A comparison study between the transport equation model and diffusion equation model for room-acoustic predictions in long spaces.

This paper compares two numerical models: diffusion equation model and transport equation model, for room-acoustic predications in long spaces. Mathematically, the diffusion equation is the asymptotic approximation to the transport equation, therefore is expected to be less accurate. In addition, the transport equation intrinsically includes the direct sound field while the diffusion equation does not. However, due to its simple form of the diffusion equation, it has certain computational advantages over the transport equation model, e.g., it is less computationally expensive. When comparing the two models with the ray-tracing based method, the transport equation is shown to be more precise, especially when the walls are highly absorptive. Nevertheless, the diffusion equation model performs fairly well provided that the absorption on the walls is low. In this case, the diffusion equation model might be preferred over the transport equation model due to a low computational load.