Directional sources in wave-based acoustic simulation

Volumetric wave-based acoustic simulation relies on the complete solution to the 3D wave equation over a spatial grid. Detailed modeling of sources, however, requires interpolation over the grid, which is complicated by the directional character of the source itself. In this article, a new model of point sources of arbitrary directivity and location with respect to an underlying grid is presented. The model is framed in the spatio-temporal domain directly through the differentiation of Dirac distributions, leading to a spatial Fourier-based approximation strategy. Various approximants are presented, of both separable and non-separable type, and allowing for optimisation over a specified wavenumber range. Such approximants are then employed in a finite difference time domain setting, yielding numerical results for sources of various types, which are then compared against exact solutions.