Modelling frequency-dependent boundaries as digital impedance filters in FDTD and K-DWM room acoustics simulations

This paper presents a new method for modelling frequency-dependent boundaries in finite difference time domain (FDTD) and Kirchhoff variable digital waveguide mesh (K-DWM) room acoustics simulations. The proposed approach allows direct incorporation of a digital impedance filter (DIF) in the multi-dimensional (i.e. 2D or 3D) FDTD boundary model of a locally reacting surface. An explicit boundary update equation is obtained by carefully constructing a suitable recursive formulation. The method is analysed in terms of pressure wave reflectance for different wall impedance filters and angles of incidence. Results obtained from numerical experiments confirm the high accuracy of the proposed digital impedance filter boundary model, the reflectance of which closely matches locally reacting surface (LRS) theory. Furthermore, a numerical boundary analysis (NBA) formula is provided as a technique for analytic evaluation of the numerical reflectance of the proposed digital impedance filter boundary formulation.