Des conditions d'interface efficaces pour le couplage de modèles océaniques
Résumé
Model coupling is an important present problem in ocean or atmosphere modelling, where regional modelling systems are designed by coupling high resolution local models to lower resolution large scale models. In this study, we investigate the use of global-in-time Schwarz algorithms for such a coupling. The efficiency of these iterative methods is closely related to the transmission conditions between the subdomains interfaces. The absorbing boundary conditions and their approximations proved to be an extremely powerful tool to deduce good transmission conditions for domain decomposition methods and coupling. The limitation of the iteration count can be achieved by developing Schwarz optimized methods : they are based on the use of absorbing boundary conditions, with optimized transmission conditions, and on the minimization of the convergence rate of the algorithm over all frequencies propagated by the numerical scheme. Several systems of equations encountered in ocean models are addressed in this study : (1) the 2-D shallow-water model, either under hyperbolic and incompletely parabolic form (i.e. systems without or with viscosity), (2) the scalar 2-D and 3-D advection-diffusion equations, which describe the evolution of tracers like temperature or salinity. Two different parameterizations of diffusion, laplacian and bi-laplacian, are considered. Efficient interface conditions for those systems are derived, and implemented in numerical experiments, in idealized or realistic testcases.
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