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

Published online by Cambridge University Press:  03 June 2015

Laura Lazar*
Affiliation:
Lab. J.A. Dieudonne, UMR 7351 CNRS UNS, University de Nice - Sophia Antipolis, 06108 Nice Cedex 02, France
Richard Pasquetti*
Affiliation:
Lab. J.A. Dieudonne, UMR 7351 CNRS UNS, University de Nice - Sophia Antipolis, 06108 Nice Cedex 02, France
Francesca Rapetti*
Affiliation:
Lab. J.A. Dieudonne, UMR 7351 CNRS UNS, University de Nice - Sophia Antipolis, 06108 Nice Cedex 02, France
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Abstract

Spectral 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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2013

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