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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
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA [2016-2019] - Université Grenoble Alpes [2016-2019], LJK - Laboratoire Jean Kuntzmann
2 LEMON - Littoral, Environment: MOdels and Numerics
CRISAM - Inria Sophia Antipolis - Méditerranée , IMAG - Institut Montpelliérain Alexander Grothendieck, HSM - Hydrosciences Montpellier
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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Submitted on : Tuesday, March 24, 2015 - 8:29:18 AM
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Eric Blayo, David Cherel, Antoine Rousseau. Towards optimized Schwarz methods for the Navier-Stokes equations. Journal of Scientific Computing, 2016, 66 (1), pp.275--295. ⟨10.1007/s10915-015-0020-9⟩. ⟨hal-00982087v3⟩



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