Sound field modeling in architectural acoustics using a diffusion equation

A numerical approach is proposed to model the reverberated sound field in rooms. The model is based on the numerical implementation of a diffusion model enabling spatial variations of the sound energy within a room, unlike the statistical theory. The proposed method allows to take into account most of complex phenomena encountered in room acoustics, like mixed reflections on walls (diffuse and specular), low and high absorption on walls, atmospheric attenuation, fitted zones. Moreover, the model can be applied to complex geometries, like multiple coupled rooms of different sizes. In this paper, the model and its numerical implementation are first detailed. Then, an application is proposed for a complex geometry defined by multiple coupled rooms with fitting objects, including low and high absorption on walls, in terms of sound level and reverberation times. The main interest of the model is that such approach requires less computational time in comparison with common approaches like ray-tracing simulations.