[1] Wan Shui, Mogens Peter Nielsen,. Solving Navier-Stokes equation by mixed interpolation method [J]. Journal of Southeast University (English Edition), 2006, 22 (1): 93-95. [doi:10.3969/j.issn.1003-7985.2006.01.020]

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Solving Navier-Stokes equation by mixed interpolation method()

混合插值法求解Navier-Stokes方程

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

22

Issue:

2006 1

Page:

93-95

Research Field:

Civil Engineering

Publishing date:

2006-03-20

Info

Title:

Solving Navier-Stokes equation by mixed interpolation method

混合插值法求解Navier-Stokes方程

Author(s):

Wan Shui¹;  Mogens Peter Nielsen²

¹ College of Transportation, Southeast University, Nanjing 210096, China
² Department of Civil Engineering, Technical University of Denmark, Lyngby, Denmark

万水¹;  Mogens Peter Nielsen²

¹东南大学交通学院, 南京 210096; ²丹麦技术大学土木工程系, 丹麦林比

Keywords:

Navier-Stokes equation;  finite element method;  incompressible viscous flow;  mixed interpolation method

Navier-Stokes 方程;  有限元法;  粘性不可压流;  混合插值法

PACS:

TU311.3

DOI:

10.3969/j.issn.1003-7985.2006.01.020

Abstract:

The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes:a diffusion process and a convection process; and the finite element equation is established.The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes.The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator(FEPG)successfully.The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carried out.The solution agrees with the experimental results very well.

利用算子分裂法将粘性不可压流体Navier-Stokes方程表述的物理过程分解为扩散和对流2个过程, 建立起它们的有限元方程.采用9节点四边形等参元中的形函数描述单元中流体的速度场, 而利用这种单元的4个顶点节点构成的插值函数描述单元中流体的压力场, 通过有限元生成系统(FEPG)进行Navier-Stokes方程的单元子程序的生成, 得到求解不可压粘性流体Navier-Stokes方程的有限元程序, 并用它对粘性不可压流体的挠圆柱流动问题进行了数值模拟, 分析结果与试验结果吻合.

References:

[1] Zienkiewicz O C, Taylor R L.The finite element method, vol.3[M]. 5th ed.Butterworth Heinemann, 2000.
[2] Smith I M, Girffiths D V.Programming the finite element method[M].3rd ed.John Wiley & Sons, Inc.1998.
[3] Taylor C, Hughes T G.Finite element programming of the Navier-Stokes equation [M].Swansea:Pineridge Press Ltd, 1981.
[4] FEPG 5.0 user’s guide [R].FEPGENSOFT Co.Ltd., 2004.(in Chinese)
[5] FEPG 5.0 theory menu [R].FEPGENSOFT Co.Ltd., 2004.(in Chinese)
[6] Zhao Xiaobao.Fluid mechanics with engineering applications [M].Nanjing:Southeast University Press, 2004.(in Chinese)

Memo

Memo:

Biography: Wan Shui(1960—), male, doctor, professor, wanshui60421@yahoo.com.

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