Towards optimized Schwarz methods for the Navier-Stokes equations

Eric Blayo 1, * David Cherel 1 Antoine Rousseau 2, 3
* Corresponding author
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
2 LEMON - Littoral, Environnement : Méthodes et Outils Numériques
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This paper presents a study of optimized Schwarz domain decomposition methods for Navier-Stokes equations. Once discretized in time, optimal transparent boundary conditions are derived for the resulting Stokes equations, and a series of local approximations for these nonlocal conditions are proposed. Their convergence properties are studied, and numerical simulations are conducted on the test case of the driven cavity. It is shown that conditions involving one or two degrees of freedom can improve the convergence properties of the original algorithm.
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Eric Blayo, David Cherel, Antoine Rousseau. Towards optimized Schwarz methods for the Navier-Stokes equations. Journal of Scientific Computing, Springer Verlag, 2016, 66 (1), pp.275--295. ⟨10.1007/s10915-015-0020-9⟩. ⟨hal-00982087v3⟩

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