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Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries

Published online by Cambridge University Press:  03 June 2015

Zakaria Belhachmi  and
Andreas Karageorghis
Zakaria Belhachmi*
Affiliation:
Laboratoire de Mathématiques, Informatique et Applications, EA CNRS, Université de Haute Alsace, Rue des Frères Lumières, 68096 Mulhouse, France
Andreas Karageorghis*
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, P.O.Box 20537, 1678 Nicosia, Cyprus
*
Corresponding author. URL: http://www.math.uha.fr/belhachmi/ Email: zakaria.belhachmi@uha.fr
Email: andreask@ucy.ac.cy
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Abstract

In this paper, we study the numerical solution of the Stokes system in deformed axisymmetric geometries. In the azimuthal direction the discretization is carried out by using truncated Fourier series, thus reducing the dimension of the problem. The resulting two-dimensional problems are discretized using the spectral element method which is based on the variational formulation in primitive variables. The meridian domain is subdivided into elements, in each of which the solution is approximated by truncated polynomial series. The results of numerical experiments for several geometries are presented.

Keywords

65N3565N55Spectral element methodStokes equationsvariational formulationdeformed geometriesFourier expansion

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Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 4 , August 2011 , pp. 448 - 469
Copyright
Copyright © Global-Science Press 2011

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