The Acoustic Diffusion Model for Single and Coupled Interior Volumes Using the Boundary Element Method

Recently, a new model for the propagation of sound in interior volumes known as the acoustic diffusion model has been explored as an alternative method for acoustic predictions and analysis. The model uses statistical methods standard in high frequency room acoustics to compute a spatial distribution of acoustic energy over time as a diffusion process. For volumes coupled through a structural partition, the energy consumed by structural vibration and acoustic energy transmitted between volumes is incorporated through an acoustic transmission coefficient. In this paper, Boundary Element Method (BEM) solutions to single and multiple volume models are developed. The integral form of the 3-D acoustic diffusion model is derived using the Laplace transform and Green’s Second Identity. The solution using the BEM is developed as well as an efficient Laplace transform inversion scheme to obtain both steady state and transient interior acoustic energy. Several volume configurations with varying geometry are examined as the diffusion model and its BEM solution are analyzed and compared to conventional room acoustics analysis methods. Advantages of this method over conventional methods such as computational efficiency, applicability to high frequencies, and robustness to different problems are revealed as the comparisons are made in different coupled volumes. Introduction The indoor propagation of sound, sometimes referred to as room acoustics or architectural acoustics, is an important branch of acoustics to study and understand. Humans spend much of their time indoors, whether at home, at work, or in school, so it comes as no surprise that noise is commonly experienced inside. Room acoustics has been studied for many years; traditional mathematical models include the wave equation, geometrical acoustics, and statistical analysis. However, new improvements are still being sought in its prediction today. The most fundamental mathematical model of sound propagation is the acoustic wave equation, a partial differential equation which can be solved analytically for only very simple volume geometries 1 . The wave equation in any more complex volume must be solved numerically using methods like the Finite Element Method (FEM), the Boundary Element Method (BEM), or the Finite Difference (FD) technique. These methods are computationally intensive and generally only applicable at low frequencies. Predicting sound indoors is also commonly carried out using techniques in geometrical acoustics, e.g. the image source method and ray tracing 2 . Although accurate prediction of indoor sound is possible with these techniques, they rely on input acoustic properties of materials, e.g. absorption and scattering coefficients, which are inherently difficult to measure. Also, these methods rarely account for structural motion in the transmission of sound through partitions and, thus, encounter difficulties in problems of this type. Statistical analyses of uniform sound energy in rooms are also common methods of predicting indoor acoustics. These techniques are only useful at high frequencies when there are no effects of individual resonant modes, if