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