Commun. Comput. Phys., 13 (2013), pp. 1309-1329.


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

Laura Lazar 1, Richard Pasquetti 1*, Francesca Rapetti 1

1 Lab. J.A. Dieudonne, UMR 7351 CNRS UNS, Universite de Nice - Sophia Antipolis, 06108 Nice Cedex 02, France.

Received 18 January 2012; Accepted (in revised version) 11 June 2012
Available online 8 October 2012
doi:10.4208/cicp.180112.110612a

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 a TSEM 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.

AMS subject classifications: 65M60, 65M70, 76D05

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Key words: Spectral elements, simplicial meshes, Fekete-Gauss approximation, Navier-Stokes equations, projection methods, domain decomposition.

*Corresponding author.
Email: laura.lazar@unice.fr (L. Lazar), richard.pasquetti@unice.fr (R. Pasquetti), francesca.rapetti@unice.fr (F. Rapetti)
 

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