Implementation and evaluation of a diffusion equation model based on finite difference schemes for sound field prediction in rooms

In this paper, the use of finite difference schemes for the acoustic diffusion equation model is introduced. Their features and limitations are analysed to select the adequate scheme based on both the stability conditions and the error order. The air absorption effects on the implementation are also discussed in terms of stability. To investigate the validity of the implementation, a set of simulations was conducted in a cubic room with four different absorption distributions. This evaluation was done by increasing either the spatial or the temporal resolutions of the studied scheme. The predicted values are compared with the statistical theory and geometrical models. The simulations suggested an empirical criterion for predicting the spatial and temporal resolutions that maximise the performance of the finite difference scheme.