透射边界高频失稳机理及其消除方法——SH波动

谢志南; 廖振鹏

doi:10.6052/0459-1879-11-312

透射边界高频失稳机理及其消除方法——SH波动

doi: 10.6052/0459-1879-11-312

谢志南¹,
廖振鹏^1,2

1.
中国地震局工程力学研究所, 哈尔滨 150080
2. 哈尔滨工程大学船舶学院, 哈尔滨 150001

基金项目: 国家自然科学基金(51108431,51078337)和中国地震局优秀团队研究基金资助项目.

详细信息

中图分类号: P315
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出版历程
- 收稿日期: 2011-10-31
- 修回日期: 2012-02-16
- 刊出日期: 2012-07-18

MECHANISM OF HIGH FREQUENCY INSTABILITY CAUSED BY TRANSMITTING BOUNDARY AND METHOD OF ITS ELIMINATION——SH WAVE

Xie Zhinan¹,
Liao Zhenpeng^1,2

1.
Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China
2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

Funds: The project was supported by the National Natural Science Foundation of China (51108431, 51078337) and Research Group Fund of China Earthquake Administration.

摘要

摘要: 用有限元法求解近场波动问题,须选取人工边界条件以实现对无限域稳定、高效的数值模拟. 该文探讨了SH波导有限元数值模拟中透射边界引发的高频失稳问题. 从离散模型出发,分析了内节点与人工边界节点运动方程频散曲线之间的匹配关系,揭示了高频失稳的一种机理,即二者相互耦合所得计算方案支持自发从人工边界向计算区域内行进的高频波动. 提出通过调整内节点运动方程以改变这一匹配关系,从而消除失稳的措施. 理论分析与数值结果表明该措施能有效地消除高频振荡失稳.
- 人工边界条件 /
- 数值失稳 /
- 波动 /
- 有限元 /
- 频散曲线 /
- 群速度
Abstract: To solve near-field wave problems by finite element method, absorbing boundary conditions were needed to simulate the unbound field robustly and efficiently. Taking numerical simulation of wave motion in SH waveguide as an example, high-frequency instability caused by transmitting boundary were discussed. Directly from discrete model, mechanism of instability was found by analyzing the matching relationship of motion equations of interior nodes and nodes on absorbing boundary. Results showed that instability was caused by high frequency wave, which was allowed to enter continuously from the absorbing boundary into the computational region without excitation. Thus an approach of eliminating such instability was proposed by adjusting the motion equations of interior nodes to change the matching relationship. Theoretical and numerical results showed that the present approach was efficient.
- absorbing boundary condition /
- numerical instability /
- wave motion /
- finite element /
- dispersion curve /
- group velocity

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参考文献(27)

廖振鹏. 工程波动理论导论 (第2版). 北京: 科学出版社, 2002 (Liao Zhenpeng. Introduction to Wav Motion Theories in Engineering (2nd edn). Beijing: Science Press, 2002 (in Chinese)

Bérenger JP. Perfectly Matched Layer (PML) for Computational Electromagnetics. California: Morgan and Claypool Publishers, 2007

Givoli D. Numerical Methods for Problems in Infinite Domains. Amsterdam: Elsevier, 1992

Clayton R, Engquist B. Absorbing boundary conditions for acoustic and elastic wave equations. Bulletin of the Seismological Society of America, 1977, 67(6): 1529-1540

Bayliss A, Turkel E. Radiation boundary conditions for wave-like equations. Communications on Pure and Applied Mathematics, 1980, 33(6): 707-725

Liao ZP, Wong HL, Yang BP, et al. A Transmitting boundary for transient wave analyses. Scientia Sinica(Series A). 1984, 27(10): 1063-1076

Higdon RL. Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation. Mathematics of Computation, 1986, 47(176): 437-459

Cerjan C, Kosloff D, Kosloff R, et al. A nonreflecting boundary conditions for discrete acoustic and elastic wave equations. Geophysics, 1985, 50(4): 705-708

Sochaki I, Kubichek R, George J, et al. Absorbing boundary conditions and surface waves. Geophysics, 1987, 52(1): 60-71

Bérenger JP. A perfectly matched layer for the absorption of electromagnetic waves. Journal of Computational Physics, 1994, 114(2): 185-200

Grote MJ, Keller JB. Exact nonreflecting boundary conditions for the time dependent wave equation. SIAM Journal on Applied Mathematics, 1995, 55(2): 280-297

Rowley CW, Colonius T. Discretely nonreflecting boundary conditions for linear hyperbolic systems. Journal of Computational Physics, 2000, 157(2): 500-538

Komatitsch D, Martin R. An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation. Geophysics, 2007, 72(5): SM155-SM167

Hagstrom T, Mar-Or A, Givoli D. High-order local absorbing conditions for the wave equation: Extensions and improvements. Journal of Computational Physics, 2008, 227(6): 3322-3357

Meza-Fajardo KC, Papageorgiou AS. On the stability of a non-convolutional perfectly matched layer for isotropic elastic media. Soil Dynamics and Earthquake Engineering, 2010, 30(3): 68-81

Du XL, Zhao M. A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media. Soil Dynamics and Earthquake Engineering, 2010, 30(10): 937-946

Zhao M, Du XL, Liu JB, et al. Explicit finite element artificial boundary scheme for transient scalar waves in two-dimensional unbounded waveguide. International Journal for Numerical Methods in Engineering, 2011, 87(11): 1074-1104.

Liao ZP, Zhou ZH, Zhang YH. Stable implementation of transmitting boundary in numerical simulation of wave motion. Chinese Joural of Geophysics, 2002, 45(4): 554-568

Liao ZP, Liu JB. Numerical instabilities of a local transmitting boundary. Earthquake Engineering & Structural Dynamics, 1992, 21(1): 65-77

杜修力, 赵密, 王进廷. 近场波动模拟的人工应力边界条件.力学学报, 2006, 38(1): 49-56 (Du Xiuli, Zhao Mi, Wang Jinting. A stress artificial boundary in FEA for near-field wave problem. Chinese Journal of Theoretical and Mechanics, 2006, 38(1): 49-56 (in Chinese)

谢志南. 波动数值模拟人工边界的稳定问题. [博士论文].哈尔滨: 中国地震局工程力学研究所, 2011 (Xie Zhinan. Stability problems of artificial boundary conditions in numerical wave simulation. [PhD Thesis]. Dalian: Institute of Engineering Mechanics, China Earthquake Administration, 2011 (in Chinese)

廖振鹏,谢志南. 波动数值模拟的稳定性. 哈尔滨工程大学学报, 2011, 32(9): 1254-1261 (Liao Zhenpeng, Xie Zhinan. stability of numerical simulation of wave motion. Journal of Harbin Engineering University, 2011, 32(9): 1254-1261 (in Chinese)

关慧敏,廖振鹏. 局部人工边界稳定性的一种分析方法. 力学学报,1996, 28(3): 376-380 (Guan Huimin, Liao Zhenpeng. A method for the stability analysis of local artificial boundaries. Acta Mechanica Sinica,1996, 28(3): 376-380 (in Chinese)

景立平, 廖振鹏, 邹经湘. 多次透射公式的一种高频失稳机制. 地震工程与工程振动, 2002, 22(1): 7-13 (Jing Liping, Liao Zhenpeng, Zou Jingxiang. A high-frequency instability mechanism in numerical realization of multi-transmitting formula. Earthquake Engineering and Engineering Vibration, 2002, 22(1): 7-13 (in Chinese)

Gustafsson B, Kreiss HO, Sundström A. Stability theory of difference approximations for initial boundary value problems II. Mathematics of Computation, 1972, 26(119): 649-686

Trefethen LN. Group velocity interpretation of the stability theory of Gustafsson Kreiss and Sundstrom. Journal of Computational Physics, 1983, 49(2): 199-217

Godunov S, Ryabenkii V. Spectral stability criteria for boundary value problems for non-self-adjoint difference equations. Russian Mathematical Surveys, 1963, 18(3): 1-12

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