Comptes Rendus
Numerical Analysis
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]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 581-585.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.03.009

Jean-Luc Guermond 1 ; Peter D. Minev 2

1 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
2 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
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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/

[1] A.J. Chorin Numerical solution of the Navier–Stokes equations, Math. Comp., Volume 22 (1968), pp. 745-762

[2] J. Douglas Alternating direction methods for three space variables, Numer. Math., Volume 4 (1962), pp. 41-63

[3] J.-L. Guermond, P. Minev, A. Salgado, Convergence analysis of new class of direction splitting algorithm for the Navier–Stokes equations, 2010, in preparation

[4] J.-L. Guermond; P. Minev; J. Shen An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., Volume 195 (2006), pp. 6011-6054

[5] J.L. Guermond; Jie Shen On the error estimates for the rotational pressure-correction projection methods, Math. Comp., Volume 73 (2004) no. 248, pp. 1719-1737 (electronic)

[6] R. Rannacher On Chorin's Projection Method for the Incompressible Navier–Stokes Equations, Lecture Notes in Mathematics, vol. 1530, 1992

[7] J. Shen On error estimates of projection methods for the Navier–Stokes equations: second-order schemes, Math. Comp., Volume 65 (July 1996) no. 215, pp. 1039-1065

[8] R. Temam Sur l'approximation de la solution des équations de Navier–Stokes par la méthode des pas fractionnaires ii, Arch. Rat. Mech. Anal., Volume 33 (1969), pp. 377-385

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