Virtual room acoustics using finite difference methods. How to model and analyse frequency-dependent boundaries?

In this paper, we present new methods for constructing and analysing frequency-dependent boundaries in room acoustic modelling with the use of finite difference time domain (FDTD) techniques. Novel FDTD formulations of simple locally reacting wall models with complex impedance are proposed and analysed in terms of pressure wave reflectance for different wall impedances and angles of incidence. The analysis is done using both numerical experiments and analytic evaluation. For the numerical experiments, a compact implicit scheme of 4th-order accuracy is used for updating the room interior grid points, the results of which are analysed in both time and frequency domains. The simulation results show that the 2D frequency-dependent locally reacting wall models adhere well to their theoretical counterparts, particularly at low frequencies. Furthermore, they validate the analytic evaluation method, which paves the way for using either method as a tool for analysis of numerical reflectance.