无限维Hamilton系统稳态解的保结构算法

秦于越; 邓子辰; 胡伟鹏

doi:10.3879/j.issn.1000-0887.2014.01.003

无限维Hamilton系统稳态解的保结构算法

doi: 10.3879/j.issn.1000-0887.2014.01.003

¹西北工业大学工程力学系, 西安 710072;²大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116024

基金项目: 国家自然科学基金(11172239；11372252；11372253)；高校博士点基金(20106102110019；20126102110023)；大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802；GZ1312)

详细信息

作者简介:
秦于越(1980—)，女，重庆人，博士生(E-mail: 769482448@qq.com);

中图分类号: O175.24
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出版历程
- 收稿日期: 2013-10-15
- 修回日期: 2013-10-22
- 刊出日期: 2014-01-15

Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System

¹Department of Engineering Mechanics, Northwestern Polythechnical University, Xi’an 710072, P.R.China;²State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China(11172239；11372252；11372253)

摘要

摘要: 基于Hamilton变分原理和Bridges意义下的多辛积分理论，提出了保持无穷维Hamilton系统稳态解能流通量和动量通量的保结构分析方法．针对复杂的无穷维Hamilton系统的多辛对称形式，首先讨论了其稳态解所满足的对称形式的守恒律问题；随后，以一个典型的无穷维Hamilton系统——Zufiria方程为例，采用box离散格式，模拟了其稳态解，并验证了算法的保结构性能．研究结果显示：采用保结构算法能够较好地模拟无穷维Hamilton系统的稳态解，并保持了无穷维Hamilton系统稳态解的能流通量和动量通量两个重要力学参量．这一研究结果将为复杂无穷维Hamilton系统稳态解的数值分析提供新的途径.
- 无穷维Hamilton系统 /
- 保结构 /
- 稳态解 /
- 动量通量
Abstract: Based on Hamilton variational principle and Bridges’ multi-symplectic integration theory, a new structure-preserving algorithm was proposed to simulate the steady-state solution to the complex infinite dimensional Hamilton system. With Zufiria’s Boussinesq-type equations as an example, the high-order partial differential equation describing the steady-state solution to the Zufiria model was rewritten into a symmetric form under the energy flux conservation law and momentum flux conservation law firstly; then the box scheme for the symmetric form was constructed to simulate the steady-state solution to the Zufiria model. The numerical results show that the box scheme can well simulate the steady-state solution to the Zufiria model while properly preserving the momentum flux conservation law.
- infinite dimensional Hamilton system /
- structure-preserving /
- steady-state solution /
- momentum flux

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参考文献(10)

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