Page 228 - 应用声学2019年第4期

第 38 卷 第 4 期 Vol. 38, No. 4
2019 年 7 月 Journal of Applied Acoustics July, 2019

⋄ 李启虎院士八十华诞学术论文 ⋄

正交曲线坐标系在变化地形声场计算中的应用 ∗

高善国 1,2† 李淑秋 1,2 王桂喜 1,2

(1 中国科学院先进水下信息技术重点实验室 北京 100190)
(2 中国科学院声学研究所水声工程中心 北京 100190)

摘要 变化地形声场计算是越来越经常碰到的情况。变化地形往往给声场计算带来计算量增大、求解精度下
降的问题。坐标系选择是声场计算中非常重要的问题，该文研究基于地形的合适正交曲线坐标系选取规则。
在此坐标系中求解 Helmholtz 方程，能够极大简化求解过程，提高计算精度。结合简正波理论，从新的角度展
示了正交曲线坐标系在某些典型变化地形线源声场计算问题中的应用。对于几种典型的海洋声波导问题，可
以利用合适的曲线坐标系简化问题，给出更直观的物理图像。
关键词 声场计算，正交曲线坐标系，Helmholtz 方程
中图法分类号: O427.1 文献标识码: A 文章编号: 1000-310X(2019)04-0688-09
DOI: 10.11684/j.issn.1000-310X.2019.04.028

Applications of orthogonal curvilinear coordinates in sound field computation
with non-flat sea floor

GAO Shanguo 1,2 LI Shuqiu 1,2 WANG Guixi 1,2

(1 Key Laboratory of Science and Technology on Advanced Underwater Acoustic Signal Processing, Chinese Academy of
Sciences, Beijing 100190, China)
(2 Underwater Acoustic Engineering Center, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China)

Abstract Sound field computations with non-flat sea floor are more and more popular now. Variation of
sea floor brings problems like increasing calculation quantity or reducing the accuracy. Selection of coordinate
system in sound field computation is very important. In the paper, we study the selection method of suitable
coordinate system based on topography, which can improve computation accuracy and reduce calculation load
greatly. Combined with normal modes theory, we show applications of orthogonal curvilinear coordinates in
sound field computation with some typical non-flat sea floor and line source from a new perspective. For
several typical problems of ocean acoustic waveguide, we can simplify the problem by using suitable curvilinear
coordinate system and give more intuitive physical images.
Key words Sound field computation, Orthogonal curvilinear coordinates, Helmholtz equation

2019-03-04 收稿; 2019-05-07 定稿
国家自然科学基金项目 (11504402) , 领域基金项目 (1826140451020116ZK02001)
∗
作者简介: 高善国 (1984- ), 男, 山东临沂人, 博士, 副研究员, 研究方向: 水声信号处理、海洋声学。
† 通讯作者 E-mail: sggao@mail.ioa.ac.cn