Optimized Schwarz Waveform Relaxation for the Primitive Equations of the Ocean

In this article we are interested in the derivation of efficient domain decomposition methods for the viscous primitive equations of the ocean. We consider the rotating three-dimensional incompressible hydrostatic Navier–Stokes equations with free surface. Performing an asymptotic analysis of the system in the regime of small Rossby numbers, we compute an approximate Dirichlet to Neumann operator and build an optimized Schwarz waveform relaxation algorithm. We establish that the algorithm is well defined and provide numerical evidence of the convergence of the method.