Numerical modeling of urban sound fields by a diffusion process

In this paper, we present the numerical implementation of a sound field model used in urban acoustics. The mathematical model being based on a classic diffusion equation for the sound energy, a simple finite difference scheme is applied. We give also some finite difference equations for simple boundary conditions, like absorption by a wall and at building edges. The two-dimensional numerical scheme is then compared to analytical solutions of the sound field propagation in a rectangular street with a good agreement, both in the steady state and in the time varying state. Finally it is suggested that the adjustment of usual softwares for heat transfer could be an interesting and low cost way to develop powerful acoustic softwares for the prediction of noise in urban areas.