An iterative procedure to solve a coupled two-fluids turbulence model
Ecuaciones Diferenciales y Analisis Numerico, Universidad de
2 CEA, DAM, DIF, 91297 Arpajon, France.
3 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris Cedex, France.
Revised: 1 August 2009
This paper introduces a scheme for the numerical approximation of a model for two turbulent flows with coupling at an interface. We consider the variational formulation of the coupled model, where the turbulent kinetic energy equation is formulated by transposition. We prove the convergence of the approximation to this formulation for 3D flows for large turbulent viscosities and smooth enough flows, whenever bounded in W1,p Sobolev norms for p large enough. Under the same assumptions, we show that the limit is a solution of the initial problem. Finally, we give some numerical experiments to enlighten the theoretical work.
Mathematics Subject Classification: 63N30 / 76M10
Key words: Ocean-atmosphere coupling / turbulent flows / convergence analysis / iterative method / spectral method
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