Sound-field modeling in architectural acoustics by a transport theory: Application to street canyons

Abstract

The transport theory of sound particles is applied to the sound field modeling in architectural acoustics. A theoretical description is proposed for empty enclosures with complex boundary conditions, including both specular and diffuse reflections. As an example, the model is applied to street canyons. Therefore, an asymptotic approach is proposed to reduce the transport equation to a diffusion equation defined by only one parameter, the diffusion coefficient. This coefficient is a function of the reflection law of the building façades, the ratio of specular and diffuse reflections, as well as the street width. The model is then compared to Monte Carlo simulations of the propagation of sound particles in complex enclosures. As expected by the asymptotic approach, the model is in agreement with numerical results, but mainly for small street width and very diffuse reflections. Finally, a discussion is proposed in the conclusion, on the model's capabilities.