Comptes Rendus
A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder
Comptes Rendus. Mécanique, Volume 333 (2005) no. 1, pp. 51-57.

This article deals with a numerical method for solving the unsteady, incompressible Navier–Stokes equations in domains with arbitrarily-shaped boundaries, where the boundary is represented using the Cartesian grid approach. We introduce a novel cut-cell discretization which preserves the spectral properties of convection and diffusion. Here, convection is discretized by a skew-symmetric operator and diffusion is approximated by a symmetric, positive-definite coefficient matrix. Such a symmetry-preserving discretization conserves the kinetic energy (if the dissipation is turned off) and is stable on any grid. The method is successfully tested for an incompressible, unsteady flow around a circular cylinder at Re=100.

Cet article décrit une méthode numérique de résolution des équations de Navier–Stokes incompressibles instationnaires dans des domaines de géométries arbitraires. Nous partons d'une grille cartésienne, modifiée près de la frontière par une nouvelle méthode de découpage de maille, compatible avec les propriétés spectrales des opérateurs de convection et de diffusion. Ainsi, les termes de convection sont discrétisés avec un opérateur discret anti-symétrique (skew-symmetric) et les termes de diffusion sont approchés par un opérateur discret symétrique défini positif. Une telle discrétisation préservant la symétrie permet de conserver l'énergie cinétique (quand la viscosité est negligée) et elle est stable sur n'importe quelle grille. La méthode a été testée avec succès dans le cas de écoulement incompressible instationnaire autour d'un cylindre de section circulaire pour une valeur du nombre de Reynolds Re=100.

Published online:
DOI: 10.1016/j.crme.2004.09.021
Keywords: Computational fluid mechanics, Cartesian grid method, Symmetry-preserving discretization
Mot clés : Mécanique des fluides numérique, Approximation de grille cartésienne, Discrétisation préservant la symétrie

Roel Verstappen 1; Marc Dröge 1

1 Research Institute of Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands
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Roel Verstappen; Marc Dröge. A symmetry-preserving Cartesian grid method for computing a viscous flow past a circular cylinder. Comptes Rendus. Mécanique, Volume 333 (2005) no. 1, pp. 51-57. doi : 10.1016/j.crme.2004.09.021. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.09.021/

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