Simulation of the acoustics of coupled rooms by numerical resolution of a diffusion equation

Over the last few years, some studies showed that the acoustic energy density in closed or semi-closed spaces may be the solution of a diffusion equation. This theory allows non-uniform repartition of energy, and is especially relevant in room acoustics for long rooms or complex
spaces such as networks of rooms. In this work, the three-dimensional diffusion equation is solved directly by using a finite-element solver. This approach is used to simulate the acoustics of coupled rooms in terms of spatial variations of intensity levels and sound decay. The obtained results match satisfactorily with a model based on the classical statistical theory of room acoustics, but it allows to perform a finer spatial description of the acoustics of coupled rooms.