海洋声学中三维抛物方程非均匀网格模型  

A three-dimensional parabolic equation using non-uniform depth and horizontal grids in ocean acoustics

作　　者：徐传秀 杨士莪 朴胜春[1,2] 张海刚 唐骏[1,2] 刘佳琪 XU Chuanxiu;YANG Shie;PIAO Shengchun;ZHANG Haigang;TANG Jun;LIU Jiaq(Science and Technology on Underwater Acoustic Laboratory, Harbin Engineering University Harbin 150001;College of Underwater Acoustic Engineering, Harbin Engineering University Harbin 150001)

机构地区：[1]哈尔滨工程大学水声技术重点实验室,哈尔滨150001 [2]哈尔滨工程大学水声工程学院,哈尔滨150001

出　　处：《声学学报》2018年第4期453-462,共10页Acta Acustica

基　　金：国家自然科学基金项目(11474073,11234002,11704337);国家重点研发计划项目(2016YFC1400100)资助

摘　　要：在海洋声学中,三维抛物方程模型可以有效考虑三维空间的声传播效应。然而,采用三维抛物方程模型分析三维空间内的声传播问题时,计算时间较长,并且需要消耗较大的计算机内存,因此给远距离声场的快速精确计算带来了很大困难。为此,将非均匀网格Galerkin离散化方法用于三维直角坐标系下的水声抛物方程模型中,深度算子和水平算子Galerkin离散方式由均匀网格变为非均匀网格。仿真结果表明,三维直角坐标系下非均匀网格离散的抛物方程模型,在保持计算精度、提高计算速度的同时,可以实现远距离声场的快速预报。另外,针对远距离局部海底地形与距离有关的三维声传播问题,给出了声场快速计算方法;在海底保持水平的区域,采用经典Kraken模型,重构抛物方程算法的初始场,随后依次递推求解地形与距离有关海底下的三维声场。采用改进模型,证明了远距离楔形波导声强增强效应。Three-dimensional parabolic equation models can be used to analyze three-dimensional （3-D） sound propagation effects in ocean acoustics. However, long calculation time and large computer memory must be consumed when the models are used to analyze 3-D sound propagation problems, which makes it very difficult to calculate long-range sound fields accurately. Therefore, a non-uniform depth and horizontal grid scheme is applied to a 3-D parabolic equation model in Cartesian coordinates. Some numerical examples show that the improved parabolic equation model can calculate long-range sound propagation problems at higher rate of speed and accuracy. To consider 3-D sound propagation problems where the environmental parameters are rauge-independent in short range but range-dependent in long range, the the computer code Kraken is used to build the starting sound field and is adopted to calculate the 3-D sound field recursively. A long-range wedge-shaped waveguide problem is considered in the rebuilt model to show an energy enhancement phenomenon.

关 键 词：非均匀网格 三维空间 抛物方程 网格模型 海洋声学 GALERKIN 直角坐标系 离散化方法 

分 类 号：TB56[交通运输工程—水声工程]