Diffusion equation modeling in room-acoustic applications

Abstract

The diffusion equation application in room acoustic simulations can be traced back to 1969. However, much attention from room-acoustic community to the diffusion equation was given in the late 1990s and the early 2000s. In the literature, the acoustic diffusion equation may be considered as an approximation of the acoustic transport equation. The diffusion equation modeling has been considered suitable for applications in enclosed spaces with proportionate dimensions. The most intriguing features of the diffusion equation are its computational efficiency due to a sparse meshing condition and its capability of energy flux solutions due to Fick’s law. Since the late 2000s, the diffusion equation modeling has evolved with boundary conditions formulated by the rigorous physical–mathematical theory [Jing and Xiang, JASA 123, 145–153 (2008]] and its validity has also been systematically investigated [Xiang et al., JASA 133, 3975–3985 (2013)]. This paper reviews the vibrant development in the room-acoustics during this era and discusses wide range of applications from coupled-volume systems, historically significant worship spaces to recent investigations on sound absorption measurements in reverberation chambers. This paper also discusses its link to the acoustic transport equation and compares the modeling results of both. Different numerical approaches to solving the diffusion equations will also be reviewed.