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  董青,周正华,苏杰,刘厚毅,宋加密.消除多次透射公式高频振荡失稳的一种措施[J].震灾防御技术,2018,(3):571-577, DOI:10.11899/zzfy20180308.

消除多次透射公式高频振荡失稳的一种措施
摘要:    多次透射公式(MTF)物理概念简单,便于在计算机上实现时空解藕的高精度波动数值模拟。然而,MTF与其它局部人工边界条件类似,存在数值模拟失稳问题,如高频振荡便是可能出现的失稳现象。本文在分析MTF高频振荡失稳机理的基础上,提出了在波动有限元数值模拟中消除MTF高频振荡失稳的一种措施,即在整个有限元数值模拟区内施加与应变速率成正比的较小粘性阻尼;同时,讨论了这一稳定措施的有效性及其对数值计算精度的影响,并通过数值试验检验了这一稳定措施的可行性。结果表明,消除高频振荡失稳的措施行之有效,且只对波动有限元数值模拟中无意义的高频分量具有抑制作用,而对有意义的较低频段内的波动有限元数值模拟精度影响较小。
作者单位
董青 南京工业大学, 交通运输工程学院, 南京 210009 
周正华 南京工业大学, 交通运输工程学院, 南京 210009 
苏杰 南京工业大学, 交通运输工程学院, 南京 210009 
刘厚毅 南京工业大学, 交通运输工程学院, 南京 210009 
宋加密 南京工业大学, 交通运输工程学院, 南京 210009 
关  键  词:单侧波  粘性阻尼  数值模拟  散射问题  波源问题
DOI:10.11899/zzfy20180308
基金项目:国家自然科学基金项目(41374049)
收稿日期:2018-02-11
作者简介:董青,女,生于1992年。硕士研究生。主要从事岩土力学研究。E-mail:2458810997@qq.com
通讯作者:周正华,男,生于1962年。研究员。研究领域:防灾减灾与防护工程。E-mail:bjsmoc@163.com
The Measure Against High Frequency Oscillating Instability of Multi-transmitting Formula
Abstract:      Multi-Transmitting Formula (MTF) based on one-dimensional description on general kinematic characteristics of one-way wave and direct numerical simulation has simple physical concepts, and it is easy to realize the high precision and decoupling wave motion numerical simulation on the computer. However, Multi-Transmitting Formula, similar as other local artificial boundary conditions, is also a local artificial boundary condition which existed numerical instability problems, in which high-frequency oscillation instability is one of the instability phenomenon. Through the discussion of the mechanism of high frequency oscillation instability of Multi-Transmitting Formula, we present a measure to eliminate high frequency oscillation instability in wave numerical simulation. Through numerical simulation, the feasibility of the stabilization measure is verified. The results show that this stabilization measure is effective and of significantly cutting effectiveness on high-frequency component that is meaningless for wave motion numerical simulation. However, its effect on the wave motion numerical simulation was too small to ignore in the lower frequency band.
Keywords:  One-way wave  Viscous damping  Numerical simulation  The scattering problem  Source problem
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