Structure-preserving properties of Störmer-Verlet scheme for mathematical pendulum

doi:10.1007/s10483-017-2233-8

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (9): 1225-1232.doi: https://doi.org/10.1007/s10483-017-2233-8

Structure-preserving properties of Störmer-Verlet scheme for mathematical pendulum

Weipeng HU^1,2, Mingzhe SONG¹, Zichen DENG^1,2

1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China;
2. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, Liaoning Province, China

收稿日期:2016-10-17 修回日期:2016-12-28 出版日期:2017-09-01 发布日期:2017-09-01
通讯作者: Weipeng HU,E-mail:wphu@nwpu.edu.cn E-mail:wphu@nwpu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos.11672241,11372253,and 11432010),the Astronautics Supporting Technology Foundation of China (No.2015-HT-XGD),and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (Nos.GZ1312 and GZ1605)

Structure-preserving properties of Störmer-Verlet scheme for mathematical pendulum

Weipeng HU^1,2, Mingzhe SONG¹, Zichen DENG^1,2

1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China;
2. State Key Laboratory of Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian 116023, Liaoning Province, China

Received:2016-10-17 Revised:2016-12-28 Online:2017-09-01 Published:2017-09-01
Contact: Weipeng HU E-mail:wphu@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos.11672241,11372253,and 11432010),the Astronautics Supporting Technology Foundation of China (No.2015-HT-XGD),and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (Nos.GZ1312 and GZ1605)

摘要/Abstract

摘要：

The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symplectic method, the inherent conservation law in the frequency domain is hardly conserved. By considering a mathematical pendulum model, a Störmer-Verlet scheme is first constructed in a Hamiltonian framework. The conservation law of the Störmer-Verlet scheme is derived, including the total energy expressed in the time domain and periodicity in the frequency domain. To track the structure-preserving properties of the Störmer-Verlet scheme associated with the conservation law, the motion of the mathematical pendulum is simulated with different time step lengths. The numerical results illustrate that the Störmer-Verlet scheme can preserve the total energy of the model but cannot preserve periodicity at all. A phase correction is performed for the Störmer-Verlet scheme. The results imply that the phase correction can improve the conservative property of periodicity of the Störmer-Verlet scheme.

关键词: two-dimension mixing layer, unstability, suspended solid particles, numerical computation, phase correction, Hamiltonian system, structurepreserving, mathematical pendulum, symplectic, Störmer-Verlet scheme

Abstract:

Key words: two-dimension mixing layer, unstability, suspended solid particles, numerical computation, structurepreserving, mathematical pendulum, phase correction, Hamiltonian system, symplectic, Störmer-Verlet scheme

中图分类号:

37J15
37M15

Weipeng HU, Mingzhe SONG, Zichen DENG. Structure-preserving properties of Störmer-Verlet scheme for mathematical pendulum[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(9): 1225-1232.

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Structure-preserving properties of Störmer-Verlet scheme for mathematical pendulum

Structure-preserving properties of Störmer-Verlet scheme for mathematical pendulum

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