Hostname: page-component-84b7d79bbc-5lx2p Total loading time: 0 Render date: 2024-08-01T08:18:09.046Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-Dimensional Stokes Flow Solution Using Combined Boundary Element and Finite Element Methods

Published online by Cambridge University Press:  05 May 2011

D.L. Young ,
Y.H. Liu  and
T.I. Eldho
D.L. Young*
Affiliation:
Department of Civil Engineering & Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Y.H. Liu*
Affiliation:
Department of Civil Engineering & Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
T.I. Eldho*
Affiliation:
Department of Civil Engineering & Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Professor
**Graduate student
***Postdoc
Get access

Abstract

This paper describes a model using boundary element and finite element methods for the solution of three-dimensional incompressible viscous flows in slow motion, using velocity-vorticity variables. The method involves the solution of diffusion-advection type vorticity equations for vorticity whose solenoidal vorticity components are obtained by solving a Poisson equation involving the velocity and vorticity components. The Poisson equations are solved using boundary elements and the vorticity diffusion type equations are solved using finite elements and both are combined. Here the results of Stokes flow with very low Reynolds number, in a typical cavity flow are presented and compared with other model results. The combined BEM-FEM model has been found to be efficient and satisfactory.

Keywords

Velocity-vorticity methodStokes flowBoundary elementsFinite elements
Type
Articles
Information
Journal of Mechanics , Volume 15 , Issue 4 , December 1999 , pp. 169 - 176
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Anderson, D. A., Tannehill, J. C. and Fletcher, R. H., Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, New York (1984).Google Scholar
2.Gunzaburger, M. D., “Finite Element Theory and Application,” Proc. of ICASE/NASA Langly Workshop, Dwoyer, D. L., Hussaini, M. Y. and Voigt, R. G., editors, New York, Springer-Verlag (1987).Google Scholar
3.Power, H. and Wrobel, L. C, Boundary Integral Methods in Fluid Mechanics, Computational Mechanics Publications, Southampton (1995).Google Scholar
4.Taylor, C. and Hughes, T. G., Finite Element Programming of the Navier-Stokes Equations, Pineridge Press Limited, Swansea (1981).Google Scholar
5.Reddy, J. N., Finite Element Method, McGraw-Hill Inc., New York (1993).Google Scholar
6.Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., Boundary Element Techniques—Theory and Applications in Engineering, Springer-Verlag, Berlin (1984).CrossRefGoogle Scholar
7.Liggett, J. A., Fluid Mechanics, McGraw-Hill Inc., New York (1994).Google Scholar
8.Currie, I. G., Fundamental Mechanics of Fluids, McGraw-Hill Co., New York (1974).Google Scholar
9.Burggraf, O. R., “Analytical and Numerical Studies of the Structure of Steady Separated Flows,” J. Fluid Mech., 24 (1), pp. 113–151 (1966).Google Scholar
10.Young, D. L. and Lin, Q. H., “Application of Finite Element Method to 2-D Flows,” Proc. 3rd Nat. Conf Hydraulic Engg.Taipei, pp. 223–242 (1986).Google Scholar
11.Young, D. L. and Yang, S. K., “Simulation of Two-Dimensional Steady Stokes Flows by the Velocity-Vorticity Boundary Element Method,” Proc. 20th Nat. Mechanics ConferenceTaipei, pp. 422–429 (1996).Google Scholar