On the use of a diffusion equation for room-acoustic prediction

Abstract

This paper presents an alternative model for predicting the reverberant sound field in empty rooms with diffusely reflecting boundaries, based on the generalization and the numerical implementation of a diffusion equation for the energy density. The paper focuses on the source term and the boundary conditions of the diffusion equation, both for the steady state and the time-varying state, in order to make computational use of the model. In addition, theoretical analysis of the diffusion equation shows that the diffusion model may be considered as an extension of the classical theory of reverberation to nondiffuse sound fields. The numerical model is first applied to a cubic room and shows a very good agreement with statistical theory. Two numerical applications are also given for a long room and a flat room; results are in good agreement with numerical results from a ray-tracing software. The main advantage of the present model is its capability to be applied regardless of the complexity of the room shape, and that it gives results at any receiver location, with a low calculation time.