Including scattering within the room acoustics diffusion model: An analytical approach

Over the last 20 years, a statistical acoustic model has been developed to predict the reverberant sound field in buildings. This model is based on the assumption that the propagation of the reverberant sound field follows a transport process and, as an approximation, a diffusion process that can be easily solved numerically. This model, initially designed and validated for rooms with purely diffuse reflections, is extended in the present study to mixed reflections, with a proportion of specular and diffuse reflections defined by a scattering coefficient. The proposed mathematical developments lead to an analytical expression of the diffusion constant that is a function of the scattering coefficient, but also on the absorption coefficient of the walls. The results obtained with this extended diffusion model are then compared with the classical diffusion model, as well as with a sound particles tracing approach considering mixed wall reflections. The comparison shows a good agreement for long rooms with uniform low absorption (α = 0.01) and uniform scattering. For a larger absorption (α = 0.1), the agreement is moderate, due to the fact that the proposed expression of the diffusion coefficient does not vary spatially. In addition, the proposed model is for now limited to uniform diffusion and should be extended in the future to more general cases.