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.
Mots clés : 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {693--713},
publisher = {EDP-Sciences},
volume = {44},
number = {4},
year = {2010},
doi = {10.1051/m2an/2010015},
mrnumber = {2683579},
zbl = {1234.76037},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2010015/}
}
TY - JOUR AU - Chacón Rebollo, Tomas AU - Del Pino, Stéphane AU - Yakoubi, Driss TI - An iterative procedure to solve a coupled two-fluids turbulence model JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 693 EP - 713 VL - 44 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2010015/ DO - 10.1051/m2an/2010015 LA - en ID - M2AN_2010__44_4_693_0 ER -
%0 Journal Article %A Chacón Rebollo, Tomas %A Del Pino, Stéphane %A Yakoubi, Driss %T An iterative procedure to solve a coupled two-fluids turbulence model %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 693-713 %V 44 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2010015/ %R 10.1051/m2an/2010015 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 4, pp. 693-713. doi : 10.1051/m2an/2010015. http://www.numdam.org/articles/10.1051/m2an/2010015/
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