ACTA ACUSTICA UNITED WITH ACUSTICA Vol. 105 (2019) 231 – 239 DOI 10.3813/AAA.919304 Room Acoustic Simulations Using the Finite Element Method and Diffuse Absorption Coefficients Diego M. Murillo, Filippo M. Fazi, Jeremy Astley Institute of Sound and Vibration Research, University of Southampton, University Road, Southampton SO17 1BJ, United Kingdom. diego.murillo@usbmed.edu.co Summary An alternative approach based on the use of reverberation time measurements to characterize the boundary con- ditions on Finite Element room acoustic simulations is proposed. The methodology relies on the estimation of the mean absorption of the room using Sabine/Eyring reverberation equations. From this information, diffuse absorption coefficients are calibrated and the specific acoustic impedance of the absorbing surfaces is calculated. The implications of assuming that the specific acoustic impedance is entirely resistive are also considered. An analysis of the accuracy of the proposed approach is presented for a reference case. The results indicate that the suggested methodology leads to a more accurate prediction of the modal behaviour of the enclosures compared to geometrical acoustic simulations. However, the assumption of a purely resistive specific acoustic impedance leads to shift in frequency which can be compensated for by synthesizing complex impedance phases that provides the same diffuse absorption coefficients. PACS no. 43.55.Br, 43.55.Ka 1. Introduction Geometrical Acoustics (GA) is a well-established tech- nique to simulate the acoustic behaviour of enclosures [1]. It is founded on the assumption that sound waves can be replaced by rays travelling in the room with each ray car- rying a portion of the energy produced by the source [2]. However, the postulation of waves propagating as rays is only sensible when the wavelength is small compared to the dimension of the surfaces of the room, otherwise, wave effects such as diffraction are relevant [3]. Recently, new approaches for edge diffraction calculation have been pro- posed [4, 5], nevertheless, assumptions of infinite planes or rigid surfaces constrain their application. Alternatively, the propagation of the sound in a com- pressible medium is calculated by solving the wave equa- tion. An analytical solution is only possible in a few cases under specific conditions and for simple geometries, which leads to the implementation of numerical methods. The Fi- nite Element Method (FEM) has been extensively used since the late 1960s to analyse and solve problems in acoustics [6]. Room Impulse Responses (RIRs) are cal- culated by solving the Helmholtz equation numerically for a range of frequencies and by applying the inverse Fourier transform at specific field points. The Finite El- ement Method applied directly in the time domain is an- other recent approach [7]. The main advantage compared Received 27 February 2017, accepted 10 November 2018. to GA methods lies in the accuracy of the results at low frequencies because room resonances are predominant and wave effects such as diffraction are inherently included in the solution. FEM also allows more accurate low fre- quency interactive auralizations in which the listener can hear the modal behaviour of the enclosure as they move e.g. from null to non-null acoustic pressure zones [8]. However, its high computational cost constrains its use at higher frequencies and for larger enclosures. The use of FEM for room acoustic simulations is com- monly addressed by assuming that the surfaces of the en- closure are locally reactive [2]. The boundaries of the do- main can be simply characterized by the specific acous- tic impedance [6]. Nevertheless, information on the val- ues of the specific acoustic impedance available in the existing scientific literature is insufficient for many room acoustic simulations, which limits the implementation of the approach. These values are often determined by mea- surements based on laboratory or in-situ methods. The impedance tube is a well-known technique to estimate the specific acoustic impedance and the absorption coefficient of materials [9]. A limitation of this technique lies in the fact that it requires a sample of the material to be measured in the laboratory which in turn, can lead to significant dif- ferences compared to the behaviour of the material in-situ [10]. Different in-situ methods using pressure-pressure (p- p) [11] and pressure-particle velocity (p-u) [12, 13] probes have been proposed, but the frequency range where the es- timation is reliable (> 300 Hz) limits their use for low fre- quency FE simulations. © S. Hirzel Verlag · EAA 231