Finite Element Solution of a Stream Function-Vorticity System and Its Application to the Navier Stokes Equations

DOI: 10.4236/am.2013.41A039   PDF   HTML     4,657 Downloads   7,485 Views   Citations

Abstract

The finite element solution of a generalized Stokes system in terms of the flow variables stream function and vorticity is studied. This system results from a time discretization of the time-dependent Stokes system in stream function-vorticity formulation, or yet by the application of the characteristics method to solve the Navier-Stokes equations in the same representation. Numerical results presented for both cases illustrate the good behaviour of the adopted approach.

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F. Ghadi, V. Ruas and M. Wakrim, "Finite Element Solution of a Stream Function-Vorticity System and Its Application to the Navier Stokes Equations," Applied Mathematics, Vol. 4 No. 1A, 2013, pp. 257-262. doi: 10.4236/am.2013.41A039.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] F. A. Ghadi, V. Ruas and M. Wakrim, “A Mixed Finite Element to Solve the Stokes Problem in the Stream Function and Vorticity Formulation,” Hiroshima Mathematical Journal, Vol. 28, No. 3, 1998, pp. 381-398.
[2] R. Glowinski and O. Pironneau, “Numerical Methods for the First Bi-Harmonic Equation and for the Two-Dimensional Stokes Problem,” SIAM Review, Vol. 21, No. 2, 1979, pp. 167-212. doi:10.1137/1021028
[3] F. A. Ghadi, V. Ruas and M. Wakrim, “A Mixed Method to Solve the Evolutionary Stokes Problem in the Stream Function and Vorticity Formulation,” Proceedings of LUXFEM, Luxemburg, 13-14 November 2003.
[4] F. A. Ghadi, V. Ruas and M. Wakrim, “Numerical Solution to the Time—Dependent Incompressible Navier-Stokes Equations by Piecewise Linear Finite Elements,” Journal of Computational and Applied Mathematics, Vol. 215, No. 2, 2008, pp. 429-437. doi:10.1016/j.cam.2006.03.047

  
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