含压力基Navier-Stokes方程最优动力系统建模和分析

王金城; 齐进; 吴锤结

doi:10.21656/1000-0887.400276

含压力基Navier-Stokes方程最优动力系统建模和分析

doi: 10.21656/1000-0887.400276

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
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出版历程
- 收稿日期: 2019-09-06
- 修回日期: 2020-03-04
- 刊出日期: 2020-08-01

Modelling and Analysis of Optimal Dynamical Systems of Incompressible Navier-Stokes Equations With Pressure Base Functions

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

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

摘要

摘要: 研究了采用压力基函数和速度基函数的Navier-Stokes方程的最优截断低维动力系统建模理论.在黏性不可压缩流体中模拟了并排三方柱绕流流场，对此流场进行了含压力基函数和速度基函数的Navier-Stokes方程的最优动力系统建模，并以此为工具分析了三方柱绕流最优动力系统的动力学特性.得到了如下结论：三方柱绕流的最优动力系统的动力学行为为混沌，它与双方柱绕流场的极限环动力学特性有着本质的区别，因此可以通过多柱绕流增进尾流的复杂性，从而促进流体混合.
- 压力基函数 /
- 最优动力系统 /
- 多方柱绕流 /
- 混沌
Abstract: The modelling theory for optimal truncated low-dimensional dynamical systems of Navier-Stokes equations with pressure base functions and velocity base functions was studied. In the viscous incompressible fluid, the flow field around 3 square columns was simulated. According to that flow problem, the optimal dynamical systems of the Navier-Stokes equations with pressure base functions and velocity base functions were modelled and studied. The results show that, the dynamics behavior of the optimal dynamical systems around the 3 square columns is chaos, which is essentially different from the limit cycle dynamics behavior of the flow field around 2 square columns, so the complexity of the wake increases in the multi-column flow, which thereby means promotion of fluid mixing.
- pressure base function /
- optimal dynamical system /
- flow around multiple square columns /
- chaos

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参考文献(13)

[1]	WU C J. Optimal truncated low-dimensional dynamical systems[J]. Discrete and Continuous Dynamical Systems,1996,〖STHZ〗 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]. Acta Mechanica Sinica,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.
[7]	王金城, 齐进, 吴锤结. 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[J]. 应用数学和力学, 2020,41(3): 235-249.(WANG Jincheng, QI Jin, WU Chuijie. Dynamics analysis and modelling of optimal dynamical systems of the fluctuation velocity equations of incompressible Navier-Stokes equations[J]. Applied Mathematics and Mechanics,2020,41(3): 235-249.(in Chinese))
[8]	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))
[9]	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))
[10]	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))
[11]	章本照. 流体力学中的有限元方法[M]. 北京: 机械工业出版社, 1986.(ZHANG Benzhao. Finite Element Method in Fluid Mechanics [M]. Beijing: China Machine Press, 1986.(in Chinese))
[12]	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.
[13]	SIROVICH L. Turbulence and the dynamics of coherent structures, part Ⅲ: dynamics and scaling[J]. Quarterly of Applied Mathematics,1987,45(3): 583-590.

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含压力基Navier-Stokes方程最优动力系统建模和分析

doi: 10.21656/1000-0887.400276

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).

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Modelling and Analysis of Optimal Dynamical Systems of Incompressible Navier-Stokes Equations With Pressure Base Functions

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留言板

含压力基Navier-Stokes方程最优动力系统建模和分析

doi: 10.21656/1000-0887.400276

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).

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出版历程

Modelling and Analysis of Optimal Dynamical Systems of Incompressible Navier-Stokes Equations With Pressure Base Functions

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).