二维流体力学变分通用公式

何吉欢

二维流体力学变分通用公式

何吉欢

上海大学上海市应用数学和力学研究所, 上海200072

基金项目: 国家重点基础研究发展规划项目(973项目)资助项目(1998020318)

详细信息

作者简介:
何吉欢(1965- ),男,浙江诸暨人,上海大学博士,乌克兰科学院名誉教授,已发表论文100多篇,1998年获得英国Literati奖,现在担任International Journal of Nonlinear Scienceand Numerical Simulation杂志主编,同时担任International Journal of Turbo&Jet-Engines等5种国际杂志的编委.

中图分类号: O351
计量
- 文章访问数: 2528
- HTML全文浏览量: 87
- PDF下载量: 1640
- 被引次数: 0
出版历程
- 收稿日期: 2000-06-22
- 修回日期: 2001-04-08
- 刊出日期: 2001-09-15

A Universal Variational Formulation for Two Dimensional Fluid Mechanics

HE Ji-huan

Shanghai Insititute of Mathematics and Mechanics, Shanghai University, Shanghai 200072, P R China

摘要

摘要: 推导得到了二维流体力学变分通用公式,该公式适用于任何二维守恒型流体力学方程,得到的泛函受约于所谓的参数约束方程(控制方程中各参数间的相互关系式)。消除参数约束,我们可以十分方便地从通用公式导得广义变分原理。几个实例证明这种方法是有效的、简单的,并具有普遍的意义。
- 流体力学 /
- 变分原理
Abstract: A universal variational formulation for two dimensional fluid mechanics is obtained,which is subject to the so-called parameter-constrained equations(the relationship between paramters in two governing equations).By eliminating the constraints,the generalied variational principle(GVPs)can be readily derived from the formulation.The formulation can be applied to any conditions in case the governing equations can be converted into conservative forms.Some illustrative examples are given to testify the effectiveness and simplicity of the method.
- fluid mechanics /
- variational theory

HTML全文

参考文献(25)

[1]	钱伟长. 广义变分原理[M]. 北京:知识出版社,1985.
[2]	Lin C C. Hydrodynamics of liquid helium, Ⅱ: Liquid helium[A]. In: G Careri Ed. Proceedings of International School of Pysics[C]. course XXI, New York: Academic Press,1963,93-146.
[3]	钱伟长. 高阶拉氏乘子法和弹性理论中更一般的广义变分原理[J]. 应用数学和力学,1983,4(2):137-150.
[4]	钱伟长. 粘性流体力学的变分原理和广义变原理[J]. 应用数学和力学,1984,5(3):305-323.
[5]	刘高联. 流体力学变分原理的建立与变换的系统途径[J]. 工程热物理学报,1990,11(2):136-142.
[6]	刘高联. 流体力学变分原理及有限元法研究的进展[J]. 上海力学,1989, 10(3):73-80.
[7]	Herivel J W. The derivation of the equations of motion of an ideal fluid by Hamilton's principle[J]. Proc Cambridge Philos Soc,1955,51:344-349.
[8]	何吉欢. 简论林家翘约束[A]. 见庄逢甘主编. 现代力学与科技进步[C]. 北京:清华大学出版社,1997,603-604.
[9]	何吉欢. 流体力学变分原理建立的新途径及林家翘约束[D]. 博士学位论文. 上海:上海大学,1997.
[10]	何吉欢. 流体力学广义变分原理[M]. 上海: 上海大学出版社,2000.
[11]	Bretherton F P. A note on Hamilton's principle for perfect fluids[J]. J Fluid Mech,1970,44(1):19-31.
[12]	Salmon R. Hamiltoinian fluid mechanics[J]. Ann Rev Fluid Mech,1988,20:225-256.
[13]	HE Ji-huan. Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbomachinery aerodynamics[J]. Int J Turbo & Jet-Engines,1997,14(1):23-28.
[14]	HE Ji-huan. A family of variational principles for compressible rotational blade-to-blade flow using semi-inverse method[J]. Int J Turbo & Jet-Engines,1998,15(2):95-100.
[15]	HE Ji-huan. Hybrid problems of determining unknown shape of bladings in compressible S2-flow in mixed-flow turbomachinery via variational technique[J]. Aircraft Engineering and Aerospace Technology,1999,71(2):154-159.
[16]	HE Ji-huan. Inverse problems of determining the unknown shape of oscillating airfoils in compressible 2D unsteady flow via variational technique[J]. Aircraft Engineering and Aerospce Technology,2000,72(1):18-24.
[17]	HE Ji-huan. Generalized Hellinger-Reissner principle[J]. ASME Journal of Applied Mechanics,2000,67(2):326-331.
[18]	HE Ji-huan. A variational principle for thermopiezoelectricity based on Chandrasekha-raiah's generalized linear theory[J]. J University of Shanghai for Science and Technology,1999,21(4):356-365.
[19]	HE Ji-huan. Coupled variational principles of piezoelectricity[J]. Int J Engineering Science,2000,39(3):323-341.
[20]	HE Ji-huan. A variational model for micropolar fluids in lubrication journal bearing[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2000,1(2):139-141.
[21]	HE Ji-huan. Classical variational model for the micropolar elastodynamics[J]. International Journal of Nonlinear Sciences and Numerical Simulation,2000,1(2):133-138.
[22]	何吉欢. 论弹性力学广义变分原理的临界变分现象[J]. 上海理工大学学报,1999,21(2):127-130.
[23]	何吉欢. 流体力学中的临界变分现象及其消除方法[J]. 上海理工大学学报,1999,21(1):29-35.
[24]	何吉欢. 弹性理论中的临界变分及消除方法[J]. 上海力学,1997,18(4):305-310.
[25]	LIU Gao-lian. A term-condensing method and generalized potential, stream & path functions for 3-D compressible viscous flow[A]. In: Proceeding Second Asian Congress of Fluid Mechanics[C]. Beijing: Science Press,1983,698-704.