Spectral Element Discretization of the Circular Driven Cavity. Part III: The Stokes Equations in Primitive Variables

2003 ◽  
Vol 5 (1) ◽  
pp. 24-69 ◽  
Author(s):  
A. Karageorghis ◽  
Z. Belhachmi ◽  
C. Bernardi
Keyword(s):  
Stokes Equations ◽  
Spectral Element ◽  
Element Discretization ◽  
Driven Cavity ◽  
Primitive Variables

Fekete-Gauss Spectral Elements for Incompressible Navier-Stokes Flows: The Two-Dimensional Case

2013 ◽  
Vol 13 (5) ◽  
pp. 1309-1329 ◽  
Author(s):  
Laura Lazar ◽  
Richard Pasquetti ◽  
Francesca Rapetti
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Schur Complement ◽  
Spectral Element ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Flow Past A Cylinder ◽  
Accuracy Study

AbstractSpectral element methods on simplicial meshes, say TSEM, show both the advantages of spectral and finite element methods, i.e., spectral accuracy and geometrical flexibility. We present aTSEM solver of the two-dimensional (2D) incompressible Navier-Stokes equations, with possible extension to the 3D case. It uses a projection method in time and piecewise polynomial basis functions of arbitrary degree in space. The so-called Fekete-Gauss TSEM is employed,i.e., Fekete (resp. Gauss) points of the triangle are used as interpolation (resp. quadrature) points. For the sake of consistency, isoparametric elements are used to approximate curved geometries. The resolution algorithm is based on an efficient Schur complement method, so that one only solves for the element boundary nodes. Moreover, the algebraic system is never assembled, therefore the number of degrees of freedom is not limiting. An accuracy study is carried out and results are provided for classical benchmarks: the driven cavity flow, the flow between eccentric cylinders and the flow past a cylinder.

Spectral Element Discretization of the Stokes Equations in Deformed Axisymmetric Geometries

2011 ◽  
Vol 3 (4) ◽  
pp. 448-469 ◽  
Author(s):  
Zakaria Belhachmi ◽  
Andreas Karageorghis
Keyword(s):  
Variational Formulation ◽  
Numerical Experiments ◽  
Spectral Element Method ◽  
Stokes System ◽  
Stokes Equations ◽  
Spectral Element ◽  
Azimuthal Direction ◽  
Element Discretization ◽  
Polynomial Series ◽  
Truncated Fourier Series

AbstractIn 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.

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