Special Issue on Efficient Numerical Methods; Guest Editors: B. Nolte and S. MarburgNo Access

VALIDATION OF ACOUSTIC MODELS FOR TIME-HARMONIC DISSIPATIVE SCATTERING PROBLEMS

Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Partially funded by MEC (Spain) research project DPI2004-05504-C02-02 and Xunta de Galicia project PGIDIT05PXIC20705PN (Spain).

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LUIS HERVELLA-NIETO

Departamento de Matemáticas, Universidade da Coruña, 15707 A Coruña, Spain

Partially funded by MEC (Spain) research projects DPI2004-05504-C02-02 and MTM2004-05796-C02-01.

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ANDRÉS PRIETO

Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Partially funded by MEC (Spain) research project DPI2004-05504-C02-02 and Xunta de Galicia project PGIDIT05PXIC20705PN (Spain).

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RODOLFO RODRÍGUEZ

GI2MA, Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Partially funded by FONDAP in Applied Mathematics (Chile).

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https://doi.org/10.1142/S0218396X07003238Cited by:11 (Source: Crossref)

Abstract

The aim of this paper is to study the time-harmonic scattering problem in a coupled fluid-porous medium system. We consider two different models for the treatment of porous materials: the Allard–Champoux equations and an approximate model based on a wall impedance condition. Both models are compared by computing analytically their respective solutions for unbounded planar obstacles, considering successively plane and spherical waves. A numerical method combining an optimal bounded PML and finite elements is also introduced to compute the solutions of both problems for more general axisymmetric geometries. This method is used to compare the solutions for a spherical absorber.

Keywords:

References

J.-F. Allard , Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials ( Elsevier , New York , 1993 ) . Google Scholar
M. A. Delany and E. N. Bazley, Appl. Acoust. 3, 105 (1970), DOI: 10.1016/0003-682X(70)90031-9. Google Scholar
P. M. Morse and K. U. Ingard , Theoretical Acoustics ( McGraw-Hill , New York , 1978 ) . Google Scholar
K. Attenborough, J. Acoust. Soc. Am. 73, 785 (1983), DOI: 10.1121/1.389045. Web of Science, Google Scholar
J.-F. Allard and Y. Champoux, J. Acoust. Soc. Am. 91(6), 3346 (1992), DOI: 10.1121/1.402824. Web of Science, Google Scholar
M. A. Biot, J. Acoust. Soc. Am. 28, 168 (1956), DOI: 10.1121/1.1908239. Web of Science, Google Scholar
M. A. Biot, J. Acoust. Soc. Am. 28, 179 (1956), DOI: 10.1121/1.1908241. Web of Science, Google Scholar
J. F. Allard, A. Aknine and C. Depollier, J. Acoust. Soc. Am. 79, 1734 (1986), DOI: 10.1121/1.393234. Web of Science, Google Scholar
Th. Clopeauet al., Math. Comput. Modell. 33, 821 (2001), DOI: 10.1016/S0895-7177(00)00283-1. Web of Science, Google Scholar
A. Bermúdez, J. L. Ferrín and A. Prieto, Comput. Meth. Appl. Mech. Eng. 195, 1914 (2006). Web of Science, Google Scholar
L. L. Beranek and I. L. Vér , Noise and Vibration Control Engineering: Principles and Applications ( John Wiley & Sons , New York , 1992 ) . Google Scholar
V. Easwaran, W. Lauriks and J. P. Coyette, J. Acoust. Soc. Am. 100, 2989 (1996), DOI: 10.1121/1.417111. Web of Science, Google Scholar
R. Panneton and N. Atalla, J. Acoust. Soc. Am. 101, 3287 (1997), DOI: 10.1121/1.418345. Web of Science, Google Scholar
A. Bermúdez, J. L. Ferrín and A. Prieto, Int. J. Numer. Meth. Eng. 62, 1295 (2005). Web of Science, Google Scholar
B. Engquist and A. Majda, Math. Comput. 31, 629 (1977). Web of Science, Google Scholar
F. Ihlenburg , Finite Element of Analysis of Acoustical Scattering ( Springer-Verlag , New York , 1998 ) . Google Scholar
R. J. Astley, Int. J. Numer. Meth. Eng. 49, 951 (2000). Web of Science, Google Scholar
J. P. Berenger, J. Comput. Phys. 114, 185 (1994), DOI: 10.1006/jcph.1994.1159. Web of Science, Google Scholar
F. Collino and P. Monk, Comput. Meth. Appl. Mech. Eng. 164, 157 (1998), DOI: 10.1016/S0045-7825(98)00052-8. Web of Science, Google Scholar
A. Bermúdezet al., J. Comput. Phys. 223, 469 (2007). Web of Science, Google Scholar
L. M. Brekhovskikh and O. A. Godin , Acoustics of Layered Media I: Plane and Quasi-Plane Waves ( Springer , Berlin , 1999 ) . Google Scholar
D. G. Crighton , Modern Methods in Analytical Acoustics ( Springer-Verlag , London , 1992 ) . Google Scholar
R. Bracewell , The Fourier Transform and Its Applications ( McGraw-Hill , New York , 1999 ) . Google Scholar
W. Gander and W. Gautschi, BIT 40, 84 (2000), DOI: 10.1023/A:1022318402393. Web of Science, Google Scholar
A. Bermúdezet al., C. R. Acad. Sci. Paris, Ser. I 339, 803 (2004). Web of Science, Google Scholar
P. G. Petropoulus, SIAM J. Appl. Math. 60, 1037 (2000). Web of Science, Google Scholar
W. C. Chew and W. H. Weedom, Microwave Opt. Technol. Lett. 7, 599 (1994), DOI: 10.1002/mop.4650071304. Web of Science, Google Scholar
F. Collino and P. Monk, SIAM J. Sci. Comput. 19, 2061 (1998), DOI: 10.1137/S1064827596301406. Web of Science, Google Scholar
Y. Arnaoudov, G. Dassios and V. Kostopoulos, J. Acoust. Soc. Am. 104, 1929 (1998), DOI: 10.1121/1.423614. Web of Science, Google Scholar
P. J. Morris, J. Acoust. Soc. Am. 98, 3536 (1995), DOI: 10.1121/1.413786. Web of Science, Google Scholar