Volume 3, Issue 4
Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries

Adv. Appl. Math. Mech., 3 (2011), pp. 448-469.

Published online: 2011-03

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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

Spectral element method Stokes equations variational formulation deformed geometries Fourier expansion

65N35 65N55

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@Article{AAMM-3-448, author = {Zakaria Belhachmi and Andreas Karageorghis}, title = {Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2011}, volume = {3}, number = {4}, pages = {448--469}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1050}, url = {http://global-sci.org/intro/article_detail/aamm/178.html} }
TY - JOUR T1 - Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries AU - Zakaria Belhachmi & Andreas Karageorghis JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 448 EP - 469 PY - 2011 DA - 2011/03 SN - 3 DO - http://dor.org/10.4208/aamm.10-m1050 UR - https://global-sci.org/intro/article_detail/aamm/178.html KW - Spectral element method KW - Stokes equations KW - variational formulation KW - deformed geometries KW - Fourier expansion AB -

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.

Zakaria Belhachmi & Andreas Karageorghis. (1970). Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries. Advances in Applied Mathematics and Mechanics. 3 (4). 448-469. doi:10.4208/aamm.10-m1050
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