[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.
Accepté le :
Publié le :
Jean-Luc Guermond 1 ; Peter D. Minev 2
@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/
[1] Numerical solution of the Navier–Stokes equations, Math. Comp., Volume 22 (1968), pp. 745-762
[2] 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] An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., Volume 195 (2006), pp. 6011-6054
[5] On the error estimates for the rotational pressure-correction projection methods, Math. Comp., Volume 73 (2004) no. 248, pp. 1719-1737 (electronic)
[6] On Chorin's Projection Method for the Incompressible Navier–Stokes Equations, Lecture Notes in Mathematics, vol. 1530, 1992
[7] 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] 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
Cité par Sources :
Commentaires - Politique