# American Institute of Mathematical Sciences

October  2016, 9(5): 1565-1574. doi: 10.3934/dcdss.2016063

## About interface conditions for coupling hydrostatic and nonhydrostatic Navier-Stokes flows

 1 Univ. Grenoble Alpes, LJK, BP 53, 38041 Grenoble cedex 9, France 2 Inria and Institut Montpelliérain Alexander Grothendieck, Team LEM0N, Bat 5 - CC05 017, 860 rue Saint-Priest, 34095 Montpellier Cedex 5, France

Received  June 2015 Revised  August 2015 Published  October 2016

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 $\delta=H/L\ll 1$) 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.
Citation: Eric Blayo, Antoine Rousseau. About interface conditions for coupling hydrostatic and nonhydrostatic Navier-Stokes flows. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1565-1574. doi: 10.3934/dcdss.2016063
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