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, *
* Auteur correspondant
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, UJF - Université Joseph Fourier - Grenoble 1, INPG - Institut National Polytechnique de Grenoble
4 LEMON - Littoral, Environnement : Méthodes et Outils Numériques
CRISAM - Inria Sophia Antipolis - Méditerranée
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.
Type de document :
Article dans une revue
SMAI Journal of Computational Mathematics, Société de Mathématiques Appliquées et Industrielles (SMAI), 2017, 3, pp.117-137. 〈http://smai-jcm.cedram.org/smai-jcm-bin/item?id=SMAI-JCM_2017__3__117_0〉. 〈10.5802/smai-jcm.22〉
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https://hal.inria.fr/hal-01467335
Contributeur : Antoine Rousseau <>
Soumis le : mardi 14 février 2017 - 12:39:28
Dernière modification le : mercredi 11 avril 2018 - 01:59:15

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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. 〈http://smai-jcm.cedram.org/smai-jcm-bin/item?id=SMAI-JCM_2017__3__117_0〉. 〈10.5802/smai-jcm.22〉. 〈hal-01467335〉

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