Time-domain boundary conditions for outdoor ground surfaces

Abstract

Finite-difference time-domain techniques are promising for detailed dynamic simulations of sound propagation in complex atmospheric environments. Success of such simulations requires the development of new techniques to accurately handle the reflective and absorptive properties of a porous ground. One method of treating the ground boundary condition in the time domain [Salomons et al., Acta Acust. 88, 483–492 (2002)] is to use modified fluid dynamic equations, where the ground is considered as a porous medium described by its physical properties. However, this approach significantly increases computation time, as the domain must be extended into the ground and a large number of grid points are needed. Standard impedance models for the ground boundary condition are frequency-domain models, which generally are non-causal [Y. H. Berthelot, J. Acoust. Soc. Am. 109, 1736–1739 (2001)]. The development of a time-domain boundary condition from these models requires removing the singularity from the impedance equation when transforming from the frequency domain to the time domain. Alternatively, as the impedance boundary condition is a flux equation, a time-domain boundary condition can be derived from first principles, using the physical properties of the ground. We report on our development of a time-domain ground boundary condition.