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[1]邢浩洁,李鸿晶.波动切比雪夫谱元模拟的时间积分方法研究[J].南京工业大学学报(自然科学版),2017,39(02):70-76.[doi:10.3969/j.issn.1671-7627.2017.02.012]
 XING Haojie,LI Hongjing.Investigation of time integration method for Chebyshev spectral element simulation of wave motion[J].Journal of NANJING TECH UNIVERSITY(NATURAL SCIENCE EDITION),2017,39(02):70-76.[doi:10.3969/j.issn.1671-7627.2017.02.012]
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波动切比雪夫谱元模拟的时间积分方法研究()
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《南京工业大学学报(自然科学版)》[ISSN:1671-7627/CN:32-1670/N]

卷:
39
期数:
2017年02期
页码:
70-76
栏目:
出版日期:
2017-03-20

文章信息/Info

Title:
Investigation of time integration method for Chebyshev spectral element simulation of wave motion
文章编号:
1671-7627(2017)02-0070-07
作者:
邢浩洁李鸿晶
南京工业大学 土木工程学院,江苏 南京 211800
Author(s):
XING HaojieLI Hongjing
College of Civil Engineering,Nanjing Tech University,Nanjing 211800,China
关键词:
波动数值模拟 切比雪夫谱元法 时间积分方法 中心差分法
Keywords:
numerical simulation of wave motion Chebyshev spectral element method time integration method central difference method
分类号:
TU435
DOI:
10.3969/j.issn.1671-7627.2017.02.012
文献标志码:
A
摘要:
由于在波动切比雪夫谱元模拟中使用隐式时间积分方法存在计算效率较低、不易施加边界条件以及波动输入不便的问题,而中心差分法是能够平衡精度和计算效率的较优选择,并以一维波动模型探讨相应的波动输入方法和时域积分稳定条件。通过输入Ricker子波以及复合正弦波的数值算例证实了方法的有效性,并接着分析不同计算参数对模拟精度的影响。结果表明:空间上一个最短波长尺度内的谱元节点数、单元阶次分别取不低于5和4时能够达到比较理想的精度,而时间步长变化对精度的影响不大。
Abstract:
If an implicit time integration method was employed in Chebyshev spectral element simulation of wave motion,it would lead to lower computation efficiency and difficulties of implementing boundary conditions and applying incident waves.Then the advantages of central difference method,which may keep a good balance between accuracy and efficiency,were discussed,and the corresponding wave input method and stability criterion of time-domain integration were also investigated.The method was examined by one-dimensional numerical simulations with incident Ricker wavelet and composite sine waves,and then the influences of computation parameters on the accuracy were analyzed.Computation results indicated that when the number of spectral element nodes in one minimum spatial wavelength and the element order were not lower than 5 and 4,respectively,desired accuracy could be achieved,while the variation of time step had little influence on the accuracy.

参考文献/References:

[1] 廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.
[2] PRIOLO E,SERIANI G.A numerical investigation of Chebyshev spectral element method for acoustic wave propagation[C]//Proceedings of the 13th IMACS Conference on Comparative Applied Mathematics.Dublin:[s.n.],1991,2:551.
[3] SERIANI G,PRIOLO E.Spectral element method for acoustic wave simulation in heterogeneous media[J].Finite elements in analysis and design,1994,16(3):337.
[4] KOMATITSCH D,VILOTTE J P.The spectral element method:an efficient tool to simulate the seismic response of 2D and 3D geological structures[J].Bulletin of the seismological society of America,1998,88(2):368.
[5] 王秀明,SERIANI G,林伟军.利用谱元法计算弹性波场的若干理论问题[J].中国科学:G辑,2007,37(1):1.
[6] 林伟军.弹性波传播模拟的 Chebyshev 谱元法[J].声学学报,2007,32(6):525.
[7] 严珍珍,张怀,杨长春,等.汶川大地震地震波传播的谱元法数值模拟研究[J].中国科学:D辑,2009,39(4):393.
[8] CHE C X,WANG X M,LIN W J.The Chebyshev spectral element method using staggered predictor and corrector for elastic wave simulations[J].Applied geophysics,2010,7(2):1744.
[9] SERIANI G,SU C.Wave propagation modeling in highly heterogeneous media by a poly-grid Chebyshev spectral element method[J].Journal of computational acoustics,2012,20(2):1.
[10] 李孝波,薄景山,齐文浩,等.地震动模拟中的谱元法[J].地球物理学进展,2014(5):2029.
[11] NEWMARK N M.A Method of Computation for Structural Dynamics[J].Journal of the engineering mechanics division,1959,85(1):67.
[12] WILSON E L,FARHOOMAND I,BATHE K J.Nonlinear dynamic analysis of complex structures[J].Earthquake engineering & structural dynamics,1972,1(3):241.
[13] HOUBOLT J C.A recurrence matrix solution for the dynamic response of elastic aircraft[J].Journal of the aeronautical sciences,1950,17(9):540.
[14] DOKAINISH M A,SUBBARAJ K.A survey of direct time-integration methods in computational structural dynamics:I.explicit methods[J].Computers & structures,1989,32(6):1371.
[15] SUBBARAJ K,DOKAINISH M A.A survey of direct time-integration methods in computational structural dynamics:II.implicit methods[J].Computers & structures,1989,32(6):1387.
[16] COOK R D,MALKUS D S,PLESHA M E.Concepts and applications of finite element analysis:a treatment of the finite element method as used for the analysis of displacement,strain,and stress[M].3rd ed.New York:John Wiley&Sons Inc.,1989.
[17] 李小军.地震工程中动力方程求解的逐步积分方法[J].工程力学,1996,13(2):110.
[18] HUGHES T J R.The finite element method:linear static and dynamic finite element analysis[M].Upper Saddle River:Prentice-Hall Inc.,1987.
[19] SCHUBERTH B.The spectral element method for seismic wave propagation:theory,implementation and comparison to finite difference methods[D].München:Ludwig Maximilians Universität München,2003.
[20] 刘晶波,廖振鹏.离散网格中的弹性波动(Ⅲ):时域离散化对波传播规律的影响[J].地震工程与工程振动,1990,10(2):1.
[21] 朱昌允,秦国良,徐忠.谱元方法求解波动方程时显式与隐式差分方法的比较[J].西安交通大学学报,2008,42(9):1142.
[22] KRIEG R D.Unconditional stability in numerical time integration methods[J].Journal of applied mechanics,1973,40(2):417.
[23] 李小军,廖振鹏,杜修力.有阻尼体系动力问题的一种显式差分解法[J].地震工程与工程振动,1992,12(4):74.
[24] 杜修力,王进廷.阻尼弹性结构动力计算的显式差分法[J].工程力学,2000,17(5):37.
[25] 王进廷,杜修力.有阻尼体系动力分析的一种显式差分法[J].工程力学,2002,19(3):109.
[26] 周正华,李山有,侯兴民.阻尼振动方程的一种显式直接积分方法[J].世界地震工程,1999,15(1):41.
[27] 周正华,周扣华.有阻尼振动方程常用显式积分格式稳定性分析[J].地震工程与工程振动,2001,21(3):22.
[28] COHEN G C.Higher-order numerical methods for transient wave equations[M].Berlin:Springer-Verlag,2002.
[29] DE BASABE J D.High-order finite element methods for seismic wave propagation[D].Austin:University of Texas,2009.

备注/Memo

备注/Memo:
收稿日期:2015-09-10
基金项目:国家自然科学基金(51278245)
作者简介:邢浩洁(1989—),男,安徽庐江人,硕士,主要研究方向为岩土工程抗震领域的波动数值模拟方法; 李鸿晶(联系人),教授,E-mail:harbiner@163.com.
引用本文:邢浩洁,李鸿晶.波动切比雪夫谱元模拟的时间积分方法研究[J].南京工业大学学报(自然科学版),2017,39(2):70-76..
更新日期/Last Update: 2017-03-20