Determination of a diffusion coefficient function for long rooms using a least square optimization approach

Over the last decades, considerable attention has been devoted to the improvement of the diffusion equation model within the field of room acoustics. It has been found that this model is subject to certain limitations, with one constraint regarding the diffusion coefficient. The diffusion coefficient, a parameter integrated into the model, is a value that scales the sound intensity to the gradient of the sound energy density. Currently, this value is often treated as a constant, but research has shown that it is spatially dependent. This paper explains a method to optimise the diffusion coefficient for long rooms such as corridors and tunnels comparing the results with the radiosity method model and using the least-square function optimization, minimising the difference between results of both method. We optimize the parameters of a diffusion coefficient function, which includes the theoretical mean free path value, targeting a function that can be applied to a range of enlongated spaces.