M. De and L. Combustion, Pour les pas de temps considérés, l'expérience numérique a montré qu'une convergence de la phase de relaxation à 10 -2 est suffisante lorsque l'on adopte une procédure de surrelaxation . Pour obtenir une solution équivalente lorsque l'on n'utilise pas cette procédure

H. R. Abgrall, Généralisation du schéma de Roe pour le calcul d'écoulements de mélanges de gaz à concentrations variables, La Recherche Aérospatiale, vol.6, pp.31-43, 1988.

R. Abgrall, Extension of Roe's approximate Riemann solver to equilibrium and non equilibrium flows, Proceedings of the eighth GAMM conference on numerical methods in fluid mechanics, pp.1-10, 1990.

R. Abgrall and J. L. Montagne, Généralisation du schéma d'Osher 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. M. Beam, R. , and M. Warming, An implicit finite-difference algorithm for hyperbolic systems in conservation-law form, Journal of Computational Physics, vol.22, issue.1, pp.67-110, 1976.
DOI : 10.1016/0021-9991(76)90110-8

H. Berestycki and B. Larrouturou, Quelques aspects mathématiques de la propagation des flammes prémélangées, 1988.

M. B. Artzi, The generalized Riemann problem for reactive flows, Journal of Computational Physics, vol.81, issue.1, pp.70-101, 1989.
DOI : 10.1016/0021-9991(89)90065-X

F. Benkhaldoun, Etude numérique de modèles mathématiques décrivant la propagation de flammes dans un milieu gazeux bidimensionnel, Thèse, 1988.

A. Bourgeade, Le problème de Riemann généralisé, 1986.

A. Bourgeade, Quelques méthodes numériques pour le traitement des écoulements réactifs, 1988.

A. Bourlioux, A. Majda, and V. Roytburd, Theoretical and Numerical Structure for Unstable One-Dimensional Detonations, SIAM Journal on Applied Mathematics, vol.51, issue.2
DOI : 10.1137/0151016

J. D. Buckmaster-k and G. S. Ludford, Theory of laminar flames, 1982.

G. V. Candler and R. W. Mccormack, The computation of hypersonic flows in chemical and thermal nonequilibrium, Third National Aero-Space Plane Technology Symposium, 1987.

D. Chargy, Simulation numérique de l'interaction réactive de deux jets gazeux transsoniques, 1988.

D. Chargy, R. Abgrall, L. Fezoui, and B. Larrouturou, Comparison of several numerical schemes for multi-component one-dimensional flows, 1990.

D. Chargy, A. Dervieux, and B. Larrouturou, Upwind adaptive finite-element investigations of the two-dimensionnal reactive interaction of supersonic gaseous jets, Int. J. Num. Meth. Fluids, issue.11, pp.751-767, 1990.

D. Chargy, A. Dervieux, B. Larrouturou, M. Loriot, and N. Maman, Simulation numérique de l'interaction réactive de jets gazeux transsoniques, 1990.

D. Chargy, A. Dervieux, B. Larrouturou, and M. Loriot, Simulation numérique de l'interaction réactive d'un mélange gazeux H2-02 dans une tête de chambre, 1990.

P. Clavin, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Progress in Energy and Combustion Science, vol.11, issue.1, pp.1-59, 1985.
DOI : 10.1016/0360-1285(85)90012-7

P. Colella, A. Majda, V. J. Roytburd, and . Sei, Theoretical and Numerical Structure for Reacting Shock Waves, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.4, pp.1059-1080, 1986.
DOI : 10.1137/0907073

R. Courant and K. O. Friedrichs, Supersonic flow and shock waves, 1976.
DOI : 10.1007/978-1-4684-9364-1

A. Dervieux, L. Fezoui, and B. Larrouturou, Upwind numerical methods for compressible flows

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

G. Fernandez, Simulation numérique d'écou -ments réactifs a petit nombre de Mach, Thèse, 1989.

G. Fernandez, Implicit conservative upwind schemes for strongly transient Flows, Rapport INRIA N°, vol.873, 1988.
URL : https://hal.archives-ouvertes.fr/inria-00075681

G. Fernandez and B. Larroüturou, Hyperbolic schemes for multi-component Euler equations", Nonlinear hyperbolic equations -Theory, numerical methods and applications, Notes on numerical Fluid Mechanics, vol.24, pp.128-138, 1989.

L. Fezoui, Résolution des équations d'Euler par un schéma de van Leer en éléments finis, 1985.

L. Fezoui, S. Lanteri, B. Larrouturou, and C. Olivier, Résolution numérique des équations de Navier-Stokes pour un fluide compressible en maillage triangulaire, 1989.

W. Fickett and W. C. Davis, Detonation, 1979.

J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Communications on Pure and Applied Mathematics, vol.12, issue.4, pp.697-715, 1965.
DOI : 10.1002/cpa.3160180408

N. Glinsky, L. Fezoui, M. C. Ciccoli, and J. A. Desideri, Non-Equilibrium Hypersonic flow Computations by Implicit Second-Order Upwind Finite-Elements, Proceedings of the eighth GAMM conference on numerical methods in fluid mechanics, pp.159-168, 1990.
DOI : 10.1007/978-3-663-13975-1_17

A. Habbal, A. Dervieux, H. Guillard, and B. Larrouturou, Explicit calculations of reactive flows with an upwind finite-element hydrodynamical code, 1987.

A. Harten, High resolution schemes for hyperbolic conservation laws, Journal of Computational Physics, vol.49, issue.3, pp.357-393, 1983.
DOI : 10.1016/0021-9991(83)90136-5

A. Harten, P. D. , 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

A. Harten and J. M. Hyman, Self adjusting grid methods for one-dimensional hyperbolic conservation laws, Journal of Computational Physics, vol.50, issue.2, pp.235-269, 1983.
DOI : 10.1016/0021-9991(83)90066-9

K. Kailasanath, E. S. Oran, and J. P. Boris, Numerical simulations of flames and detonations, Lecture Notes in Physics, issue.351, 1989.
DOI : 10.1007/3-540-51968-8_77

R. J. Kee, J. A. Miller, and T. H. Jefferson, CHEMKIN: A general-purpose, problem-independent, transportable, fortran chemical kinetics code package, 1980.

S. N. Kruskov, FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES, Mathematics of the USSR-Sbornik, vol.10, issue.2, pp.217-243, 1970.
DOI : 10.1070/SM1970v010n02ABEH002156

M. H. Lallemand, Schémas décentrés multigrilles pour la résolution des équations d'Euler en éléments finis, Thèse, 1988.

B. Larrouturou, Etude mathématique et modélisation numérique de phénomènes de combustion, Thèse, 1987.

B. Larrouturou, Modèle de la combustion en phase gazeuse

B. Larrouturou, How to preserve the mass fractions positivity when computing compressible multi-component flows, Journal of Computational Physics, vol.95, issue.1
DOI : 10.1016/0021-9991(91)90253-H
URL : https://hal.archives-ouvertes.fr/inria-00075479

B. Larrouturou, Recent progress in reactive flow computations, Computing methods in applied sciences, 1990.

B. Larrouturou and L. Fezoui, On the equation of multi-component perfect or real gas inviscid flowNon linear hyperbolic problems, Carasso Charrier Hanouzet & Joly eds. Lecture Notes in Mathematics, pp.69-98, 1402.

A. Lerat, Propriété d'homogénéité et decomposition des flux en dynamique des gaz, J. Méc. Théor. Appl, vol.2, issue.2, pp.185-213, 1983.

A. Le-roux, Approximation de quelques problèmes hyperboliques non linéaires, Thèse, 1979.

R. J. Leveque-&-h and . Yee, A study of numerical methods for hyperbolic conservation laws whith stiff source terms, 1988.

R. Me and C. , A numerical method for solving the equation of compressible viscous flows, AIAA journal, vol.20, pp.1275-1281, 1982.

A. Majda, High Mach number combustion Combustion and chemical reactors, LeGture in Appl. Math, vol.24, issue.1, pp.109-184, 1986.

A. Majda, A Qualitative Model for Dynamic Combustion, SIAM Journal on Applied Mathematics, vol.41, issue.1, 1981.
DOI : 10.1137/0141006

N. Maman-&-b and . Larrouturou, On the use of dynamical finite-element mesh adaptation for 2D simulation of unsteady flame propagation

J. L. Montagne, H. C. Yee-&-m, and . Vinokur, Comparative study of high-resolution shock-capturing schemes for a real gas, AIAA Journal, vol.27, issue.10, 1987.
DOI : 10.2514/3.10269

S. Osher-&-f and . Solomon, Upwind difference schemes for hyperbolic systems of conservation laws, Mathematics of Computation, vol.38, issue.158, pp.339-374, 1982.
DOI : 10.1090/S0025-5718-1982-0645656-0

N. Peters, Discussion of test problem A", Numerical methods in laminar flame propagation, Notes on Numerical Fluid Mechanics, vol.6, pp.1-14, 1982.

N. Peters, Introduction to combustion science, Lecture Course, 1989.

F. Picon, Etude de schémas implicites pour un écoulement monodimensionnel réactif, 1988.

J. Regere, Simulation numérique d'écoulements visqueux compressibles tridimensionnels, 1988.

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

P. L. Roe, Some contributions to the modeling of discontinuous flows, Proc. AMS/SIAM Seminar, 1983.

G. A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, Journal of Computational Physics, vol.27, issue.1, pp.1-31, 1977.
DOI : 10.1016/0021-9991(78)90023-2

S. P. Spekreijse, Multigrid solution of the steady Euler equations, 1987.

J. Steger and R. F. Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, Journal of Computational Physics, vol.40, issue.2, pp.263-293, 1981.
DOI : 10.1016/0021-9991(81)90210-2

B. Stoufflet, Résolution numérique des équations d'Euler des fluides parfaits compressibles par des schémas implicites en éléments finis, Thèse, 1984.

B. S. Periaux, L. Fezoui, and A. Dervieux, Numerical simulation of 3-D hypersonic Euler flow around space vehicles using adapted finite elements, 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 II -Monotonicity and conservation combined in a second-order scheme, J. Comp. Phys, vol.14, pp.361-370, 1974.

B. Van and . Leer, Upstream -Centered Finite Difference Schemes for Ideal Compressible Flow, J. Comp. Phys, vol.23, pp.263-275, 1977.

B. Van and . Leer, Flux-vector splitting for the Euler equations, fluid dynamics, pp.507-512, 1982.

B. Van-leer, J. L. Thomas, P. L. Roe, and R. W. Newsome, A comparison of numerical flux formulas for the Euler and Navier-Stokes equations, 1987.

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

D. H. Wagner, The Existence and Behavior of Viscous Structure for Plane Detonation Waves, SIAM Journal on Mathematical Analysis, vol.20, issue.5, pp.1035-1054, 1989.
DOI : 10.1137/0520069

F. A. Williams, Combustion theory, 1985.
URL : https://hal.archives-ouvertes.fr/hal-00014918

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