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
2 LEMON - Littoral, Environment: MOdels and Numerics
3 IMAG - Institut Montpelliérain Alexander Grothendieck

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.

Mots clés: Navier-Stokes equations; optimized boundary con-ditions; coupling methods; Schwarz alternating method; hydrostatic approximation

Domaines: Modélisation et simulation

Eric Blayo, Antoine Rousseau. About Interface Conditions for Coupling Hydrostatic and Nonhydrostatic Navier-Stokes Flows. Discrete and Continuous Dynamical Systems - Series S, 2016, 9 (5), pp.1565-1574. ⟨10.3934/dcdss.2016063⟩. ⟨hal-01185255⟩