正交曲线坐标系在变化地形声场计算中的应用

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英文篇名：Applications of orthogonal curvilinear coordinates in sound field computation with non-flat sea floor 作者：高善国 ; 李淑秋 ; 王桂喜 英文作者：GAO Shanguo;LI Shuqiu;WANG Guixi;Key Laboratory of Science and Technology on Advanced Underwater Acoustic Signal Processing, Chinese Academy of Sciences;Underwater Acoustic Engineering Center, Institute of Acoustics, Chinese Academy of Sciences; 关键词：声场计算 ; 正交曲线坐标系 ; Helmholtz方程 英文关键词：Sound field computation;;Orthogonal curvilinear coordinates;;Helmholtz equation 中文刊名：应用声学 英文刊名：Journal of Applied Acoustics 机构：中国科学院先进水下信息技术重点实验室;中国科学院声学研究所水声工程中心; 出版日期：2019-07-18 16:28 出版单位：应用声学 年：2019 期：04 基金：国家自然科学基金项目(11504402);; 领域基金项目(1826140451020116ZK02001) 语种：中文; 页：228-236 页数：9 CN：11-2121/O4 ISSN：1000-310X 分类号：P229.1;P733.2

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。
        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.

引文

[1]Higdon R L.Numerical modeling of ocean circulation[J].Acta Numerica,2006,15:385-470.
    [2]Lan H Q,Zhang Z J.Comparative study of the freesurface boundary condition in two-dimensional finitedifference elastic wave field simulation[J].Journal of Geophysics and Engineering,2011,8(2):275-286.
    [3]Lan H Q,Zhang Z J.Three-dimensional wave-field simulation in heterogeneous transversely isotropic medium with irregular free surface[J].Bulletin of the Seismological Society of America,2011,101(3):1354-1370.
    [4]Jensen F B,Kuperman W A,Porter M B,et al.Computational ocean acoustics[M].Berlin:Springer,2011:337-456.
    [5]Willatzen M,Voon L C L Y.Separable boundary-value problems in physics[M].Morten Willatzen and Lok C.Lew Yan Voon Wiley-VCH,2011:39-78.
    [6]Morse P M,Feshbach H.Methods of theoretical physics:part II[M].New York:McGraw-Hill,1953.
    [7]Buckingham M J,Tolstoy A.An analytical solution for benchmark problem 1:the‘ideal’wedge[J].Journal of the Acoustical Society of America,1990,87(4):1511-1511.
    [8]Luo W Y,Yang C M,Qin J X,et al.Sound propagation in a wedge with a rigid bottom[J].Chinese Physics Letters,2012,29(10):104303.
    [9]Luo W Y,Yang C M,Qin J X,et al.Benchmark solutions for sound propagation in an ideal wedge[J].Chinese Physics B,2013,22(5):054301.
    [10]王竹溪,郭敦仁.特殊函数概论[M].北京:北京大学出版社,2000:337-635.