On the efficient modeling of generic source directivity in Gaussian beam tracing.

Abstract

For large-distance sound propagation with complex obstacles, the Gaussian beam tracing (GBT) method is often applied. An omnidirectional source model is commonly implemented in GBT, which, however, neglects the influence of generic directivity patterns of practical acoustic problems. There have been efforts to synthesize or reproduce the target directivity pattern over an observation surface by using multiple distributed point sources. However, the efficiency and applicability of general applications still call for improvement. More specifically, rays from each of the point sources and their traces in the space should be computed and superposed to estimate the sound field, making the computational cost largely dependent on the complexity of the source directivity pattern. In this work, a complex-valued radiation function model is developed to realize the generic source directivity for GBT computation. One advantage of the method is that only one source is required such that computation cost can be greatly reduced. Rays are emitted from the source with direction-dependent amplitude and phase to realize the target directivity pattern. The development of the radiation function is associated with the GBT method. The verification cases show that this method can give good agreement with analytical or wave-based numerical solutions. Capabilities of modeling a complex source model of the spinning sound field to mimic the propeller noise are studied, and the result matches well with analytical solutions. Finally, a demonstration case of a four-propeller-powered drone in an urban region is conducted.