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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 581-585 (mai 2010)
Doi : 10.1016/j.crma.2010.03.009
Received : 14 February 2010 ;  accepted : 12 Mars 2010
A new class of fractional step techniques for the incompressible Navier–Stokes equations using direction splitting
Une nouvelle classe de techniques de pas fractionnaires basée sur les directions alternées pour les équations de Navier–Stokes incompressibles

Jean-Luc Guermond a, 1 , Peter D. Minev b
a Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA 
b Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 


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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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.

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1  Permanent address: LIMSI (CNRS-UPR 3251), BP 133, 91403 Orsay, France.

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