A numerical method for the solution of the three-dimensional acoustic wave equation in a marine environment considering complex sources

Abstract

The need to understand how complex acoustic sources propagate noise in a realistic environment is of growing interest. In this work, we propose a numerical model for the simulation of noise generated by sources with directivity and propagating in ocean waveguides. The numerical model solves the wave equation for the acoustic pressure in the physical space using a second-order accurate finite difference method (FDTD). The source is implemented using an improved form of the hard-source method, which implicitly takes into consideration the reflection of acoustic waves associated to the presence of the ocean free surface, through the use of the method of images. This novel method is shown to improve the results with respect to the standard hard source implementation. We first validate the numerical method considering both analytical solutions and benchmark cases for the case of a monopole and then explore the acoustic energy patterns developed in the case of dipole and quadrupole sources. Specifically, the algorithm and the implementation of complex sources are evaluated first in a semi-infinite fluid layer and then considering two classical waveguides: the Ideal one and the Pekeris one. The comparison with analytical results shows the numerical method’s accuracy and that incorporating free surface effects in the hard source implementation improves results. In addition, the study shows that the acoustic response in the near field, of the order of few kilometers from the source, is strongly influenced by the source’s directivity and orientation relative to the free surface. The results of this paper have implications for future research aimed at characterizing and quantifying ship propeller noise in realistic waveguides. Indeed, this preliminary work is necessary to proceed to more complex numerical experiments, such as considering a real propeller signal as a source or considering stratification of the medium or propagation in confined domains such as experimental tanks.