An iterative procedure to solve a coupled two-fluids turbulence model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 4, p. 693-713

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.

DOI : https://doi.org/10.1051/m2an/2010015
Classification:  63N30,  76M10
Keywords: ocean-atmosphere coupling, turbulent flows, convergence analysis, iterative method, spectral method
@article{M2AN_2010__44_4_693_0,
     author = {Chac\'on Rebollo, Tomas and Del Pino, St\'ephane and Yakoubi, Driss},
     title = {An iterative procedure to solve a coupled two-fluids turbulence model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {4},
     year = {2010},
     pages = {693-713},
     doi = {10.1051/m2an/2010015},
     zbl = {1234.76037},
     mrnumber = {2683579},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2010__44_4_693_0}
}
Chacón Rebollo, Tomas; Del Pino, Stéphane; Yakoubi, Driss. An iterative procedure to solve a coupled two-fluids turbulence model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 4, pp. 693-713. doi : 10.1051/m2an/2010015. http://www.numdam.org/item/M2AN_2010__44_4_693_0/

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