About Interface Conditions for Coupling Hydrostatic and Nonhydrostatic Navier-Stokes Flows

Eric Blayo 1 Antoine Rousseau 2, 3
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 : In this work we are interested in the search of interface conditions to couple hydrostatic and nonhydrostatic ocean models. To this aim, we consider simplified systems and use a time discretization to handle linear equations. We recall the links between the two models (with the particular role of the aspect ratio δ = H/L 1) and introduce an iterative method based on the Schwarz algorithm (widely used in domain decomposition methods). The convergence of this method depends strongly on the choice of interface conditions: this is why we look for exact absorbing conditions and their approximations in order to provide tractable and efficient coupling algorithms.
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Eric Blayo, Antoine Rousseau. About Interface Conditions for Coupling Hydrostatic and Nonhydrostatic Navier-Stokes Flows. Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences, 2016, 9 (5), pp.1565-1574. ⟨10.3934/dcdss.2016063⟩. ⟨hal-01185255⟩

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