Time-domain propagation in porous media using the auxiliary differential equation method: Application for outdoor acoustics

Abstract

Time-domain sound propagation equations in porous media usually involve convolutions, which can be computationally cumbersome. Indeed, a naïve approach would require to store the acoustic variables at every time-step, which would lead to an unacceptable memory space for long range propagation. To reduce the computational burden associated to convolutions, an efficient numerical method, referred to as the auxiliary differential equation (ADE) method, originated from the computational electromagnetic community and presented in Dragna et al. [J. Acoust. Soc. Am. 138, 1030–1042 (2015)] is proposed. The idea behind is to approximate the relaxation functions, which depend on the porous media properties, by rational functions in the frequency-domain. The time variation of the convolution is thus given by first-order differential equations which can be solved using standard time-marching schemes. The accuracy of the method is investigated and compared to that of recursive convolution methods. The ADE method is then applied for outdoor sound propagation using the time-domain rigid-frame model proposed by Wilson et al. [Appl. Acoust. 68, 173–200 (2007)] in the ground. Results obtained with Wilson's model are compared at long range to those obtained with Zwikker and Kosten's equations and with an equivalent impedance surface for different flow resistivities.