Recently, a new model for the propagation of sound in interior volumes known as the acoustic diffusion equation 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 has been incorporated through a simple acoustic transmission coefficient. In this paper, a Boundary Element Method (BEM) solution to the simple diffusion model is developed. The integral form of the 3D acoustic diffusion equation for coupled volumes 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. In addition, a fully coupled model where both structural and acoustic energy are computed as a diffusion process is proposed. A simple volume configuration is examined as the diffusion models are analyzed and compared to conventional room acoustics analysis methods. Advantages of the energy diffusion methods over conventional methods, such as computation of energy distributions and accurate transmission from one volume to another, are revealed as the comparisons are made.
Comparative Evaluation of Ray Tracing and Diffusion Equation Modeling in Room Acoustics Design of Subway Stations
