An efficient realization of frequency dependent boundary conditions in an acoustic finite-difference time-domain model

The finite-difference time-domain (FDTD) method provides a simple and accurate way of solving initial boundary value problems. However, most acoustic problems involve frequency dependent boundary conditions, and it is not easy to include such boundary conditions in an FDTD model. Although solutions to this problem exist, most of them have high computational costs, and stability cannot always be ensured. In this work, a solution is proposed based on “mixing modelling strategies”; this involves separating the FDTD mesh and the boundary conditions (a digital filter representation of the impedance) and combining them into a global solution. This solution is based on an interaction model that involves wave digital filters. The proposed method is validated with several test cases.