Xie Zhinan, Matzen René, Cristini Paul, Komatitsch Dimitri, Martin Roland
Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China.
Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
J Acoust Soc Am. 2016 Jul;140(1):165. doi: 10.1121/1.4954736.
A time-domain Legendre spectral-element method is described for full-wave simulation of ocean acoustics models, i.e., coupled fluid-solid problems in unbounded or semi-infinite domains, taking into account shear wave propagation in the ocean bottom. The technique can accommodate range-dependent and depth-dependent wave speed and density, as well as steep ocean floor topography. For truncation of the infinite domain, to efficiently absorb outgoing waves, a fluid-solid complex-frequency-shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique. The complex stretching is rigorously taken into account in the derivation of the fluid-solid matching condition inside the absorbing layer, which has never been done before in the time domain. Two implementations are designed: a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high-order time schemes, leading to reduced numerical dispersion and dissipation, a topic of importance, in particular, in long-range ocean acoustics simulations. The method is validated for a two dimensional fluid-solid Pekeris waveguide and for a three dimensional seamount model, which shows that the technique is accurate and numerically long-time stable. Compared with widely used paraxial absorbing boundary conditions, the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves.
本文描述了一种用于海洋声学模型全波模拟的时域勒让德谱元法，即无界或半无限域中的流固耦合问题，同时考虑了海底中的剪切波传播。该技术可以处理与距离和深度相关的波速和密度，以及陡峭的海底地形。为了截断无限域并有效吸收出射波，基于复坐标拉伸技术引入了一种流固复频移非分裂完全匹配层。在吸收层内流固匹配条件的推导中严格考虑了复拉伸，这在时域中以前从未做过。设计了两种实现方式：卷积公式和辅助微分方程公式，因为后者允许实现高阶时间格式，从而减少数值色散和耗散，这在特别是长距离海洋声学模拟中是一个重要的问题。该方法在二维流固Pekeris波导和三维海山模型上得到了验证，结果表明该技术是准确的且在数值上具有长时间稳定性。与广泛使用的傍轴吸收边界条件相比，完全匹配层在吸收体波和界面波方面效率显著更高。
