F. E. Culick, Combustion instabilities in liquid-fueled propulsion systems ? an overview, 1988.

J. C. Oefelein and V. Yang, Comprehensive review of liquid-propellant combustion instabilities in F-1 engines, Journal of Propulsion and Power, vol.9, issue.5, pp.657-677, 1993.
DOI : 10.2514/3.23674

V. Yang and W. Anderson, Liquid rocket engine combustion instability, Progress in Astronautics and Aeronautics, 1995.

L. Crocco, Aspects of Combustion Stability in Liquid Propellant Rocket Motors Part I: Fundamentals. Low Frequency Instability With Monopropellants, Journal of the American Rocket Society, vol.21, issue.6, pp.163-178, 1951.
DOI : 10.2514/8.4393

L. Crocco, Aspects of Combustion Stability in Liquid Propellant Rocket Motors Part II: Low Frequency Instability with Bipropellants. High Frequency Instability, Journal of the American Rocket Society, vol.22, issue.1, pp.7-16, 1952.
DOI : 10.2514/8.4410

L. Crocco and S. I. Cheng, Theory of combustion instability in liquid propellant rocket motors, Butterworths Science, issue.8, 1956.

H. S. Tsien, Servo-Stabilization of Combustion in Rocket Motors, Journal of the American Rocket Society, vol.22, issue.5, pp.256-263, 1952.
DOI : 10.2514/8.4488

M. Summerfield, A Theory of Unstable Combustion in Liquid Propellant Rocket Systems, Journal of the American Rocket Society, vol.21, issue.5, pp.108-114, 1951.
DOI : 10.2514/8.4374

F. E. Marble and D. W. Cox, Servo-Stabilization of Low-Frequency Oscillations in a Liquid Bipropellant Rocket Motor, Journal of the American Rocket Society, vol.23, issue.2, 1953.
DOI : 10.2514/8.4542

D. J. Harrje and F. H. Reardon, Liquid propellant rocket instability, 1972.

F. E. Culick, Unsteady motions in combustion chambers for propulsion systems , The Research and Technology Organisation (RTO) of NATO, 2006.

A. Duvvur, C. H. Chiang, and W. A. Sirignano, Oscillatory fuel droplet vaporization - Driving mechanism for combustion instability, Journal of Propulsion and Power, vol.12, issue.2, pp.358-365, 1996.
DOI : 10.2514/3.24036

V. S. Burnley and F. E. Culick, On the Energy Transfer between Transverse Acoustic Modes in a Cylindrical Combustion Chamber, Combustion Science and Technology, vol.144, issue.1-6, pp.1-19, 1999.
DOI : 10.1016/S0082-0784(71)80051-6

C. C. Chao and S. D. Heister, Contributions of atomization to F-1 engine combustion instabilities, Engineering Analysis with Boundary Elements, vol.28, issue.9, pp.1045-1053, 2004.
DOI : 10.1016/j.enganabound.2004.04.003

B. Chehroudi, Physical Hypothesis for the Combustion Instability in Cryogenic Liquid Rocket Engines, Journal of Propulsion and Power, vol.26, issue.6, pp.1153-1160, 2010.
DOI : 10.2514/1.38451

C. T. Haddad and J. Majdalani, Transverse Waves in Simulated Liquid Rocket Engines, AIAA Journal, vol.51, issue.3, pp.591-605, 2013.
DOI : 10.2514/1.J051912

P. P. Popov, A. Sideris, and W. Sirignano, Stochastic modelling of transverse wave instability in a liquid-propellant rocket engine, Journal of Fluid Mechanics, vol.3, pp.745-62, 2014.
DOI : 10.1016/S0017-9310(99)00315-4

W. A. Sirignano, Driving Mechanisms for Combustion Instability, Combustion Science and Technology, vol.13, issue.4, pp.162-205, 2015.
DOI : 10.1080/00102200500287613

C. H. Sohn, P. O. Box, A. A. Shibanov, and V. P. Pikalov, On the method for hot-fire modeling of high-frequency combustion instability in liquid rocket engines, KSME International Journal, vol.18, issue.1, pp.1010-1018, 2004.
DOI : 10.1016/S0010-2180(01)00336-4

F. Richecoeur, P. Scouflaire, S. Ducruix, and S. , High-Frequency Transverse Acoustic Coupling in a Multiple-Injector Cryogenic Combustor, Journal of Propulsion and Power, vol.22, issue.4, pp.790-799, 2006.
DOI : 10.2514/1.18539
URL : https://hal.archives-ouvertes.fr/hal-00184034

C. H. Sohn, W. S. Seol, A. Shibanov, and V. P. Pikalov, Combustion Stability Boundaries of the Subscale Rocket Chamber with Impinging Jet Injectors, Journal of Propulsion and Power, vol.23, issue.1, pp.131-139, 2007.
DOI : 10.2514/1.19937

D. W. Davis and B. Chehroudi, Measurements in an Acoustically Driven Coaxial Jet under Sub-, Near-, and Supercritical Conditions, Journal of Propulsion and Power, vol.23, issue.2, pp.364-374, 2007.
DOI : 10.2514/1.19340

K. Miller, J. Sisco, N. Nugent, and W. Anderson, Combustion Instability with a Single-Element Swirl Injector, Journal of Propulsion and Power, vol.23, issue.5, pp.1102-1112, 2007.
DOI : 10.2514/1.26826

Y. Méry, S. Ducruix, P. Scouflaire, and S. , Injection coupling with high amplitude transverse modes: Experimentation and simulation, Comptes Rendus M??canique, vol.337, issue.6-7, pp.426-437, 2009.
DOI : 10.1016/j.crme.2009.06.009

C. Sohn, Y. Kim, Y. Kim, and V. Pikalov, A scaling method for combustion stability rating of coaxial gas-liquid injectors in a subscale chamber, Journal of Mechanical Science and Technology, vol.26, issue.6, pp.3691-3699, 2012.
DOI : 10.1007/s12206-012-0843-3

Y. Méry, L. Hakim, P. Scouflaire, L. Vingert, S. Ducruix et al., Experimental investigation of cryogenic flame dynamics under transverse acoustic modulations, Comptes Rendus M??canique, vol.341, issue.1-2, pp.100-109, 2013.
DOI : 10.1016/j.crme.2012.10.013

S. Gröning, D. Suslov, M. Oschwald, and T. Sattelmayer, Stability behaviour of a cylindrical rocket engine combustion chamber operated with liquid hydrogen and liquid oxygen, 5th European Conference for Aerospace Sciences (EUCASS), 2013.

S. Gröning, D. Suslov, J. Hardi, and M. Oschwald, Influence of hydrogen temperature on the acoustics of a rocket engine combustion chamber operated with lox/h2 at representative conditions, Proceedings of Space Propulsion, 2014.

J. S. Hardi, H. C. Martinez, M. Oschwald, and B. B. Dally, LOx Jet Atomization Under Transverse Acoustic Oscillations, Journal of Propulsion and Power, vol.30, issue.2, pp.337-349, 2014.
DOI : 10.2514/1.B34979

J. S. Hardi, S. K. Beinke, M. Oschwald, and B. B. Dally, Coupling of Cryogenic Oxygen???Hydrogen Flames to Longitudinal and Transverse Acoustic Instabilities, Journal of Propulsion and Power, vol.30, issue.4, pp.991-1004, 2014.
DOI : 10.2514/1.B35003

L. Crocco, D. T. Harrje, and F. H. Reardon, Transverse Combustion Instability in Liquid Propellant Rocket Motors, ARS Journal, vol.32, issue.3, pp.366-373, 1962.
DOI : 10.2514/8.6022

S. Feng, W. Nie, B. He, and F. Zhuang, Control Effects of Baffle on Combustion Instability in a LOX/GH2 Rocket Engine, Journal of Spacecraft and Rockets, vol.47, issue.3, pp.419-426, 2010.
DOI : 10.2514/1.46240

J. M. Quinlan, A. T. Kirkpatrick, D. Milano, C. E. Mitchell, and T. D. Hinerman, Analytical and Numerical Development of a Baffled Liquid Rocket Combustion Stability Code, Journal of Propulsion and Power, vol.28, issue.1, pp.122-131, 2012.
DOI : 10.2514/1.B34276

D. You, D. D. Ku, and V. Yang, Acoustic Waves in Baffled Combustion Chamber with Radial and Circumferential Blades, Journal of Propulsion and Power, vol.29, issue.6, pp.1-15, 2013.
DOI : 10.2514/1.B34923

S. Gröning, J. S. Hardi, D. Suslov, and M. Oschwald, Injector-Driven Combustion Instabilities in a Hydrogen/Oxygen Rocket Combustor, Journal of Propulsion and Power, vol.32, issue.3, 2016.
DOI : 10.2514/1.B35768

Y. Huang and V. Yang, Dynamics and stability of lean-premixed swirl-stabilized combustion, Progress in Energy and Combustion Science, vol.35, issue.4, pp.293-364, 2009.
DOI : 10.1016/j.pecs.2009.01.002

P. Wolf, G. Staffelbach, A. Roux, L. Gicquel, T. Poinsot et al., Massively parallel LES of azimuthal thermo-acoustic instabilities in annular gas turbines, Comptes Rendus M??canique, vol.337, issue.6-7, pp.6-7, 2009.
DOI : 10.1016/j.crme.2009.06.003

P. Wolf, R. Balakrishnan, G. Staffelbach, L. Gicquel, and T. Poinsot, Using LES to study reacting flows and instabilities in annular combustion chambers, Flow, Turbul, Combust, vol.88, pp.191-206, 2012.

M. E. Harvazinski, W. Anderson, and C. Merkle, Analysis of Self-Excited Combustion Instabilities Using Two- and Three-Dimensional Simulations, Journal of Propulsion and Power, vol.29, issue.2, pp.396-409, 2013.
DOI : 10.2514/1.B34732

S. Srinivasan, R. Ranjan, and S. Menon, Flame dynamics during combustion instability in a high-pressure, shear-coaxial injector combustor, Flow, Turbul, Combust, vol.94, issue.1, pp.237-262, 2015.

C. J. Morgan, K. J. Shipley, and W. E. Anderson, Comparative Evaluation Between Experiment and Simulation for a Transverse Instability, Journal of Propulsion and Power, vol.31, issue.6, pp.1-11, 2015.
DOI : 10.2514/1.B35759

]. L. Hakim, T. Schmitt, S. Ducruix, and S. , Numerical simulation of cryogenic flames under high frequency acoustic modulation 23rd ICDERS, pp.24-29

L. Hakim, T. Schmitt, S. Ducruix, and S. , Dynamics of a transcritical coaxial flame under a high-frequency transverse acoustic forcing: Influence of the modulation frequency on the flame response, Combustion and Flame, vol.162, issue.10, pp.3482-3502, 2015.
DOI : 10.1016/j.combustflame.2015.05.022
URL : https://hal.archives-ouvertes.fr/hal-01229487

L. Hakim, A. Ruiz, T. Schmitt, M. Boileau, G. Staffelbach et al., Large eddy simulations of multiple transcritical coaxial flames submitted to a high-frequency transverse acoustic modulation, Proceedings of the Combustion Institute, vol.35, issue.2, pp.1461-1468, 2015.
DOI : 10.1016/j.proci.2014.05.142
URL : https://hal.archives-ouvertes.fr/hal-01229478

W. A. Sirignano and P. P. Popov, Two-Dimensional Model for Liquid-Rocket Transverse Combustion Instability, AIAA Journal, vol.51, issue.12, pp.2919-2934, 2013.
DOI : 10.2514/1.J052512

P. P. Popov, W. A. Sirignano, and A. Sideris, Propellant Injector Influence on Liquid-Propellant Rocket Engine Instability, Journal of Propulsion and Power, vol.31, issue.1, pp.320-331, 2014.
DOI : 10.2514/1.B35400

G. Staffelbach, L. Gicquel, G. Boudier, and T. Poinsot, Large Eddy Simulation of self excited azimuthal modes in annular combustors, Proceedings of the Combustion Institute, vol.32, issue.2, pp.2909-2916, 2009.
DOI : 10.1016/j.proci.2008.05.033

P. Wolf, G. Staffelbach, L. Gicquel, J. Muller, and T. Poinsot, Acoustic and Large Eddy Simulation studies of azimuthal modes in annular combustion chambers, Combustion and Flame, vol.159, issue.11, pp.3398-3413, 2012.
DOI : 10.1016/j.combustflame.2012.06.016
URL : https://hal.archives-ouvertes.fr/hal-00801825

R. Garby, L. Selle, and T. Poinsot, Large-Eddy Simulation of combustion instabilities in a variable-length combustor, Comptes Rendus M??canique, vol.341, issue.1-2, pp.220-229, 2013.
DOI : 10.1016/j.crme.2012.10.020

L. Selle, R. Blouquin, M. Théron, L. Dorey, M. Schmid et al., Prediction and Analysis of Combustion Instabilities in a Model Rocket Engine, Journal of Propulsion and Power, vol.30, issue.4, pp.978-990, 2014.
DOI : 10.2514/1.B35146

T. Schmitt, L. Selle, A. Ruiz, and B. Cuenot, Large-Eddy Simulation of Supercritical-Pressure Round Jets, AIAA Journal, vol.48, issue.9, pp.2133-2144, 2010.
DOI : 10.2514/1.J050288

T. Schmitt, J. C. Rodriguez, I. Leyva, and S. , Experiments and numerical simulation of mixing under supercritical conditions, Physics of Fluids, vol.24, issue.5, p.55104, 2012.
DOI : 10.1063/1.3701374

B. J. Mcbride and S. Gordon, Computer program for calculation of complex chemical equilibrium compositions and applications: I. analysis, Reference Publication, p.1311, 1994.

T. Schmitt, Simulation des grandes échelles de la combustion turbulente en régime supercritique, CERFACS -CFD Team, 2009.

T. Schönfeld and M. Rudgyard, Steady and unsteady flow simulations using the hybrid flow solver AVBP, AIAA Journal, vol.37, issue.11, pp.1378-1385, 1999.
DOI : 10.2514/3.14333

V. Moureau, G. Lartigue, Y. Sommerer, C. Angelberger, O. Colin et al., Numerical methods for unsteady compressible multi-component reacting flows on fixed and moving grids, Journal of Computational Physics, vol.202, issue.2, pp.710-736, 2005.
DOI : 10.1016/j.jcp.2004.08.003

L. Quartapelle and V. Selmin, High-order Taylor?Galerkin methods for non-linear multidimensional problems, 1993.

O. Colin and M. Rudgyard, Development of High-Order Taylor???Galerkin Schemes for LES, Journal of Computational Physics, vol.162, issue.2
DOI : 10.1006/jcph.2000.6538

G. Soave, Equilibrium constants from a modified Redlich-Kwong equation of state, Chemical Engineering Science, vol.27, issue.6, pp.1197-1203, 1972.
DOI : 10.1016/0009-2509(72)80096-4

T. H. Chung, M. Ajlan, L. L. Lee, and K. E. Starling, Generalized multiparameter correlation for nonpolar and polar fluid transport properties, Industrial & Engineering Chemistry Research, vol.27, issue.4, pp.671-679, 1988.
DOI : 10.1021/ie00076a024

F. Nicoud and F. Ducros, Subgrid-scale stress modelling based on the square of the velocity gradient tensor, Flow, Turbul, Combust, vol.62, issue.3, pp.183-200, 1999.

T. Schmitt, Y. Méry, M. Boileau, and S. , Large-Eddy Simulation of oxygen/methane flames under transcritical conditions, Proceedings of the Combustion Institute, vol.33, issue.1, pp.1383-1390, 2011.
DOI : 10.1016/j.proci.2010.07.036
URL : https://hal.archives-ouvertes.fr/hal-00497345

T. Poinsot and S. Lele, Boundary conditions for direct simulations of compressible viscous flows, Journal of Computational Physics, vol.101, issue.1, pp.104-129, 1992.
DOI : 10.1016/0021-9991(92)90046-2

A. Urbano, L. Selle, G. Staffelbach, B. Cuenot, T. Schmitt et al., Large Eddy Simulation of a model scale rocket engine, 9th Mediterranean Combustion Symposium, 2015.

F. Nicoud, L. Benoit, C. Sensiau, and T. Poinsot, Acoustic Modes in Combustors with Complex Impedances and Multidimensional Active Flames, AIAA Journal, vol.45, issue.2, pp.426-441, 2007.
DOI : 10.2514/1.24933
URL : https://hal.archives-ouvertes.fr/hal-00908192

P. Salas, Aspects numériques et physiques des instabilités de combustion dans les chambres de combustion annulaires

C. F. Silva, F. Nicoud, T. Schuller, D. Durox, and S. , Combining a Helmholtz solver with the flame describing function to assess combustion instability in a premixed swirled combustor, Combustion and Flame, vol.160, issue.9, pp.1743-1754, 2013.
DOI : 10.1016/j.combustflame.2013.03.020
URL : https://hal.archives-ouvertes.fr/hal-00854137

M. P. Juniper, Triggering in thermoacoustics, International Journal of Spray and Combustion Dynamics, vol.3, issue.3, pp.217-238, 2012.
DOI : 10.1260/1756-8277.4.3.217

S. J. Illingworth, I. C. Waugh, and M. P. Juniper, Finding thermoacoustic limit cycles for a ducted Burke-Schumann flame, Proceedings of the Combustion Institute, vol.34, issue.1, pp.911-920, 2013.
DOI : 10.1016/j.proci.2012.06.017

M. K. Myers, Transport of energy by disturbances in arbitrary steady flows, Journal of Fluid Mechanics, vol.14, issue.-1, pp.383-400, 1991.
DOI : 10.1103/PhysRev.73.68

D. Durox, T. Schuller, N. Noiray, A. Birbaud, and S. , Rayleigh criterion and acoustic energy balance in unconfined self-sustained oscillating flames, Combustion and Flame, vol.156, issue.1, pp.416-429, 2008.
DOI : 10.1016/j.combustflame.2008.07.016

T. Poinsot and D. Veynante, Theoretical and numerical combustion
URL : https://hal.archives-ouvertes.fr/hal-00270731

M. J. Brear, F. Nicoud, M. Talei, A. Giauque, and E. R. Hawkes, Disturbance energy transport and sound production in gaseous combustion, Journal of Fluid Mechanics, vol.X, pp.53-73, 2012.
DOI : 10.1016/j.jcp.2008.01.038
URL : https://hal.archives-ouvertes.fr/hal-00789934

F. E. Marble and S. , Acoustic disturbance from gas non-uniformities convected through a nozzle, Journal of Sound and Vibration, vol.55, issue.2, pp.225-243, 1977.
DOI : 10.1016/0022-460X(77)90596-X

I. Duran and S. Moreau, Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion, Journal of Fluid Mechanics, vol.467, pp.190-231, 2013.
DOI : 10.1016/j.jsv.2011.01.025

J. S. Hardi, Experimental investigation of high frequency combustion instability in cryogenic oxygen?hydrogen rocket engines, 2012.

H. Kawashima, J. S. Hardi, S. C. Webster, and M. Oschwald, Combustor resonance frequency under unstable combustion, 30th International Symposium on Space Technology and Science (ISTS), JAXA, 2015.

S. Webster, J. Hardi, and M. Oschwald, One-dimensional model describing eigenmode frequency shift during transverse excitation, 6th European Conference for Aeronautical and Space Sciences (EUCASS), 2015.

F. Baillot, J. Blaisot, G. Boisdron, and C. Dumouchel, Behaviour of an air-assisted jet submitted to a transverse high-frequency acoustic field, Journal of Fluid Mechanics, vol.187, issue.305, pp.10-1017, 2009.
DOI : 10.1002/(SICI)1520-6440(199810)81:10<1::AID-ECJC1>3.0.CO;2-9

J. R. Dawson and N. A. Worth, Flame dynamics and unsteady heat release rate of self-excited azimuthal modes in an annular combustor, Combustion and Flame, vol.161, issue.10, pp.2565-2578, 2014.
DOI : 10.1016/j.combustflame.2014.03.021

J. O. Connor, V. Acharya, and T. Lieuwen, Transverse combustion instabilities: Acoustic , fluid mechanic, and flame processes, Prog. Energy Combust. Sci, vol.49, 2015.