Simulating transient scattering from obstacles with frequency-dependent surface impedance

This paper presents an algorithm which couples the time domain Boundary Element Method (BEM) with a digital filter surface model. This aims to achieve the same extent of applicability and accuracy for transient sounds as is available for time-harmonic excitation with the established approach of substituting locally-reacting surface impedance directly into the frequency domain BEM formulation. Accurate representation of surface properties is crucial in obtaining realistic simulations, and the obstacles and boundaries typically encountered in real-world scenarios exhibit frequency-dependent surface impedance. In the time domain such frequency-dependency can be modelled using digital filters, and by this approach surface-impedance has been successfully incorporated into some recent FDTD models, but the best way of achieving this for time domain BEM is currently unresolved. The surface model used herein uses a digital filter to implement surface reflection coefficient – the accuracy of this approach for non-normal incidence plane waves has previously been questioned in the FDTD literature so performance in this scenario is specifically investigated. Accuracy is evaluated by comparison of results with the analytical plane wave pressure reflection coefficient and a frequency domain BEM with impedance boundary conditions. Computational cost and effect on algorithm stability are also considered