2. Instabilités-de-kelvin-helmholtz-en and . Porteur, Nous présenterons dans la partie suivante un autre cas test en géométrie 3D

. Références, Third computational aeroacoustics workshop on benchmark problems " ? NASA Ohio aerospace institute, 1999.

A. Agarwal, P. Morris, R. Mani, and ?. , Calculation of Sound Propagation in Nonuniform Flows: Suppression of Instability Waves, AIAA Journal, vol.42, issue.1, pp.80-88, 2004.
DOI : 10.2514/1.619

L. Anne, J. Cioni, L. Fezoui, and F. Poupaud, A parallel FVTD Maxwell solver using 3D unstructured meshes, 13th Annual Review of Progress in Applied Computational Electromagnetics (PIERS), pp.359-365, 1997.

H. Atkins, Continued development of the discontinous Galerkin method for computational aeroacoustic applications, 1997.

C. Bailly, W. Béchara, S. Candel, and P. Lafon, Stochastic approach of noise modeling for free turbulent flows, AIAA Journal, vol.32, pp.455-463, 1994.

C. Bailly and J. Clarisse, Bogey ? " Workshop sur les conditions aux limites numériques : conditions non réfléchissantes en aéroacoustique, 2002.

C. Bailly, D. Juvé, and ?. , Numerical Solution of Acoustic Propagation Problems Using Linearized Euler Equations, AIAA Journal, vol.38, issue.1, pp.22-29, 2000.
DOI : 10.2514/2.949

A. Bayliss, E. Turkel, and ?. , Far field boundary conditions for compressible flows, Journal of Computational Physics, vol.48, issue.2, pp.182-199, 1982.
DOI : 10.1016/0021-9991(82)90046-8

E. Becache, S. Fauqueux, and P. Joly, Stability of perfectly matched layers, group velocities and anisotropic waves, Journal of Computational Physics, vol.188, issue.2, 2001.
DOI : 10.1016/S0021-9991(03)00184-0

URL : https://hal.archives-ouvertes.fr/hal-00989051

J. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, Journal of Computational Physics, vol.114, issue.2, pp.185-200, 1994.
DOI : 10.1006/jcph.1994.1159

M. Bernacki, L. Fezoui, S. Lanteri, S. Piperno, and ?. , Parallel discontinuous Galerkin unstructured mesh solvers for the calculation of three-dimensional wave propagation problems, Applied Mathematical Modelling, vol.30, issue.8, 2005.
DOI : 10.1016/j.apm.2005.06.015

URL : https://hal.archives-ouvertes.fr/hal-00607722

M. Bernacki, S. Lanteri, S. Piperno, and ?. , Time-domain parallel simulation of heterogeneous wave propagation on unstructured grids using explicit, non-diffusive, discontinous Galerkin methods, Journal of Computational Acoustics, 2004.

M. Bernacki, S. Piperno, and ?. , Schémas en volumes finis avec flux centrés : applicationà application`applicationà l'aéroacoustique, 2002.

C. Bogey and ?. , Calcul direct du bruit aérodynamique et validation de modèles acoustiques hybrides, Thèse, Ecole centrale de Lyon, 2000.

C. Bogey and C. Bailly, Three-dimensional non-reflective boundary conditions for acoustic simulations : far field formulation and validation test cases, Acta Acustica, vol.88, issue.4, pp.463-471, 2002.

C. Bogey, C. Bailly, D. Juvé, and ?. , Computation of flow noise using source termes in linearized Euler's equations, AIAA Journal, vol.40, issue.2, pp.225-243, 2002.

F. Bourdel, P. Helluy, and P. Mazet, Resolution of the non-stationary or harmonic Maxwell equations by a discontinous finite element method, Computing Methods in Applied Sciences and Engineering Nova Science, pp.405-422, 1991.

S. Candel and ?. , Numerical solution of conservation equations arising in linear wave theory: application to aeroacoustics, Journal of Fluid Mechanics, vol.30, issue.03, pp.465-493, 1977.
DOI : 10.1016/0022-460X(72)90718-3

B. Cockburn, G. Karniadakis, and C. Shu, The development of discontinous Galerkin methods, Lecture notes in Computational Science and Engineering, vol.11, 2000.

B. Cockburn and C. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems, Journal of Scientific Computing, vol.16, issue.3, pp.173-261, 2001.
DOI : 10.1023/A:1012873910884

T. Colonius and S. Lele, Sound generation in a mixing layer, Journal of Fluid Mechanics, vol.330, pp.375-409, 1997.
DOI : 10.1017/S0022112096003928

P. Delorme, C. Peyret, and ?. , Galerkin discontinous method for computational aeroacoustics

A. Dhia, G. Legendre, E. Luneville, and ?. , Analyse mathématique de l'´ equation de Galbrun enécoulementenécoulement uniforme, Série IIb, vol.8, 2001.

J. Diaz, P. Joly, and ?. , Stabilized Perfectly Matched Layer for Advective Acoustics, Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (Jyvaskyla, 2003.
DOI : 10.1007/978-3-642-55856-6_18

A. Dowling, J. F. Williams, M. Goldstein, and ?. , Sound Production in a Moving Stream, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.288, issue.1353, pp.321-349, 1978.
DOI : 10.1098/rsta.1978.0019

B. Engquist, A. Majda, and ?. , Absorbing boundary conditions for the numerical simulation of waves, Mathematics of Computation, vol.31, issue.139, pp.629-651, 1977.
DOI : 10.1090/S0025-5718-1977-0436612-4

A. Ern and J. , Guermond ? Theory and practice of finite elements, Applied Mathematical Sciences, vol.159, 2004.

R. Eymard and T. Gallouet, Herbin ? The finite volume method, 2000.

L. Fezoui, S. Lanteri, S. Lohrengel, S. Piperno, and ?. , Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.39, issue.6, 2005.
DOI : 10.1051/m2an:2005049

URL : https://hal.archives-ouvertes.fr/hal-00210500

L. Fezoui, M. Remaki, S. Piperno, and ?. , A nondiffusive finite volume scheme for the three-dimensional Maxwell's equations on unstructured meshes, SIAM J. Numer. Anal, vol.39, issue.6, pp.2089-2108, 2002.

R. Fjørtoft, Application of integral theorems in deriving criteria of stability for laminar flows and the baroclinic circular vortex, Geophys.Pub.Oslo, vol.17, pp.1-52, 1950.

M. Giles, Non-reflecting boundary conditions for Euler equation calculations, 9th Computational Fluid Dynamics Conference, pp.2050-2058, 1990.
DOI : 10.2514/6.1989-1942

D. Givoli and ?. , Non-reflecting boundary conditions, Journal of Computational Physics, vol.94, issue.1, pp.1-29, 1991.
DOI : 10.1016/0021-9991(91)90135-8

T. Gonzalez and ?. , Contributions aux conditions d'interface et conditions aux limites pour le système d'´ equations d'Euler compressible, Thèse, 2000.

T. Hagstrom, S. Hariharan, and ?. , Accurate boundary conditions for exterior problems in gas dynamics, Mathematics of Computation, vol.51, issue.184, pp.581-597, 1988.
DOI : 10.1090/S0025-5718-1988-0935075-7

A. Harten and ?. , On the symmetric form of systems of conservation laws with entropy, Journal of Computational Physics, vol.49, issue.1, 1981.
DOI : 10.1016/0021-9991(83)90118-3

J. Hestaven, T. Warburton, and ?. , Nodal High-Order Methods on Unstructured Grids, Journal of Computational Physics, vol.181, issue.1, pp.186-221, 2002.
DOI : 10.1006/jcph.2002.7118

J. Hestaven and ?. , On the Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations, Journal of Computational Physics, vol.142, issue.1, pp.129-147, 1998.
DOI : 10.1006/jcph.1998.5938

F. Hu, On Absorbing Boundary Conditions for Linearized Euler Equations by a Perfectly Matched Layer, Journal of Computational Physics, vol.129, issue.1, pp.201-219, 1996.
DOI : 10.1006/jcph.1996.0244

G. Karypis, V. Kumar, and ?. , Parallel multilevel k-way partitioning scheme for irregular graphs, Proceedings of the 1996 ACM/IEEE conference on Supercomputing (CDROM) , Supercomputing '96, pp.278-300, 1999.
DOI : 10.1145/369028.369103

D. Kröner and ?. , Absorbing Boundary Conditions for the Linearized Euler Equations in 2-D, Mathematics of Computation, vol.57, issue.195, 1991.
DOI : 10.2307/2938667

S. Lanteri and ?. , Parallel solutions of compressible flows using overlapping and non-overlapping mesh partitioning strategies, Parallel Computing, vol.22, issue.7, pp.943-968, 1996.
DOI : 10.1016/0167-8191(96)00036-1

P. , L. Saint, and P. Raviart, On a finite element method for solving the neutron transport equation Mathematical Aspects of Finite Elements in Partial Differential Equations (I. C. de Boor Academic press, pp.89-145, 1974.

G. Legendre, Rayonnement acoustique dans un fluide enécoulementenécoulement : analyse mathématique et numérique de l'´ equation de Galbrun, Thèse, 2003.

S. Lele and ?. , Compact finite difference schemes with spectral-like resolution, Journal of Computational Physics, vol.103, issue.1, pp.20-26, 1992.
DOI : 10.1016/0021-9991(92)90324-R

S. Lele, P. Moin, and M. Wang, Computation of quadrupole noise using acoustic analogy, AIAA Journal, vol.34, issue.11, pp.2247-2254, 1996.

M. Lesieur, New Trends in Large-Eddy Simulations of Turbulence, Annual Review of Fluid Mechanics, vol.28, issue.1, pp.45-82, 1996.
DOI : 10.1146/annurev.fl.28.010196.000401

G. Lilley, The generation and radiation of supersonic jet noiseIV-theory of turbulence generated jet noise, noise radiation from upstream sources, and combustion noise. Part II : Generation of sound in a mixing region, Air Force Aero Propulsion Laboratory AFAPL-TR, pp.72-53, 1972.

J. Lions and J. , Well-posed absorbing layer for hyperbolic problems, Numerische Mathematik, vol.92, issue.3, pp.535-562, 2002.
DOI : 10.1007/s002110100263

D. Lockard, H. Atkins, and ?. , Efficient implemantations of the quadrature-free discontinous Galerkine method, AIAA Journal, vol.99, issue.3309, pp.1-11, 1999.

O. Marsden, C. Bailly, C. Bogey, and ?. , Noise Radiated by a High-Reynolds-number 3-D Airfoil, 11th AIAA/CEAS Aeroacoustics Conference, pp.1-11
DOI : 10.2514/6.2005-2817

A. Michalke and ?. , On the inviscid instability of the hyperbolictangent velocity profile, Journal of Fluid Mechanics, vol.8, issue.04, pp.543-556, 1964.
DOI : 10.1017/S0022112064000908

C. Peyret and G. Elias, Finite-element method to study harmonic aeroacoustics problems, The Journal of the Acoustical Society of America, vol.110, issue.2, pp.661-668, 2001.
DOI : 10.1121/1.1378355

O. Phillips and ?. , On the generation of sound by supersonic turbulent shear layers, Journal of Fluid Mechanics, vol.27, issue.01, pp.1-28, 1960.
DOI : 10.1017/S0022112057000233

A. Pierce and ?. , Wave equation for sound in fluids with unsteady inhomogeneous flow, The Journal of the Acoustical Society of America, vol.87, issue.6, pp.2292-2299, 1990.
DOI : 10.1121/1.399073

S. Piperno, L. Fezoui, and ?. , A discontinous Galerkin FVTD method for 3D Maxwell equations, 2003.

T. Poinsot, S. Lele, and ?. , 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

B. Poirée and ?. , Petites perturbations d'unécoulementunécoulement tournant, Acustica, vol.59, pp.85-94, 1985.

L. Rayleigh and ?. , On the stability of certain fluid motions, Proc.Math.Soc.London, vol.11, issue.1, pp.474-487, 1880.

W. Reed, Triangular mesh methods for the neutron transport equation, 1973.

J. Shang, R. Fithen, and ?. , A Comparative Study of Characteristic-Based Algorithms for the Maxwell Equations, Journal of Computational Physics, vol.125, issue.2, pp.378-394, 1996.
DOI : 10.1006/jcph.1996.0100

H. Shen, C. Tam, and ?. , Numerical Simulation of the Generation of Axisymmetric Mode Jet Screech Tones, AIAA Journal, vol.36, issue.10, pp.1801-1807, 1998.
DOI : 10.2514/2.295

C. Tam and ?. , Computational aeroacoustics - Issues and methods, AIAA Journal, vol.33, issue.10, pp.1788-1796, 1995.
DOI : 10.2514/3.12728

C. Tam and L. , Perfectly Matched Layer as an Absorbing Boundary Condition for the Linearized Euler Equations in Open and Ducted Domains, Journal of Computational Physics, vol.144, issue.1, pp.213-234, 1998.
DOI : 10.1006/jcph.1998.5997

C. Tam and Z. Dong, RADIATION AND OUTFLOW BOUNDARY CONDITIONS FOR DIRECT COMPUTATION OF ACOUSTIC AND FLOW DISTURBANCES IN A NONUNIFORM MEAN FLOW, Journal of Computational Acoustics, vol.04, issue.02, pp.175-201, 1996.
DOI : 10.1142/S0218396X96000040

C. Tam, J. Hardin, and ?. , NASA Ohio aerospace institute, second computational aeroacoustics workshop on benchmark problems, 1997.

C. Tam, J. Hardin, J. Ristorcelli, and ?. , NASA Ohio aerospace institute, workshop on benchmark problems in computational aeroacoustics, 1995.

C. Tam and J. Webb, Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics, Journal of Computational Physics, vol.107, issue.2, pp.262-281, 1993.
DOI : 10.1006/jcph.1993.1142

K. Thompson and ?. , Time dependent boundary conditions for hyperbolic systems, Journal of Computational Physics, vol.68, issue.1, pp.1-24, 1987.
DOI : 10.1016/0021-9991(87)90041-6

J. Vila, Convergence and error estimates in finite volume schemes for general multidimensional scalar conservation laws. I. Explicite monotone schemes, ESAIM: Mathematical Modelling and Numerical Analysis, vol.28, issue.3, pp.267-295, 1994.
DOI : 10.1051/m2an/1994280302671