Time-Domain Simulation of Directive Sources in 3-D Digital Waveguide Mesh-Based Acoustical Models

Digital waveguide mesh (DWM) models offer a simple, accurate, time-domain, numerical solution of the wave equation. A specific case where such accurate and computationally simple solutions are needed is the acoustical modeling of open or closed volumes. It is possible to model 3-D propagation of waves in enclosures such as rooms using DWM models. Generally, idealized omnidirectional sources are used for obtaining the impulse response in the DWM. However, real-life sound sources are never completely isotropic, causing wavefronts with directional properties. This paper presents two methods to simulate analytical and empirical directivities in 3-D DWM models in the far-field. The first method is based on the direct excitation of the mesh with the velocity component of the directional source and is used to simulate analytical sources. The second method is based on the weighting of velocity components generated by an omnidirectional source at different octave-bands and is used to simulate sources with frequency-dependent empirical directivity functions. A simple interpolation method for obtaining a closed-form description of the directivity function from incomplete directivity data is also proposed. Simulation results are presented for two sources in an acoustical model of a rectangular room.