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Boundary conditions and Schwarz waveform relaxation method for linear viscous Shallow Water equations in hydrodynamics

Eric Blayo 1 Antoine Rousseau 2, 3, 4 Manel Tayachi Pigeonnat 5, * 
* 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
4 LEMON - Littoral, Environment: MOdels and Numerics
CRISAM - Inria Sophia Antipolis - Méditerranée , IMAG - Institut Montpelliérain Alexander Grothendieck, HSM - Hydrosciences Montpellier
Abstract : We propose in the present work an extension of the Schwarz waveform relaxation method to the case of viscous shallow water system with advection term. We first show the difficulties that arise when approximating the Dirichlet to Neumann operators if we consider an asymptotic analysis based on large Reynolds number regime and a small domain aspect ratio. Therefore we focus on the design of a Schwarz algorithm with Robin like boundary conditions. We prove the well-posedness and the convergence of the algorithm.
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Submitted on : Monday, April 4, 2022 - 5:15:41 PM
Last modification on : Tuesday, May 17, 2022 - 2:32:04 PM

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Eric Blayo, Antoine Rousseau, Manel Tayachi Pigeonnat. Boundary conditions and Schwarz waveform relaxation method for linear viscous Shallow Water equations in hydrodynamics. SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2017, 3, pp.117-137. ⟨10.5802/smai-jcm.22⟩. ⟨hal-01467335⟩

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