OPTIMIZED SCHWARZ WAVEFORM RELAXATION FOR THE PRIMITIVE EQUATIONS OF THE OCEAN

OPTIMIZED SCHWARZ WAVEFORM RELAXATION FOR THE PRIMITIVE EQUATIONS OF THE OCEAN E. AUDUSSE?, P. DREYFUSS† , AND B. MERLET. ‡ Abstract. 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 Mechan- ics, Primitive Equations, Finite Volume Methods AMS subject classifications. 65M55, 76D05, 76M12. 1. Introduction. A precise knowledge of ocean parameters (velocity, tempera- ture...) is an essential tool to obtain climate and meteorological forecast. This task is nowadays of major importance and the need of global or regional simulations of the evolution of the ocean is strong. Moreover the large size of global simulations and the interaction between global and regional models require the introduction of efficient domain decomposition methods. The evolution of the ocean is commonly modelized by the use of the viscous primitive equations. In our context, the primitive equations may be regarded as a refinement of the viscous shallow water equations.

• optimized schwarz waveform


• transmission condition


• domain decomposition


• find efficient


• interaction between classical


• relaxation algorithm


• u0 ·


• schwarz waveform