Comptes Rendus
no. 7
Introduction of acoustical diffraction in the radiative transfer method
[Introduction de la diffraction acoustique dans la méthode du transfert radiatif]

Présenté par : Gérard Iooss

Emeline Reboul1  ; Alain Le Bot1  ; Joël Perret-Liaudet1
1 LTDS – UMR 5513, École centrale de Lyon, 69134 Ecully cedex, France
Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 505-511.

Cette Note présente une méthode originale permettant d'inclure la diffraction acoustique dans la méthode du transfert radiatif. Cette nouvelle approche conduit à une meilleure description de la répartition de l'énergie acoustique. Elle repose sur l'introduction d'un coefficient de diffraction énergétique, et de sources diffractantes pour modéliser le phénomène de diffraction. L'amplitude de ces sources est déterminée en résolvant un système linéaire d'équations qui traduit le bilan d'énergie entre toutes les sources acoustiques. Cette méthode est appliquée à des problèmes bi-dimensionnels, et fournit de bons résultats excepté aux frontières géométriques.

This Note presents an original approach to include diffraction in the radiative transfer method when applied to acoustics. This approach leads to a better spatial description of the acoustical energy. An energetic diffraction coefficient and some diffraction sources are introduced to model the diffraction phenomena. The amplitudes of these sources are determined by solving a linear sytem of equations resulting from the power balance between all acoustical sources. The approach is applied on bidimensional examples and gives good results except at geometrical boundaries.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2004.03.006
Keywords: Acoustics, Waves, Vibrations, Geometrical Theory of Diffraction (GTD), Diffraction, Radiative transfer, Energy method, High frequency
Mot clés : Acoustique, Ondes, Vibrations, Théorie Géométrique de la Diffraction (TGD), Diffraction, Transfert radiatif, Méthode énergétique, Hautes fréquences
Emeline Reboul 1 ; Alain Le Bot 1 ; Joël Perret-Liaudet 1

1 LTDS – UMR 5513, École centrale de Lyon, 69134 Ecully cedex, France 
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Emeline Reboul; Alain Le Bot; Joël Perret-Liaudet. Introduction of acoustical diffraction in the radiative transfer method. Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 505-511. doi : 10.1016/j.crme.2004.03.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.006/

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[2] V. Cotoni; A. Le Bot Radiation of plane structures at high frequency using an energy method, Int. J. Acoust. Vib., Volume 6 (2001) no. 4, pp. 209-214

[3] H. Kuttruff Energetic sound propagation in rooms, Acta Acustica united with Acustica, Volume 83 (1997), pp. 622-628

[4] A. Le Bot; A. Bocquillet Comparison of an integral equation on energy and the ray-tracing technique in room acoustics, J. Acoust. Soc. Am., Volume 108 (2000) no. 4, pp. 1732-1740

[5] R.N. Miles Sound field in a rectangular enclosure with diffusely reflecting boundaries, J. Sound Vib., Volume 92 (1984) no. 2, pp. 203-226

[6] H. Kuttruff Stationary propagation of sound energy in flat enclosures with partially diffuse surface reflection, Acta Acustica united with Acustica, Volume 86 (2000), pp. 1028-1033

[7] A. Le Bot A functional equation for the specular reflection of rays, J. Acoust. Soc. Am., Volume 112 (2002) no. 4, pp. 1276-1287

[8] L.P. Franzoni; D.B. Bliss; J.W. Rouse An acoustic boundary element method based on energy and intensity variables for prediction of high-frequency broadband sound fields, J. Acoust. Soc. Am., Volume 110 (2001) no. 6, pp. 3071-3080

[9] J.B. Keller Geometrical theory of diffraction, J. Opt. Soc. Am., Volume 52 (1962) no. 2

[10] A.D. Pierce Acoustics – An Introduction to its Physical Principles and Applications, Acoustical Society of America, American Institute of Physics, New York, 1991

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