A Unifomly Valid Asymptotic Solution of the Navier-Stokes Equations

Qin Sheng-li; Zhang Ai-shu

Volume 15 Issue 11

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1994 > 15(11): 999-1011

Qin Sheng-li, Zhang Ai-shu. A Unifomly Valid Asymptotic Solution of the Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1994, 15(11): 999-1011.

Citation:

Qin Sheng-li, Zhang Ai-shu. A Unifomly Valid Asymptotic Solution of the Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1994, 15(11): 999-1011.

Citation:

Qin Sheng-li, Zhang Ai-shu. A Unifomly Valid Asymptotic Solution of the Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1994, 15(11): 999-1011.

PDF( 639 KB)

A Unifomly Valid Asymptotic Solution of the Navier-Stokes Equations

Dep. of Physics, Qufu Teachers University, Qufu, Shandong

Received Date: 1993-11-24
Publish Date: 1994-11-15

Abstract

Abstract

In this paper,problems of the flow over a flat plate in the large Reyaolds number case are studied by using the method of multiple scales^[1,2].We have obtained N-order uniformly valid asymptotic solutions of the Navier-Stokes equations.
- Navier-Stokes equations,
- the potential flow,
- the stream function,
- the boundary correction,
- the method of multiple scales

FullText(HTML)

References(8)

References

[1]	Jiang Fu-ru,On the asymptotic solutions for a class of nonlinear reduced wave equations,Scientia Sinica,(Series A),7(1983),239-50.
[2]	江福汝,关于环形和圆形薄板在各种支承条件下的非对称弯曲问题,应用数学和力学.3(5) (1982),884-695.
[3]	Fung,Y,C,,A.First Course in Continuum Mechanics,Printice-Hall,Inc.,Englewood Cliffs,New Jersey(1977).
[4]	Carr ier,G.F. and Lin,C.C.,On the nature of the boundary layer near the leadingedge of a flat plate,Quart,Appl. Math.,VI,(1948).63-88.
[5]	秦圣立、张爱淑.关于具有初始挠度的圆形薄板的跳跃问题,应用数学和力学.8(5)(1987),447-458.
[6]	秦圣立、张爱淑,关于环形薄板的屈曲问题,应用数学和力学,6(8)(1985),169-183.
[7]	Hermann Schlichting,Boundarp-layer Theory,7th ed,,McGraw-Hill Book Compang,New York(1979).
[8]	田纪伟、高智.简化Navier-Stokes(SNS)方程在二维层流边界层分离点邻域的特性.中国科学,A辑,3(1992),282-292.

Relative Articles

[1]	WU Feng, SUN Yan, ZHONG Wan-xie. Inter-Belt Finite Element for the Analysis of Incompressible Material Problems[J]. Applied Mathematics and Mechanics, 2013, 34(1): 1-9. doi: 10.3879/j.issn.1000-0887.2013.01.001
[2]	LI Ai-bing, ZHANG Li-feng, ZANG Zeng-liang, ZHANG Yun. Iterative and Adjusting Method for Computing Stream Function and Velocity Potential in Limited Domains and Its Convergence Analysis[J]. Applied Mathematics and Mechanics, 2012, 33(6): 651-662. doi: 10.3879/j.issn.1000-0887.2012.06.002
[3]	LI Kai-tai, SHI Feng. Hodograph Method of Flow on Two-Dimensional Manifold[J]. Applied Mathematics and Mechanics, 2010, 31(3): 337-350. doi: 10.3879/j.issn.1000-0887.2010.03.009
[4]	JIAO Yu-jian, GUO Ben-yu. Mixed Spectral Method for Exterior Problem of Navier-Stokes Equations by Using Generalized Laguerre Functions[J]. Applied Mathematics and Mechanics, 2009, 30(5): 525-537. doi: 10.3879/j.issn.1000-0887.2009.05.003
[5]	LUO Yan, FENG Min-fu. Discontinuous Element Pressure Gradient Stabilizations for the Compressible Navier-Stokes Equations Based on Local Projections[J]. Applied Mathematics and Mechanics, 2008, 29(2): 157-168.
[6]	Muhammet Yürüsoy. Similarity Solutions of Boundary Layer Equations for a Special Non-Newtonian Fluid in a Special Coordinate System[J]. Applied Mathematics and Mechanics, 2004, 25(5): 535-541.
[7]	REN Chun-feng, MA Yi-chen. Residual a Posteriori Error Estimate Two-Grid Methods for the Steady Navier-Stokes Equation With Stream Function Form[J]. Applied Mathematics and Mechanics, 2004, 25(5): 497-510.
[8]	LUO Zhen-dong, ZHU Jiang. A Nonlinear Galerkin Mixed Element Method and a Posteriori Error Estimator for the Stationary Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2002, 23(10): 1061-1072.
[9]	LUO Zhen-dong, ZHU Jiang, WANG Hui-jun. A Nonlinear Galerkin/Petrov-Least Squares Mixed Element Method for the Stationary Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2002, 23(7): 697-706.
[10]	REN Chun-feng, MA Yi-chen. Two-Grid Error Estimates for the Stream Function Form of Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2002, 23(7): 689-696.
[11]	WANG Mao-nan, XU Zhen-yuan. On the Homoclinic Orbits in a Class of Two-Degree of Freedom Systems Under the Resonance Conditions[J]. Applied Mathematics and Mechanics, 2001, 22(3): 295-306.
[12]	Feng Weibing, Li Kaitai. The Existence and Uniqueness of Weak Solution of the Flow Between Two Concentric Rotating Spheres[J]. Applied Mathematics and Mechanics, 2000, (1): 61-66.
[13]	Sun Jian'an, Zhu Zhengyou. A Mixture Differential Quadrature Method for Solving Two-Dimensional Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1259-1266.
[14]	Shi Yuaning, Liu Guangxu. Singular Perturbations for a Class of Boundary Value Problems of Higher Order Nonlinear Differential Equations[J]. Applied Mathematics and Mechanics, 1996, 17(12): 1129-1136.
[15]	Xi Zhizhong. Three-Dimensional Analysis of the Flow in the Cyclones[J]. Applied Mathematics and Mechanics, 1995, 16(6): 519-525.
[16]	Shi Wei-hui. Stability of the Navier-Stokes Equation(Ⅰ)[J]. Applied Mathematics and Mechanics, 1994, 15(9): 821-822.
[17]	zhou Zhe-wei. The Application of Multi-Scale Perturbation Method to the Stability Analysis of Plane Couette Flow[J]. Applied Mathematics and Mechanics, 1994, 15(10): 873-877.
[18]	Zhu Gang, Gu Chuan-gan, Hu Qing-kang. A Modification of Taylor-Galerkin Finite Element Method and its Application[J]. Applied Mathematics and Mechanics, 1993, 14(12): 1115-1120.
[19]	Zhou Zhe-wei. The Linear Stability of PSane Poiseuille Flow under Unsteady Distortion[J]. Applied Mathematics and Mechanics, 1991, 12(6): 509-514.
[20]	Jiang Fu-ru. An Application of the Method of Multiple Scales to Magnetohydrodynamic Flow[J]. Applied Mathematics and Mechanics, 1982, 3(1): 25-32.