G. Jao, the JA o(2) Green's function (Eq. (59) with q = q ? = 1 in Eq

G. Lo, Green's function (Eq. (59) with q = q ? = 3/4 in Eq. (A-2)). Finally, the FFT computations can be compared to the solution of the asymptotic o(2) wave equation (A-6), for both cases q = q ? = 5/8 and q = q, without expansion of Eq

G. Eo, the (frozen) o(2) Green's function (q = q ? = 5

G. Lo, ) the P L o(2) Green's function (q = q ? = 3

]. A. Bensoussan, J. L. Lions, and G. C. Papanicolaou, Asymptotic analysis for periodic structure, 1978.
DOI : 10.1090/chel/374

E. and S. Palencia, Nonhomogeneous media and vibration theory, Lectures notes in Physics, 1980.

J. L. Auriault, C. Boutin, and C. Geindreau, Homogenization of Coupled Phenomena in Heterogenous Media, 2009.
DOI : 10.1002/9780470612033

T. Levy, Propagation of waves in a fluid-saturated porous elastic solid, International Journal of Engineering Science, vol.17, issue.9, pp.1005-1014, 1979.
DOI : 10.1016/0020-7225(79)90022-3

J. L. Auriault, Dynamic behaviour of a porous medium saturated by a newtonian fluid, International Journal of Engineering Science, vol.18, issue.6, pp.775-785, 1980.
DOI : 10.1016/0020-7225(80)90025-7

M. Y. Zhou and P. Sheng, First-principles calculations of dynamic permeability in porous media, Physical Review B, vol.39, issue.16, pp.12027-12039, 1989.
DOI : 10.1103/PhysRevB.39.12027

D. M. Smeulders, R. L. Eggels, and M. E. Van-dongen, Dynamic permeability: reformulation of theory and new experimental and numerical data, Journal of Fluid Mechanics, vol.222, issue.-1, pp.245-211, 1992.
DOI : 10.1103/PhysRevLett.63.580

R. Burridge and &. J. Keller, Poroelasticity equations derived from microstructure, The Journal of the Acoustical Society of America, vol.70, issue.4, pp.1140-1146, 1981.
DOI : 10.1121/1.386945

A. N. Norris, On the viscodynamic operator in Biot's equations of poroelasticity, J. Wave Mat. Interact, vol.1, pp.365-380, 1986.

D. Lafarge, P. Lemarinier, J. F. Allard, and V. Tarnow, Dynamic compressibility of air in porous structures at audible frequencies, The Journal of the Acoustical Society of America, vol.102, issue.4, pp.1995-2006, 1997.
DOI : 10.1121/1.419690

C. Boutin, Acoustics of rigid porous media with inner resonators, submitted to, J. Acoust. Soc. Am, 2012.

D. Lafarge and N. Nemati, Nonlocal theory of sound propagation in homogeneous rigid-framed porous media, submitted to Wave Motion, 2012.

R. V. Craster, J. Kaplunov, and A. V. Pishugin, High-frequency homogenization for periodic media, Proc. R. Soc. A 466, pp.2341-2362, 2010.
DOI : 10.1126/science.1096796
URL : http://rspa.royalsocietypublishing.org/content/royprsa/466/2120/2341.full.pdf

R. V. Craster, J. Kaplunov, and J. Postnova, High-Frequency Asymptotics, Homogenisation and Localisation for Lattices, The Quarterly Journal of Mechanics and Applied Mathematics, vol.63, issue.4, pp.497-519, 2010.
DOI : 10.1093/qjmam/hbq015
URL : http://spiral.imperial.ac.uk/bitstream/10044/1/18371/2/Quarterly%20Journal%20of%20Mechanics%20and%20Applied%20Mathematics_63_4_2010.pdf

R. V. Craster, Bloch dispersion and high frequency homogenization for separable doubly-periodic structures, Wave Motion, vol.49, issue.2, pp.333-346, 2012.
DOI : 10.1016/j.wavemoti.2011.11.005
URL : https://hal.archives-ouvertes.fr/hal-00761147

C. Boutin, A. Rallu, and S. Hans, Large scale modulation of high frequency acoustic waves in periodic porous media, to appear in, J. Acoust. Soc. Am, 2012.

D. L. Johnson, J. Koplik, and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, Journal of Fluid Mechanics, vol.24, issue.-1, pp.379-402, 1987.
DOI : 10.1121/1.388036

Y. Champoux and J. F. Allard, Dynamic tortuosity and bulk modulus in air???saturated porous media, Journal of Applied Physics, vol.70, issue.4, pp.1975-1979, 1991.
DOI : 10.1063/1.349482

H. Darcy, Les fontaines publiques de la ville de, 1856.

D. Lafarge, Sound propagation in porous materials having a rigid frame saturated by gas, French). Ph.D. Dissertation, 1993.

D. K. Wilson, Relaxation???matched modeling of propagation through porous media, including fractal pore structure, The Journal of the Acoustical Society of America, vol.94, issue.2, pp.1136-1145, 1993.
DOI : 10.1121/1.406961

D. K. Wilson, Simple, relaxational models for the acoustical properties of porous media, Applied Acoustics, vol.50, issue.3, pp.171-188, 1997.
DOI : 10.1016/S0003-682X(96)00048-5

S. R. Pride, F. D. Morgan, and A. F. Gangi, Drag forces of porous-medium acoustics, Physical Review B, vol.47, issue.9, pp.4964-4978, 1993.
DOI : 10.1103/PhysRevB.47.4964

A. Cortis, Dynamic acoustic parameters of porous media: a theoretical, numerical and experimental investigation, 2002.

Z. E. Fellah, C. Depollier, M. Fellah, W. Lauriks, and J. Chapelon, Influence of dynamic tortuosity and compressibility on the propagation of transient waves in porous media, Wave Motion, vol.41, issue.2, pp.41-145, 2005.
DOI : 10.1016/j.wavemoti.2004.06.004
URL : https://hal.archives-ouvertes.fr/hal-00088187

B. D. Plyushchenkov and T. I. Turchaninov, ACOUSTIC LOGGING MODELING BY REFINED BIOT'S EQUATIONS, International Journal of Modern Physics C, vol.11, issue.02, pp.11-365, 2000.
DOI : 10.1142/S0129183100000341

D. K. Wilson, V. E. Ostashev, and S. L. Collier, Time-domain equations for sound propagation in rigid-frame porous media (L), The Journal of the Acoustical Society of America, vol.116, issue.4, pp.1889-1892, 2004.
DOI : 10.1121/1.1785691

D. K. Wilson, S. L. Collier, V. E. Ostashev, D. F. Aldridge, N. P. Symons et al., Time-domain modelling of the acoustic impedance of porous surfaces, Acta. Acust. Acust, pp.92-965, 2005.

D. K. Wilson, V. E. Ostashev, S. L. Collier, N. P. Symons, D. F. Aldridge et al., Time-domain calculations of sound interactions with outdoor ground surfaces, Applied Acoustics, vol.68, issue.2, pp.68-173, 2007.
DOI : 10.1016/j.apacoust.2005.10.004

O. Umnova and D. Turo, Time domain formulation of the equivalent fluid model for rigid porous media, The Journal of the Acoustical Society of America, vol.125, issue.4, pp.1860-1863, 2009.
DOI : 10.1121/1.3082123

Z. E. Fellah, M. Fellah, W. Lauriks, C. Depollier, J. Y. Chapelon et al., Solution in time domain of ultrasonic propagation equation in a porous material, Wave Motion, vol.38, issue.2, pp.38-151, 2003.
DOI : 10.1016/S0165-2125(03)00045-3

Z. E. Fellah, M. Fellah, W. Lauriks, and C. Depollier, Direct and inverse scattering of transient acoustic waves by a slab of rigid porous material, The Journal of the Acoustical Society of America, vol.113, issue.1, pp.61-72, 2003.
DOI : 10.1121/1.1528592

Z. E. Fellah, A. Wirgin, M. Fellah, N. Sebaa, C. Depollier et al., A time-domain model of transient acoustic wave propagation in double-layered porous media, The Journal of the Acoustical Society of America, vol.118, issue.2, pp.661-670, 2005.
DOI : 10.1121/1.1953247
URL : https://hal.archives-ouvertes.fr/hal-00088188

Z. E. Fellah, M. Fellah, F. G. Mitri, N. Sebaa, W. Lauriks et al., Transient acoustic wave propagation in air-saturated porous media at low frequencies, Journal of Applied Physics, vol.102, issue.8, pp.84906-84915, 2007.
DOI : 10.1063/1.2798930
URL : https://hal.archives-ouvertes.fr/hal-00461001

G. Chiavassa and B. Lombard, Time domain numerical modeling of wave propagation in 2D heterogeneous porous media, Journal of Computational Physics, vol.230, issue.13, pp.5288-5309, 2011.
DOI : 10.1016/j.jcp.2011.03.030
URL : https://hal.archives-ouvertes.fr/hal-00547008

G. Lefeuve-mesgouez, A. Mesgouez, G. Chiavassa, and B. Lombard, Semi-analytical and numerical methods for computing transient waves in 2D acoustic/poroelastic stratified media, Wave Motion, vol.49, issue.7, pp.667-680, 2012.
DOI : 10.1016/j.wavemoti.2012.04.006
URL : https://hal.archives-ouvertes.fr/hal-00667795

G. Chiavassa and B. Lombard, Abstract, Communications in Computational Physics, vol.7, issue.04, pp.985-1012, 2013.
DOI : 10.1016/j.crme.2003.11.004

E. Blanc, G. Chiavassa, and B. Lombard, Biot-JKD model: Simulation of 1D transient poroelastic waves with fractional derivatives, Journal of Computational Physics, vol.237, 2013.
DOI : 10.1016/j.jcp.2012.12.003
URL : https://hal.archives-ouvertes.fr/hal-00713127

J. D. Polack, X. Meynial, J. Kergomard, C. Cosnard, and M. Bruneau, Reflection function of a plane sound wave in a cylindrical tube, Revue Phys, Appl, vol.22, pp.331-337, 1987.

J. F. Allard and N. Atalla, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials, Second Edition, 2009.

D. Lafarge, The Equivalent Fluid Model, Materials and Acoustics Handbook, pp.205-228, 2009.
DOI : 10.1002/9780470611609.ch6

L. D. Landau and E. Lifshitz, Electrodynamics of continuous media, 2006.

A. Cortis, D. Smeulders, J. L. Guermond, and D. Lafarge, Influence of pore roughness on high-frequency permeability, Physics of Fluids, vol.15, issue.6, pp.1766-1775, 2003.
DOI : 10.1063/1.1571545

R. Brown, Connection between formation factor for electrical resistivity and fluid???solid coupling factor in Biot???s equations for acoustic waves in fluid???filled porous media, GEOPHYSICS, vol.45, issue.8, pp.1269-1275, 1980.
DOI : 10.1190/1.1441123

M. Avellaneda and S. Torquato, Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media, Physics of Fluids A: Fluid Dynamics, vol.3, issue.11, pp.2529-2540, 1991.
DOI : 10.1063/1.858194

D. Lafarge, Comments on ??????Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media??????, Physics of Fluids A: Fluid Dynamics, vol.5, issue.2, pp.500-503, 1992.
DOI : 10.1063/1.858873

D. L. Johnson, J. Koplik, and L. M. Schwartz, New Pore-Size Parameter Characterizing Transport in Porous Media, Physical Review Letters, vol.57, issue.20, pp.2564-2567, 1986.
DOI : 10.1103/PhysRevLett.57.2564

J. L. Auriault, L. Borne, and R. Chambon, Dynamics of porous saturated media, checking of the generalized law of Darcy, The Journal of the Acoustical Society of America, vol.77, issue.5, pp.77-1641, 1985.
DOI : 10.1121/1.391962

S. R. Pride, Governing equations for the coupled electromagnetics and acoustics of porous media, Physical Review B, vol.50, issue.21, pp.50-15678, 1994.
DOI : 10.1103/PhysRevB.50.15678

S. Torquato, Relationship between permeability and diffusion-controlled trapping constant of porous media, Physical Review Letters, vol.64, issue.22, pp.2644-2646, 1990.
DOI : 10.1103/PhysRevLett.64.2644

C. Boutin and C. Geindreau, Estimates and bounds of dynamic permeability of granular media, The Journal of the Acoustical Society of America, vol.124, issue.6, pp.3576-3593, 2008.
DOI : 10.1121/1.2999050
URL : https://hal.archives-ouvertes.fr/hal-00941175

J. Kergomard, J. D. Polack, and J. Gilbert, Propagation speed of a plane impulsive wave in a sound tube, J. Acoustique, vol.4, pp.467-483, 1991.

H. Tijdeman, On the propagation of sound waves in cylindrical tubes, Journal of Sound and Vibration, vol.39, issue.1, pp.1-33, 1975.
DOI : 10.1016/S0022-460X(75)80206-9

D. H. Keefe, Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions, The Journal of the Acoustical Society of America, vol.75, issue.1, pp.58-62, 1984.
DOI : 10.1121/1.390300