A new finite volume scheme is used for the approximation of the Navier–Stokes equations on general grids, including non matching grids. It is based on a discrete approximation of the weak form and on the definition of discrete gradient and divergence operators on each control volume. A sketch of the convergence proof is given, and the results of a numerical implementation on a non matching grids are shown. A byproduct is a finite volume scheme that is convergent for diffusion problems on general grids.
Un nouveau schéma volumes finis permet l'approximation des équations de Navier–Stokes sur des grilles générales. Ce schéma est basé sur une approximation de la formulation faible, et sur la définition d'opérateurs de gradient et divergence discrets consistants. On donne les grandes lignes de la preuve de convergence, ainsi que des résultats numériques obtenus pour un maillage non conforme. Un résultat auxiliaire est l'obtention d'un schéma de volumes finis convergent pour des problèmes de diffusion sur des grilles générales.
Accepted:
Published online:
Robert Eymard 1; Raphaèle Herbin 2
@article{CRMATH_2007__344_10_659_0,
author = {Robert Eymard and Rapha\`ele Herbin},
title = {A new colocated finite volume scheme for the incompressible {Navier{\textendash}Stokes} equations on general non matching grids},
journal = {Comptes Rendus. Math\'ematique},
pages = {659--662},
publisher = {Elsevier},
volume = {344},
number = {10},
year = {2007},
doi = {10.1016/j.crma.2007.03.025},
language = {en},
}
TY - JOUR AU - Robert Eymard AU - Raphaèle Herbin TI - A new colocated finite volume scheme for the incompressible Navier–Stokes equations on general non matching grids JO - Comptes Rendus. Mathématique PY - 2007 SP - 659 EP - 662 VL - 344 IS - 10 PB - Elsevier DO - 10.1016/j.crma.2007.03.025 LA - en ID - CRMATH_2007__344_10_659_0 ER -
%0 Journal Article %A Robert Eymard %A Raphaèle Herbin %T A new colocated finite volume scheme for the incompressible Navier–Stokes equations on general non matching grids %J Comptes Rendus. Mathématique %D 2007 %P 659-662 %V 344 %N 10 %I Elsevier %R 10.1016/j.crma.2007.03.025 %G en %F CRMATH_2007__344_10_659_0
Robert Eymard; Raphaèle Herbin. A new colocated finite volume scheme for the incompressible Navier–Stokes equations on general non matching grids. Comptes Rendus. Mathématique, Volume 344 (2007) no. 10, pp. 659-662. doi : 10.1016/j.crma.2007.03.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.025/
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