波散射问题求解中消除多次透射公式漂移失稳的一种措施

Measure for eliminating drift instability of multi-transmission formula in solution of scattering problems

在采用多次透射公式求解结构-地基体系地震反应等波散射问题时,其稳定性是人们所关注和研究的重要方面。针对其漂移失稳机制的研究表明,在将总波场分离为入射波场和散射波场从而实现波动输入和多次透射边界条件施加的过程中,采用连续介质解析解给出的入射波场与计算中的实际入射波场存在较大差别,会导致漂移失稳现象的出现。基于此,提出了一种直观的改进措施,即利用多次透射边界建立边界计算区,从而获得入射波离散数值解,并应用于波动的输入过程。数值实验验证了该措施可以有效地消除计算中的漂移失稳现象,给出更为合理的计算结果。

Using the multi-transmitting boundary formula to solve scattering problems such as seismic response analysis of soil–structure interactive system, and instability of the multi-transmitting boundary formula is an important aspect which is needed to be studied and focused on. The studies on the drift instability mechanism of multi-transmitting boundary formula show that when the total wave field is separated into incident wave field and scattered wave field for wave motion input and applying the multi-transmitting boundary condition, there is difference of incident wave field between the analytical solution in continuous medium and the real one in discrete grids, which may result in drift instability. For this problem, an improvement measure is proposed, that is, the numerical solution of incident wave is obtained by establishing the computation model for the boundary region with the multi-transmitting boundary formula, which is used in wave motion input process. The numerical experiments show that the proposed measure can effectively eliminate the drift instability in the calculation and give more reasonable results.