[Une nouvelle classe de techniques de pas fractionnaires basée sur les directions alternées pour les équations de Navier–Stokes incompressibles]
Nous proposons une nouvelle famille d'algorithmes à pas fractionnaires basés sur la technique des directions alternées pour la résolution des équations de Navier–Stokes. Chaque étape de l'algorithme consiste à résoudre une série de problèmes uni-dimensionels. On démontre que la méthode est unconditionellement stable et convergente.
A new direction-splitting-based fractional time stepping is introduced for solving the incompressible Navier–Stokes equations. The main originality of the method is that the pressure correction is computed by solving a sequence of one-dimensional elliptic problems in each spatial direction. The method is very simple to program in parallel, very fast, and has exactly the same stability and convergence properties as the Poisson-based pressure-correction technique, either in standard or rotational form.
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@article{CRMATH_2010__348_9-10_581_0,
author = {Jean-Luc Guermond and Peter D. Minev},
title = {A new class of fractional step techniques for the incompressible {Navier{\textendash}Stokes} equations using direction splitting},
journal = {Comptes Rendus. Math\'ematique},
pages = {581--585},
publisher = {Elsevier},
volume = {348},
number = {9-10},
year = {2010},
doi = {10.1016/j.crma.2010.03.009},
language = {en},
}
TY - JOUR AU - Jean-Luc Guermond AU - Peter D. Minev TI - A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting JO - Comptes Rendus. Mathématique PY - 2010 SP - 581 EP - 585 VL - 348 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2010.03.009 LA - en ID - CRMATH_2010__348_9-10_581_0 ER -
%0 Journal Article %A Jean-Luc Guermond %A Peter D. Minev %T A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting %J Comptes Rendus. Mathématique %D 2010 %P 581-585 %V 348 %N 9-10 %I Elsevier %R 10.1016/j.crma.2010.03.009 %G en %F CRMATH_2010__348_9-10_581_0
Jean-Luc Guermond; Peter D. Minev. A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 581-585. doi : 10.1016/j.crma.2010.03.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.009/
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