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 3d 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 established that the algorithm is well defined and provide numerical evidences of the convergence of the method. Key words. Domain Decomposition, Schwarz Waveform Relaxation Algorithm, Fluid Mechanics, Primitive Equations, Finite Volume Methods AMS subject classifications. 65M55, 76D05, 76M12.

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Emmanuel Audusse, Pierre Dreyfuss, Benoit Merlet
• Keywords: Primitive Equations, Schwarz Waveform Relaxation, SIAMSC 2010, Waveform Relaxation Algorithm