Simulation of three-dimensional sound propagation with multidimensional wave digital filters

The propagation of sound waves is described by partial differential equations for the acoustic pressure and the acoustic fluid velocity. The solution depends on the shape of the enclosure and on the boundary conditions. Among various methods for the discretization of partial differential equations, the multidimensional wave digital filter approach is known to yield robust algorithms for the discrete simulation of continuous problems. This paper describes the derivation of a discrete model for three-dimensional sound propagation according to multidimensional wave digital filtering principles. The correct treatment of boundary conditions for various wall impedances is shown. A numerical example for the sound propagation in three interconnected rooms of a building demonstrates the capabilities of the method.