Application Of FDTD And Fourier Diffraction Theorem To Underwater Sound Scattering

Study of target scattering characteristics is an important topic in underwater acoustics, with various applications such as underwater target recognition, precision guidance of underwater weapons, anti-stealth warfare, and ocean resource exploitation. Scattering from complex targets is a key to the problem of fast and accurate prediction of back-scattering properties of underwater objects. Aimed at finding efficient algorithms for numerical solutions to this problem, this dissertation seeks improved methods in the implementation of the finite-difference time-domain (FDTD) method to deal with scattering problems, and proposes a new method to predict target strength using the Fourier diffraction theorem.In the FDTD study, we use a local conformal FDTD technique to overcome the problem due to the errors in modeling curving surface of the scattering object with a rectangular grid. A set of FDTD iterative expressions is obtained for the polar coordinate system. Near the surface of the object, a curving grid structure is introduced, while in most of the computation domain, the conventional rectangular grid is used. This provides a better precision in modeling the object without incur excessive computation burden.To apply the FDTD method in practical projects, computation efficient must be greatly enhanced. For this purpose, parallel FDTD is a possible solution. We make used of a previously established synchronous FDTD framework, and incorporate the complex factors including sea surface and the bottom into a unified system to develop the parallel FDTD algorithm. To take account of the spreading nature of the incident wave, a weighting function is applied to ensure stability of the iteration. In the parallel implementation, segmentation of the computation domain is optimized to reduce communication of data that are shared between neighboring processing nodes. The parallel FDTD algorithm has been implemented on a cluster-based high performance parallel-computing platform with up to 27 nodes, and using MPI programming. Analysis of the parallel efficiency and comparison between theoretical study and experiment has been performed.To further speed computation of scattering characteristics, we propose a new method to achieve fast prediction of target strength. This method is based on application of the Fourier diffraction theorem in a reversed fashion as it is used in the computer tomography (CT). From the discrete Fourier transform of the target geometry and distribution of material parameters, and from the sample location in the wave number domain derived from the incident wave, we can obtain the back- or forward-scattered sound pressure via a simple one-dimensional inverse Fourier transform. This method eliminates the need for nested iteration, and avoids large amounts of redundant computation, resulting in a greatly increased speed and reduced memory requirements. The obtained field is in general agreement with the FDTD results.Experiments were carried out in a water tank. Sound pressure scattered from various targets including circular tubes, blocks, and ship models were measured. Data were collected and used in analysis. These were compared with the FDTD results. Due to inaccurate modeling of the geometry, spherical or cylindrical spreading may not be ideal in practical situations when considering far field scattering patterns. Modifications are made to correct the spreading law, leading to better results. Influence of surface scattering is also considered.