In this study, we model acoustic waves induced by moving acoustic sources in three-dimensional (3D) underwater settings based on a spectral-element method (SEM). Numerical experiments are conducted using the SEM software package SPECFEM3D_Cartesian, which facilitates fluid–solid coupling and absorbing boundary conditions. Examples presented in this paper include an unbounded fluid truncated by using absorbing boundaries, and a shallow-water waveguide modeled as a fluid–solid coupled system based on domain decomposition. In the numerical experiments, the SEM-computed pressures match their analytical counterparts. SEM solutions of pressures at points behind and ahead of modeled moving acoustic sources show a frequency shift, i.e., a Doppler effect, which matches the analytical solution. This paper contributes to the field of passive sonar-based detection of moving acoustic sources, and addresses the challenge of computing wave responses generated by side-scan sonar by using moving sources of continuous signals.

中文翻译：

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移动水下声源引起的声波的谱元模拟

在这项研究中，我们基于谱元法 (SEM) 对由移动声源在三维 (3D) 水下环境中引起的声波进行建模。数值实验使用 SEM 软件包 SPECFEM3D_Cartesian 进行，该软件包有助于流固耦合和吸收边界条件。本文介绍的示例包括使用吸收边界截断的无界流体，以及基于域分解建模为流固耦合系统的浅水波导。在数值实验中，SEM 计算的压力与其分析对应的压力相匹配。模拟移动声源后面和前面点的压力的 SEM 解显示出与解析解相匹配的频移，即多普勒效应。