Numerical solution of the time-dependent incompressible Navier-Stokes equations by piecewise linear finite elements
Pages 429 - 437
Abstract
In this paper we present a new method to solve the 2D generalized Stokes problem in terms of the stream function and the vorticity. Such problem results, for instance, from the discretization of the evolutionary Stokes system. The difficulty arising from the lack of the boundary conditions for the vorticity is overcome by means of a suitable technique for uncoupling both variables. In order to apply the above technique to the Navier-Stokes equations we linearize the advective term in the vorticity transport equation as described in the development of the paper. We illustrate the good performance of our approach by means of numerical results, obtained for benchmark driven cavity problem solved with classical piecewise linear finite element.
References
[1]
Brezzi, F. and Fortin, M., Mixed and Hybrid Finite Element Methods. 1991. Springer, Berlin.
[2]
Ghadi, F.A., Analyse mathématique et numérique des équations de Navier-Stokes en formuation fonction de courant-tourbillon, Thèse d'Etat, Faculté des Sciences. 2000. Université Ibn Zohr, Agadir, Morocco.
[3]
Ghadi, F.A., Ruas, V. and Wakrim, M., A mixed finite element to solve the Stokes problem in the stream function and vorticity formulation. Hiroshima Math. J. v28 i3. 381-398.
[4]
Ghadi, F.A., Ruas, V. and Wakrim, M., Simulation numérique par une méthode d'éléments finis optimale des équations de Navier-Stokes en formulation (¿-ω). Rev. Européenne ílém. Finis. v9 i5.
[5]
Ghadi, F.A., Ruas, V. and Wakrim, M., A mixed method to solve the evolutionary Stokes problem in the stream function and vorticity formulation. 2003. LUXFEM.
[6]
F.A. Ghadi, V. Ruas, M. Wakrim, Analysis of a mixed method to solve the Stokes problem discretized in time in term of the stream function and the vorticity, to appear.
[7]
Ghia, U., Ghia, K.N. and Shin, C.T., High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method. J. Comput. Physics. v48. 387-411.
[8]
V. Girault, P.A. Raviart, Finite Element Methods for the Navier-Stokes equations, Springer, Berlin, Heidelberg, New York, 1986.
[9]
Tezduyar, T.E., Liou, J., Ganjoo, D.K. and Behr, M., Solution techniques for the vorticity-streamfunction formulation of two-dimensional unsteady incompressible flows. Internat. J. Numer. Methods Fluids. v11. 515-539.
Index Terms
- Numerical solution of the time-dependent incompressible Navier-Stokes equations by piecewise linear finite elements
Recommendations
A conforming mixed finite element method for the Navier---Stokes/Darcy coupled problem
In this paper we develop the a priori analysis of a mixed finite element method for the coupling of fluid flow with porous media flow. Flows are governed by the Navier---Stokes and Darcy equations, respectively, and the corresponding transmission ...
Numerical Treatment of the Navier--Stokes Equations with Slip Boundary Condition
In this article we present efficient numerical methods for the Navier--Stokes equations with slip boundary conditions. A first method is based on a saddle-point formulation of the slip boundary condition. A congruent gradient (CG) method is applied to the ...
A new local stabilized nonconforming finite element method for solving stationary Navier-Stokes equations
In this paper we study a new local stabilized nonconforming finite element method based on two local Gauss integrals for solving the stationary Navier-Stokes equations. This nonconforming method utilizes the lowest equal-order pair of mixed finite ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Copyright © Elsevier B.V. © 2007.
Publisher
Elsevier Science Publishers B. V.
Netherlands
Publication History
Published: 20 May 2008
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 16 Dec 2024