Time-domain impedance boundary conditions for simulations of outdoor sound propagation

Finite difference time-domain methods are well suited to study sound propagation in the context of transportation noise. In this paper, time-domain boundary conditions are considered for impedance models classically used for outdoor grounds. These impedance models have usually been obtained in the frequency domain and cannot be translated directly into the time domain. The derivation of the time-domain boundary condition is based on the approximation of the impedance as a sum of well-chosen template functions. Because of the forms of the template functions, the recursive convolution technique can be applied; this is a fast and computationally efficient method to calculate a discrete convolution. The impedance boundary conditions are validated using a linearized Euler equations solver in one- and three-dimensional geometries; comparisons with analytical solutions in the time and frequency domains are presented. The methods used to identify the coefficients of the template functions are shown to be of great importance. Amongthe three methods described, the optimization method in the frequency domain can be recommended, because it can be applied to many impedance models and allows the values of the coefficients to be constrained, which is needed to obtain accurate numerical results.