An empirical diffusion coefficient function for the acoustic diffusion equation model in long rooms

In the diffusion equation model, the diffusion coefficient quantifies the relationship between the sound intensity and the gradient of the sound energy density. It is a crucial factor that affects the diffusion equation model, mostly for non-proportionate rooms. Previous work has indicated that this parameter varies spatially based on the rooms’ dimensions, the absorption coefficient, and the distance between source and receiver positions. In this paper, the spatially dependent diffusion coefficient is obtained by optimizing a distance-dependent function for the diffusion coefficient using reference results obtained from the radiosity method. The estimated diffusion coefficient inside long rooms is also shown to depend on the source position. The empirical function for the diffusion coefficient for long rooms is established as a quadratic polynomial function and is applicable for elongated rooms with a constant absorption coefficient lower than 0.3 and a minimum cross section of 4 m².