10.1137/1025002

P. Deuflhard, Recent Progress in Extrapolation Methods for Ordinary Differential Equations, SIAM Review, vol.27, issue.4, pp.505-540, 1985.
DOI : 10.1137/1027140

S. Osher and S. Chakravarthy, Numerical Experiments with Osher Upwind Scheme for the Euler equations, AIAA J, vol.21, issue.9, 1983.

S. Osher and F. Solomon, Upwind difference schemes for hyperbolic systems of conservation laws, Mathematics of Computation, vol.38, issue.158, pp.339-74, 1982.
DOI : 10.1090/S0025-5718-1982-0645656-0

P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, Journal of Computational Physics, vol.43, issue.2, pp.357-72, 1981.
DOI : 10.1016/0021-9991(81)90128-5

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.457.5978

P. L. Roe, Some Contributions to the Modelling of Discontinuous Flow, Lectures in Applied Mathematics, vol.22, pp.163-93, 1985.

A. Harten, High resolution schemes for hyperbolic conservation laws, Journal of Computational Physics, vol.49, issue.3, pp.357-93, 1983.
DOI : 10.1016/0021-9991(83)90136-5

S. Kruzkov, First-Order Quasilinear Equations for Several Space Variables, Math. Sbornik, vol.123, pp.228-55, 1970.

F. Dubois and G. Mehlman, A Non-parametrized entropy fix for Roe's Method, 10 tn AIAA CFD Conference, 1991.

B. Larrouturou-&-l and . Fezoui, On the equations of multi-component perfect or real gas inviscid flow", Non linear hyperbolic problems

Y. D. Larrouturou, Comparison and analysis of some numerical schemes for stiff complex chemistry problems, Math. Mod. Num. Anal, 1993.

C. P. Li, Implicit methods for computing chemically reacting flow, NASA Techn. Mem, vol.58274
DOI : 10.1007/BFb0041825

URL : http://hdl.handle.net/2060/19870003975

N. Glinsky, Simulation numérique d'écoulements hypersoniques réactifs hors équilibre chimique, 1990.

L. R. Petzold, A Description of DASSL: a differential/algebraic system solver, IMACS Trans, on Sc, 1983.

M. D. Smooke, A. A. Turnbull, R. E. Mitchell-&-d, and . Keyes, Solution of Two-Dimensional Axisymmetric Laminar Diffusion Flames by Adaptive Boundary Value Methods, Mathematical modelling in combustion and related topics
DOI : 10.1007/978-94-009-2770-4_17

N. Series, E. Nijhoff, and D. , 1: 2 3: 4: S: 6 7: S: 9: 10 M: 12: 13: 14 15, pp.261-300, 1988.

. Flg, 14 -Iso-Min[ uj ; 0.4 X T ] initiaux pour le maillage "fin" avec Pdf 1: 3

O. Mio and . Flg, 15 -Iso-crx pour le maillage "fin" avec Pdf !, p.70000

. Flg, 18 -Expérience Burrows et Kurkov: courbes ÍSO-YQH (cas Pdf) 0, p.45

. Flg, 19 -Expérience de Burrows et Kurkov: coupes de Maxf ax/f ; 0.4 / feas Pdf) 252 CHAPITRE 7, MELANGE RÉACTIF, vol.7, p.253

]. J. Bibliographie1, C. Hirschfelder, &. R. Curtiss, and . Bird, Molecular Theory of Gases and Liquids, 1954.

V. Giovangigli, Structure et extinction de flammes laminaires prémélangées, Thèse de Doctorat d'état, 1988.

T. P. Coffee and &. J. Heimerl, Transport algorithms for premixed, laminar steady-state flames, Combustion and Flame, vol.43, pp.273-89, 1981.
DOI : 10.1016/0010-2180(81)90027-4

J. O. Hirschfelder, &. Cf, and . Curtiss, Flame propagation in explosive gas mixtures, 3rd Int. Symposium on Combustion, pp.121-148, 1949.

{. , R. J. Kee, J. Warnatz, and &. J. Miller, A Fortran Computer Code Package for the evaluation of gas-phase viscosities, conductivities and diffusion coefficients, SANDIA Nat. Lab. Rep, pp.80-8003, 1980.

C. R. Wilke, A Viscosity Equation for Gas Mixtures, The Journal of Chemical Physics, vol.18, issue.4, pp.517-536, 1950.
DOI : 10.1063/1.1747673

A. Harten, High resolution schemes for hyperbolic conservation laws, Journal of Computational Physics, vol.49, issue.3, pp.357-93, 1983.
DOI : 10.1016/0021-9991(83)90136-5

H. Yee, Upwind and symmetric shock capturing schemes, NASA Tech. Mem, vol.89464, 1987.

H. Yee, On the implementation of a class of upwind schemes for system of hyperbolic conservation laws, NASA Tech. Mem, vol.86839, 1985.

N. Kroll, D. Gaitonde, and &. M. Aftosmis, A systematic comparative study of several high resolution schemes for complex problems in high speed flows, 29th Aerospace Sciences Meeting, 1991.
DOI : 10.2514/6.1991-636

S. Piperno, Accélération d'un code 2D-vommes finis structurés résolvant les équations de Navier-Stokes pour un fluide muîti-espèces réactif par un schéma implicite linéarisé, Rapport interne Dassault Aviation, 1991.

P. Rostand, &. R. Mac, and . Cormack, CFD modeling of an arc-heated jet, 21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1990.
DOI : 10.2514/6.1990-1475

P. Rostand, A prospective study of supersonic combustion, Analatom Inc Contraer Report 42F01237, 1990.

R. W. Mc-cormack and G. V. Candler, The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation, pp.135-50, 1989.

Y. D-'angeio and &. B. Larrouturou, Comparison and analysis of some numerical schemes for stiff complex chemistry problems, Math. Mod. Num. Anal, 1993.

B. Launder and &. D. Spalding, The numerical computation of turbulent flows, Computer Methods in Applied Mechanics and Engineering, vol.3, issue.2, pp.269-89, 1974.
DOI : 10.1016/0045-7825(74)90029-2

F. Chalot, Z. Johann, M. Mallet, M. Ravachol, and &. G. Rogé, Development of a finite element Navier Stokes solver with applications to turbulent and hypersonic flows, 30th Aerospace Sciences Meeting and Exhibit, pp.92-0607, 1992.
DOI : 10.2514/6.1992-670

C. Kasbarian, O. Lebigre, M. Mallet, B. Mantel, M. Ravachol et al., Development of a finite element Navier-Stokes solver using unsteady adapted grids and applications to turbulent flows, Proc. of the 1st Eur. Comp. & Fluid Dyn. Conf, 1992.

F. Chalot and M. M. Mallet-k, A comprehensive finite element Navier-Stokes solver for low and high airgraft design, pp.94-0814, 1994.

M. Baum, T. Poinsot, and &. D. Haworth-soumis-au-journ, Using direct numerical simulation to study H2 ? O2 flames with complex chemistry in turbulent flows, 1993.

S. B. Pope, Transport equation for the joint probability density function of velocity and scalars in turbulent flow, Physics of Fluids, vol.24, issue.4, pp.588-96, 1981.
DOI : 10.1063/1.863425

. Hesseiberg, Die Gesetze der ausgeglighenen atmosphärischen Bewegangen, Beitz. Phys. forden Atmosphäre, vol.12, pp.141-160, 1925.

G. Dedebant and &. P. Wehrle, Sur les équations aux valeurs probables d'un fluide turbulent, C.R.A.S, vol.206, pp.1790-1791, 1938.

L. Dufour and &. Van-mieghen, Thermodynamique de l'atmosphère, Mem. Inst. Roy. Météo, de Belgique, p.30, 1948.

A. K. Blackadar, The transformation of energy by the large scale eddy stress in the atmosphere, Meteor. Papers, vol.1, issue.4, 1950.

A. Favre and C. R. , Equations statistiques des gaz turbulents, pp.2576-79, 1958.

A. Favre, Equations des gaz turbulents compressibles, Journ. de Mécanique, vol.4, issue.3, 1965.

R. W. Bilger, A Note on Favre Averaging in Variable Density Flows, Combustion Science and Technology, vol.11, issue.5-6, pp.215-232, 1975.
DOI : 10.1063/1.1694895

J. Boussinesq, Théorie de l'écoulement tourbillonant et tumultueux des liquides dans les lits rectilignes à grande section", I-II, 1897.

O. Reynolds, On the Dynamical Theory of Incompressible Viscous Fluids and the Determination of the Criterion, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.186, issue.0, pp.123-164, 1894.
DOI : 10.1098/rsta.1895.0004

G. B. Schubauer, &. Cm, and . Tchen, Turbulent flows and heat transfer, 1959.

J. O. Hinze, Turbulence, Mac Graw Hill, 1959.
DOI : 10.1115/1.3644063

P. S. Klebanoff, Characteristics of turbulence in a boundary layer with zero pressure gradient, p.3178, 1954.

D. Vandromme, Contribution à la modélisation et la prédiction d'écoulements turbulents à masse volumique variable, 1983.

J. Cousteix, Turbulence et couche limite, Cepadues Editions, 1989.

O. Zeman, Dilatation dissipation: The concept and application in modeling compressible mixing layers, Physics of Fluids A: Fluid Dynamics, vol.2, issue.2, pp.178-88, 1990.
DOI : 10.1063/1.857767

S. Sarkar, G. Erlebacher, M. Y. Hussaini, and H. O. Kreiss, The analysis and modelling of dilatational terms in compressible turbulence, Journal of Fluid Mechanics, vol.20, issue.-1, 1989.
DOI : 10.1017/S0022112088003325

W. P. Jones and &. E. Launder, The prediction of laminarization with a two-equation model of turbulence, International Journal of Heat and Mass Transfer, vol.15, issue.2, pp.301-315, 1972.
DOI : 10.1016/0017-9310(72)90076-2

R. Struijs, P. L. Roe-k, and . Deconinck, Fluctuations Splitting Schemes for the 2D Euler equations, Von Karman Institute Repport, pp.1991-2002, 1991.

H. Blasius, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. Phys, vol.56, pp.1-37, 1908.

H. Schlichting, Boundary Layer Theory, 1955.
DOI : 10.1007/978-3-662-52919-5

D. Papamoschou and &. A. Roshko, The compressible turbulent shear layer: an experimental study, Journal of Fluid Mechanics, vol.23, issue.-1, pp.453-77, 1988.
DOI : 10.1017/S0022112058000653

G. L. Brown and &. A. Roshko, On density effects and large structure in turbulent mixing layers, Journal of Fluid Mechanics, vol.87, issue.04, pp.775-816, 1974.
DOI : 10.1017/S002211207400190X

D. W. Bogdanoff, Compressibility Effects in Turbulent Shear Layers, AIAA Journal, vol.21, issue.6, pp.926-953, 1983.
DOI : 10.2514/3.60135

S. F. Birch and &. J. Eggers, A critical review of the experimental data for developped free turbulent shear layer, Proc. of the Free Shear Flows Conference, NASA SP 321, 1972.

R. Dautray and &. J. Lions, Analyse mathématique et calcul numérique pour les sciences et les techniques, p.1391, 1984.

F. E. Marble and J. E. Broadwell, The coherent flame model for turbulent chemical reactions, 1977.

F. Lacas, Modélisation et simulation numérique de la combustion turbulente dans les moteurs fusées cryotechniques, 1989.

W. Meli, G. Koàly, and J. J. Riley, An investigation of closure Models for nonpremixed turbulent reacting flows, AIAA 93-0104, 31st Aerospace Sciences Meeting and Exhibit, 1993.

S. B. Pope, Transport equation for the joint probability density function of velocity and scalars in turbulent flow, Physics of Fluids, vol.24, issue.4, pp.588-96, 1981.
DOI : 10.1063/1.863425

A. T. Hsu, Y. P. Tsai, and M. S. Raju, PDF approach for compressible turbulent reacting flows, 31st Aerospace Sciences Meeting, 1993.
DOI : 10.2514/6.1993-87

S. Frankel, P. Drummond, and &. H. Hassan, A hybrid Reynolds averaged/PDF clodure model for supersonic turbulent combustion, AIAA 90-1573, 21st Fluid Dynamics, Plasma Dynamics and Lasers conference, 1990.

R. Chandrasekhar and &. S. Tiwari, Application of a Reynolds Stress turbulence model to a supersonic hydrogen-air diffusion flame, 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1991.
DOI : 10.2514/6.1991-1786

R. Villasenor, R. W. Pitz, and &. Chen, Interaction between chemical reaction and turbulence in supersonic non premixed HO-B-IT combustion, Aerospace Sciencs Meeting, 1991.

R. L. Gaffney, J. , J. A. White, S. S. Girimaji, and &. J. Drummond, Modelling turbulent/chemistry interactions using assumed Pdf methods, AIAA 92-3638, 28th Joint Propulsion Conference and Exhibit, 1992.

M. C. Burrows and &. P. Kurkov, Analytical and Experimental Study of Supersonic Combustion of Hydrogen in a Vitiated Stream, 1973.

L. Polaires-donnant, K) en fonction de l'angle de déflexion è\ (deg, p.44

T. Évolution-de and P. Et-y¡i, Cas état 3, p.55

I. Case, Temperature after 46 x 80 iterations (convergence), p.169

I. Case, b : OH mass fraction after 13 x 80 iterations, p.173

. Expérience-de-burrows and . Kurkov, coupes des fractions massiques en X = 35.6 cm pour le cas inerte, p.250