透射边界与谱元法的结合及对波动模拟精度的改进

Integration of transmitting boundary and spectral-element method and improvement on the accuracy of wave motion simulation

实现与高精度的谱元法具有一致精度的人工边界条件,对基于谱元法的波动数值模拟具有重要意义。给出了具有多阶精度的多次透射公式(MTF)与节点不等间距分布的谱元法的结合方法,并在通用的采用显式Newmark预估校正式和并行计算技术的谱元程序SPECFEM2D和SPECFEM3D中实现。利用改进后的谱元程序模拟了二维和三维模型下波源问题的响应,模拟结果与程序自带的黏性边界的结果及远置解的对比表明,结合MTF的谱元程序显著提高了对边界处大角度入射的体波及面波的吸收效果,消除了黏性边界存在的漂移现象。高阶MTF是与高精度的谱元法相匹配的边界条件。

The implementation of accuracy-matched artificial boundary condition to match the high-order spectral element method (SEM) has great significance for wave motion simulations based on SEM. A method was introduced, integrating the multi-transmitting formula (MTF) with multi-order accuracy and the spectral-element method characterized by nonuniformly distributed nodes. The technique was implemented in the widely used software packages called SPECFEM2D and SPECFEM3D that adopt the explicit Newmark time scheme and parallel computing technique. The responses of 2D and 3D wave source problems were simulated by using the modified SEM packages. By comparing the results with that based on viscous boundary and the extended solution, it is shown that SEM combined with MTF significantly improves the absorbing efficiency of large-angle incidence body waves and surface waves at the boundary, and removes the drifting phenomenon of the viscous boundary. High-order MTF is a proper artificial boundary condition which can match well with the high accuracy high-order SEM. © 2017, Editorial Office of Journal of Vibration and Shock. All right reserved.