Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析

王金城; 齐进; 吴锤结

doi:10.21656/1000-0887.400277

Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析

doi: 10.21656/1000-0887.400277

¹大连理工大学航空航天学院, 辽宁大连116024;²北京应用物理与计算数学研究所, 北京 100088

基金项目: 国家自然科学基金(11601033;11372068)；国家重点基础研究发展计划（973 计划）(2014CB744104）

详细信息

作者简介:
王金城（1994—），男，硕士生(E-mail: jcwangdut@foxmail.com);齐进（1977—），女，副研究员(E-mail: qi_jin@iapcm.ac.cn);吴锤结（1955—），男，教授(通讯作者. E-mail: cjwudut@dlut.edu.cn).

中图分类号: O357.41
计量
- 文章访问数: 1085
- HTML全文浏览量: 140
- PDF下载量: 453
- 被引次数: 0
出版历程
- 收稿日期: 2019-09-06
- 修回日期: 2020-01-10
- 刊出日期: 2020-03-01

Modelling and Dynamics Analysis of Optimal Dynamical Systems of Fluctuation Velocity Equations for Incompressible Navier-Stokes Equations

¹School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China;²Institute of Applied Physics and Computational Mathematics, Beijing 100088, P.R.China

Funds: The National Natural Science Foundation of China(11601033; 11372068); The National Key Basic Research Program of China (973 Program)(2014CB744104)

摘要

摘要: 研究了基于Navier-Stokes方程的脉动速度方程的最优低维动力系统建模理论.最优目标泛函为脉动速度基函数的不可压缩性和正交性.数值计算了充分发展的并排双方柱绕流问题，并基于双尺度全局最优化方法，建立了它的脉动速度的最优动力系统模型.对其相空间轨道、Poincaré截面、分岔特性、功率谱和Lyapunov指数集等动力学特性进行了分析.随着Reynolds数的增加，双方柱绕流的脉动速度方程最优动力系统具有复杂的类倍周期分岔行为.
- 脉动速度方程 /
- 最优动力系统 /
- 分岔特性 /
- 双方柱绕流
Abstract: The modelling theory of the optimal low-dimensional dynamical system of the fluctuation velocity equations of the Navier-Stokes equations was studied. The optimal target functional is the incompressibility and orthogonality of the fluctuation velocity basis function. The fully developed side-by-side two-column flow problem was numerically simulated. Based on the two-scale global optimization method, the optimal dynamical system model for its fluctuation velocity was established. The dynamics properties of the phase portraits, the Poincaré section, the bifurcation characteristics, the power spectrum and the Lyapunov exponent set were analyzed. With the increase of the Reynolds number, the optimal dynamical systems of the fluctuation velocity equations of the flow around the two columns exhibit complex quasi-periodic bifurcation behaviors.
- fluctuation velocity equation /
- dynamical system /
- bifurcation /
- flow around two square columns

HTML全文

参考文献(11)

[1]	WU C J. Large optimal truncated low-dimensional dynamical systems[J]. Discrete & Continuous Dynamical Systems: A,1996,2(4): 559-583.
[2]	WU C J, SHI H S. An optimal theory for an expansion of flow quantities to capture the flow structures[J]. Fluid Dynamics Research,1995,17(2): 67-85.
[3]	吴锤结, 赵红亮. 不依赖数据库的最优动力系统建模理论及其应用[J]. 力学学报, 2001,33(3): 289-300.(WU Chuijie, ZHAO Hongliang. A new database-free method of constructing optimal low-dimensional dynamical systems and its application[J]. Chinese Journal of Theoretical and Applied Mechanics,2001,33(3): 289-300.(in Chinese))
[4]	WU C J, WANG L. A method of constructing a database-free optimal dynamical system and a global optimal dynamical system[J]. Science in China Series G: Physics, Mechanics & Astronomy,2008,51(7): 905-915.
[5]	PENG N F, GUAN H, WU C J. Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual[J]. Science China: Physics, Mechanics & Astronomy,2016,59(4): 644-701.
[6]	PENG N F, GUAN H, WU C J. Optimal dynamical systems of Navier-Stokes equations based on generalized helical-wave bases and the fundamental elements of turbulence[J]. Science China： Physics, Mechanics & Astronomy,2016,59(11): 114713. DOI: 10.1016/S1007-5704(96)90007-6.
[7]	王金城, 齐进, 吴锤结. 不可压缩Navier-Stokes方程最优动力系统建模和分析[J]. 应用数学和力学, 2020,41(1): 1-15.(WANG Jincheng, QI Jin, WU Chuijie. Analysis and modelling of optimal dynamical systems of incompressible Navier-Stokes equations[J]. Applied Mathematics and Mechanics,2020,41(1): 1-15. (in Chinese))
[8]	黄克智, 薛明德, 陆明万. 张量分析[M]. 北京: 清华大学出版社, 2003. (HUANG Kezhi, XUE Mingde, LU Mingwan. Tensor Analysis [M]. Beijing: Tsinghua University Press, 2003.(in Chinese))
[9]	叶庆凯, 王肇明. 优化与最优控制中的计算方法[M]. 北京: 科学出版社, 1986.(YE Qingkai, WANG Zhaoming. Computational Methods of Optimization and Optimum Control [M]. Beijing: Science Press, 1986.(in Chinese))
[10]	TORREY M D, MJOLSNESS R C, STEIN L R. NASA-VOF3D: a three-dimensional computer program for incompressible flows with free surfaces[R]. Nasa Sti/Recon Technical Report N, 1987.
[11]	SIROVICH L. Turbulence and the dynamics of coherent structures, part Ⅲ: dynamics and scaling[J]. Quarterly of Applied Mathematics,1987,45(3): 583-590.

施引文献

资源附件(0)

访问统计

点击查看大图

计量

文章访问数: 1085
HTML全文浏览量: 140
PDF下载量: 453
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析

doi: 10.21656/1000-0887.400277

作者简介:
王金城（1994—），男，硕士生(E-mail: jcwangdut@foxmail.com);齐进（1977—），女，副研究员(E-mail: qi_jin@iapcm.ac.cn);吴锤结（1955—），男，教授(通讯作者. E-mail: cjwudut@dlut.edu.cn).

计量

Modelling and Dynamics Analysis of Optimal Dynamical Systems of Fluctuation Velocity Equations for Incompressible Navier-Stokes Equations

计量

目录

留言板

Navier-Stokes方程的脉动速度方程的最优动力系统建模和动力学分析

doi: 10.21656/1000-0887.400277

作者简介: 王金城（1994—），男，硕士生(E-mail: jcwangdut@foxmail.com);齐进（1977—），女，副研究员(E-mail: qi_jin@iapcm.ac.cn);吴锤结（1955—），男，教授(通讯作者. E-mail: cjwudut@dlut.edu.cn).

计量

出版历程

Modelling and Dynamics Analysis of Optimal Dynamical Systems of Fluctuation Velocity Equations for Incompressible Navier-Stokes Equations

计量

出版历程

目录

作者简介:
王金城（1994—），男，硕士生(E-mail: jcwangdut@foxmail.com);齐进（1977—），女，副研究员(E-mail: qi_jin@iapcm.ac.cn);吴锤结（1955—），男，教授(通讯作者. E-mail: cjwudut@dlut.edu.cn).