Sound field modeling in a street canyon with a diffusion equation

Abstract

The transport theory of sound particles is applied to the sound field modeling in an empty street canyon with partially diffusely reflecting facades. A diffusion equation is then derived to predict the sound field distribution and the sound decay in the street. The main parameter, namely the diffusion coefficient, is a function of the street width and the acoustic reflection laws of both building facades. For a single rectangular street, analytical solutions can be found. For more complex urban spaces, a finite-element based approach is proposed. Several numerical examples are given, like the sound propagation in a street with a nonuniform cros section, and in street intersections, for point and line sources. In comparison with ray-tracing-based models, the diffusion model requires less computation time and could be applied to the calculation of a sound map for large urban areas. However, at the present time, the diffusion coefficient can be calculated only for simple building reflection laws, like the Lambert’s one.