散射问题中消除多次透射边界高频振荡失稳措施比较分析

Comparison of Measures for Eliminating High-frequency Instability of a Multi-transmitting Boundary in Scattering Problems

摘要:

多次透射边界是一种应用广泛的人工边界，类似于其它局部人工边界，它也存在计算稳定性问题。本文分析多次透射边界高频振荡失稳的原因，通过数值试验对已有的消除高频失稳措施进行比较分析，并给出在散射问题中已有消除高频失稳措施的适用性。研究表明，对于完全弹性问题，建议用滤波方法消除高频振荡失稳，但滤波系数的取值需要依据一定的经验；对于黏弹性问题，建议适当控制阻尼取值，利用差分格式本身的高能耗特性来抑制高频振荡失稳，该方法不存在参数选取的问题，更便于应用实施。

Abstract:

The multi-transmitting boundary is a local artificial boundary widely used in the numerical simulation of near-field wave motions in infinite media. But，like other artificial boundaries，the multi-transmitting boundary is unstable in numerical simulations.In this paper，we analyze the cause of this high-frequency instability and discuss the applicability of previous stability measures by performing numerical scattering problem experiments.We found that（1）for the perfect elasticity problem，the filtering method is more suitable for eliminating high-frequency instability，but it must be used carefully because of the need to consider the empirical value of the parameters；and （2）for the viscoelastic problem，the explicit difference scheme with a suitable damping value is more suitable for eliminating high-frequency instability due to the energy dissipation of the difference scheme.This scheme is also more convenient for application because no empirical parameters must be considered.