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Two-Dimensional Incompressible Flows by Velocity-Vorticity Formulation and Finite Element Method

Published online by Cambridge University Press:  05 May 2011

Der-Chang Lo  and
Der-Liang Young
Der-Chang Lo*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Der-Liang Young*
Affiliation:
Hydrotech Research Institute, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
* Professor
* Professor
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Abstract

In this study, the motion of incompressible viscous fluid in a two-dimensional domain is solved by the finite element method using the velocity-vorticity formulation. To demonstrate the model feasibility, first of all the steady Stokes flow in a square cavity are computed. The results of square cavity flow are comparable with the numerical solutions of Burggraff (1966, FDM) [1]. Then the unsteady Navier-Stokes flow are computed and compared with other models [1∼4]. The results reveal that finite element analysis is a very powerful approach in the realm of computational fluid mechanics.

Keywords

Velocity-vorticity formulationFinite element methodNavier-Stokes equations
Type
Articles
Information
Journal of Mechanics , Volume 17 , Issue 1 , March 2001 , pp. 13 - 20
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2001

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References

REFERENCES

1Burggraff, O. R., “Analytic and Numerical Studies of Structure of Steady Separated Flows,” J. Comput. Phys., 24, pp. 131–151 (1966).Google Scholar
2Karageorghis, A. and Fairweather, G., “The Simple Layer Potential Method of Fundamental Solution for Certain Biharmonic Programs,” Int. J. Numer. Methods Fluids, 9, pp. 1221–1234 (1989).CrossRefGoogle Scholar
3Ghia, U., Ghia, K. and Shin, C., “High Re Solutions for Incompressible Flow Using the Navier-Stoke Equations and a Multigrid Method,” J. Comput Phys., 48, pp. 387–411 (1982).CrossRefGoogle Scholar
4Thomadakis, M. and Leschziner, M., “A Pressure-Correction Method for the Solution of Incompressible Viscous Flows on Unstructured Grids,” Int. J. Numer. Meth. Fluids, 22, pp. 581–601 (1996).3.0.CO;2-R>CrossRefGoogle Scholar
5Dennis, SCR, Ingham, D. B. and Cook, R. N., “Finite-Difference Methods for Calculating Steady Incompressible Flows in Three Dimensions,” J. Comput Phys., 33, pp. 325–339 (1979).CrossRefGoogle Scholar
6Gunzburger, M. D. and Peterson, J. S., “On Finite Element Approximations of the Stream Function-Vorticity and Velocity-Vorticity Equations,” Int. J. Numer. Methods Fluids., 8, pp. 1229–1240 (1988).CrossRefGoogle Scholar
7Skerget, L. and Rek, Z., “Boundary-Domain Integral Method Using a Velocity-Vorticity Formulation,” Engng. Anal Bound Elem., 15, pp. 1355–1383 (1995).CrossRefGoogle Scholar
8Batchelor, G. K., Fluid Dynamics, Cambridge University Press (1967).Google Scholar
9Liggett, J. A., Fluid Mechanics, McGraw-Hill, New York (1994).Google Scholar
10Hwu, T. Y., Young, D. L. and Chen, Y. Y., “Chaotic Advections for Stokes Flows in Circular Cavity,” J. Engineering Mech., 123, pp. 774–782 (1997).Google Scholar
11Moffatt, H. K., “Viscous and Resistive Eddies Near a Sharp Corner,” J. Fluid Mech., 18, pp. 1–18 (1964).CrossRefGoogle Scholar