An efficient multi-layer boundary element method for direct computation of sound propagation in shallow water environments

Abstract

The objective of this thesis is to develop and apply efficient three-dimensional (3D) direct simulation capabilities for underwater sound field predictions in shallow water environments. Despite the large number of theoretical and experimental studies, direct numerical simulation of the shallow water acoustic field is still challenging due to environmental complexities and large computation cost involved. In this thesis, we develop a highly efficient O(NlogN) multi-layer boundary-element method, PFFT-BEM, for direct numerical simulation of acoustic propagation and scattering in shallow water environment. This method utilizes a Pre-corrected Fast Fourier Transform (PFFT) approach to accelerate the boundary-element method and reduce the computational efforts from O(N²~³) to O(NlogN) where N is the total number of boundary unknowns.

PFFT-BEM is capable of accounting for complex topography, inhomogeneity of water properties, and dynamic environments associated with realistic coastal conditions. With the O(NlogN) efficiency and linear scalability on massively parallel high-performance computing platforms, we first conduct multilayer 3D simulations benchmarking low-mid frequency acoustics over kilometer ranges against available theoretical results and field experiments. We then apply largescale PFFT-BEM simulations to investigate two underwater acoustics problems which are of scientific interest and practical importance: (1) 3D sound scattering from rough ocean surface; (2) 3D sound propagation and scattering around underwater seamount(s). For the 3D rough surface scattering problem, several approximation models have been proposed such as the perturbation theory and Kirchhoff approximation.

These approximation models provide fast predictions of statistics for the acoustics scattering necessary for predicting the scattering effects and reverberations from the rough surfaces. The validities of these models need to be assessed by direct numerical methods. However, most existing direct numerical studies regarding the validity regions of the approximation models are limited to the 2D rough surface scattering problem. We apply direct PFFT-BEM computations to study the 3D rough surface scattering problem with a Gaussian roughness spectrum. We examine the accuracy of the approximation model results through comparisons with direct numerical simulation results by 3D PFFT-BEM with a Monte Carlo technique. We identify and quantify the 3D validity regions of the approximation models as a function of the surface roughness and correlation length. We characterize and quantify the importance of 3D scattering effects on the validities of different approximation models.

Moreover, we find that both perturbation theory and Kirchhoff approximation become inaccurate for 3D scattering problems with low grazing angles. For the problem of 3D sound propagation/scattering around underwater seamount(s), we investigate the effects of seamount geometry and sound source frequencies on the sound scatterings by the seamount using 3D PFFT-BEM simulations. In particular, we investigate the backscattering, blocking and 3D scattering effects due to the presence of the seamount. We find that the acoustics scattering effects by the seamount have a strong dependence on the source frequency, and small variations in seamount geometry (such as seamount height and cross section shape) can induce significant changes in the acoustics scattering field.