A generalized recursive convolution method for time-domain propagation in porous media

The Journal of the Acoustical Society of America
Didier DragnaPhilippe Blanc-Benon

Abstract

An efficient numerical method, referred to as the auxiliary differential equation (ADE) method, is proposed to compute convolutions between relaxation functions and acoustic variables arising in sound propagation equations in porous media. For this purpose, the relaxation functions are approximated in the frequency domain by rational functions. The time variation of the convolution is thus governed by first-order differential equations which can be straightforwardly solved. The accuracy of the method is first investigated and compared to that of recursive convolution methods. It is shown that, while recursive convolution methods are first or second-order accurate in time, the ADE method does not introduce any additional error. The ADE method is then applied for outdoor sound propagation using the equations proposed by Wilson et al. in the ground [(2007). Appl. Acoust. 68, 173-200]. A first one-dimensional case is performed showing that only five poles are necessary to accurately approximate the relaxation functions for typical applications. Finally, the ADE method is used to compute sound propagation in a three-dimensional geometry over an absorbing ground. Results obtained with Wilson's equations are compared to those obtained...Continue Reading

References

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Feb 6, 2008·The Journal of the Acoustical Society of America·T Van Renterghem, D Botteldooren
Feb 12, 2009·The Journal of the Acoustical Society of America·Jonghoon BinSoogab Lee
Apr 10, 2009·The Journal of the Acoustical Society of America·Olga Umnova, Diego Turo
Oct 26, 2010·The Journal of the Acoustical Society of America·Maarten HornikxJens Forssén
May 17, 2011·The Journal of the Acoustical Society of America·Keith AttenboroughShahram Taherzadeh
Jun 8, 2013·The Journal of the Acoustical Society of America·Didier DragnaFranck Poisson
Dec 1, 2013·The Journal of the Acoustical Society of America·Emilie BlancBruno Lombard

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Citations

Nov 2, 2015·The Journal of the Acoustical Society of America·Didier DragnaPhilippe Blanc-Benon
May 4, 2020·The Journal of the Acoustical Society of America·Huiqing Wang, Maarten Hornikx
Dec 5, 2016·The Journal of the Acoustical Society of America·Florian MonteghettiLucas Pascal
Dec 3, 2020·The Journal of the Acoustical Society of America·Finnur PindJakob Strømann-Andersen
Jan 31, 2021·The Journal of the Acoustical Society of America·Huiqing WangMaarten Hornikx
May 5, 2021·The Journal of the Acoustical Society of America·Ariane EmmanuelliPhilippe Blanc-Benon

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