Time domain representation of frequency-dependent surface impedance using finite impulse response filters in discrete Huygens’ modeling

In recent years there has been renewed interest in time-domain numerical methods in view of sound synthesis applications and the need to obtain the impulse response of acoustic systems. Discrete Huygens’ Modeling (DHM) is one of the time-domain methods available and it presents interesting characteristics, such as its simple implementation and relatively low computational cost. Although an equivalent method has been widely applied in the field of electromagnetism, its application in the area of acoustics is still limited, especially for describing absorption materials at boundaries. The main aim of this paper is to show the applicability of the Finite Impulse Response (FIR) filters to represent sound absorbing materials in a DHM model, without significantly degrading its computational performance. The DHM have been used to indirectly obtain the frequency response functions of an acoustic cavity, both with and without the presence of absorbing materials on its boundaries. Numerical results and computational times are compared with Finite Element (FE) models of the cavity. While very good agreement between the methods is observed, the computational cost of the DHM models can be orders of magnitude lower than in the case of FE models.