二维浅海波导中声场边界处理的谱无限元方法  

Spectral infinite element method for boundary processing of sound field in two-dimensional shallow water waveguide

作　　者：曹伟浩 程广利[1] 刘宝 CAO Weihao;CHENG Guangli;LIU Bao(College of Electronic Engineering,Naval Univ.of Engineering,Wuhan 430033,China)

机构地区：[1]海军工程大学电子工程学院,武汉430033

出　　处：《海军工程大学学报》2024年第1期49-55,共7页Journal of Naval University of Engineering

基　　金：国家自然科学基金资助项目(12104510);中国博士后科学基金资助项目(2022M723882);国家重点研发计划基金资助项目(2022YFC3103801)。

摘　　要：针对传统无限元法在截断声场边界上计算精度低的问题,提出了一种基于GR (Gauss-Radau)插值的谱无限元法,以高精度处理无限远边界对声场计算的影响。首先,采用映射函数构建从自然坐标系到笛卡尔坐标系的节点转换函数,获得两种坐标系之间的映射雅克比矩阵;然后,利用基于GR插值的形函数,模拟单元节点的声压,结合映射雅克比矩阵,对二维声场波动方程进行变分处理,推导了无限单元对应的积分表达式,用于模拟实际浅海波导环境下无限远处的声传播。与基于镜像法的解析解和传统无限元法结果的对比表明:所提方法结果与解析解一致性高,相对误差约为1%,验证了该方法的有效性和准确性。To solve the problem of low accuracy of the traditional infinite element method in truncated sound field boundary,a spectral infinite element method based on GR(Gauss-Radau) interpolation was proposed so as to deal with the effect of infinite boundary on sound field calculation with high precision.A node transformation function from the natural coordinate system to the Cartesian coordinate system was constructed using the mapping function,to obtain the mapping Jacobian matrix of two coordinate systems.The GR interpolation based on the shape function was used to simulate the sound pressure of the element nodes,and the mapping Jacobian matrix was combined with the variational processing of the two-dimensional wave equation of the sound field and the integral expression corresponding to the infinite element was given to simulate the sound propagation at infinite distance in the actual waveguide environment.Compared with the analytical solution based on the image method and the traditional infinite element method,the results show that the proposed method is more consistent with the analytical solution,and the relative error is about 1%,and thus the effectiveness and accuracy of the proposed method are verified.

关 键 词：二维浅海波导 谱无限元 Gauss-Radau插值 边界处理 声场计算 

分 类 号：TP242[自动化与计算机技术—检测技术与自动化装置]