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Issue ESAIM: Proc.
Volume 28, 2009
CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids
Page(s) 162 - 181
DOI http://dx.doi.org/10.1051/proc/2009045
Published online 23 November 2009

ESAIM: Proc., 2009, Vol. 28, pp. 162-181
DOI: 10.1051/proc/2009045

Numerical method for the 2D simulation of the respiration.

A. Devys1, 2, C. Grandmont3, B. Grec4, B. Maury5 and D.Yakoubi3

1  UST Lille, Lab. P. Painlevé, Cité Scientifique, F-59655 Villeneuve d'Ascq Cedex, France;
2  INRIA Lille Nord Europe, SIMPAF Project team, B.P. 70478, F-59658 Villeneuve d'Ascq Cedex, France;
3  INRIA Paris-Rocquencourt, REO Project team, BP 105, F-78153 Le Chesnay Cedex, France; &
4  Université Claude Bernard Lyon 1, Institut C. Jordan, F-69622 Villeurbanne Cedex, France;
5  Université Paris-Sud, Laboratoire de mathématiques, Bâtiment 425, bureau 130, F-91405 Orsay cedex, France;

anne.devys@math.univ-lille1.fr
celine.grandmont@inria.fr
driss.yakoubi@inria.fr
grec@math.univ-lyon1.fr
Bertrand.Maury@math.u-psud.fr

Published online: 23 November 2009

Abstract
In this article we are interested in the simulation of the air flow in the bronchial tree. The model we use has already been described in [2] and is based on a three part description of the respiratory tract. This model leads, after time discretization, to a Stokes system with non standard dissipative boundary conditions that cannot be easily and directly implemented in most FEM software, in particular in FreeFEM++ [11]. The objective is here to provide a new numerical method that could be implemented in any softwares. After describing the method, we illustrate it by two-dimensional simulations.


Résumé
Dans cet article nous nous intéressons à la simulation du flux d'air dans l'arbre bronchique. Le modèle que nous utilisons a déjà été décrit dans [2] et consiste en une description selon trois parties de l'arbre respiratoire. Ce modèle nous conduit, après discrétisation en temps, à un problème de Stokes avec des conditions au bord dissipatives non usuelles qui ne peuvent être implémentées facilement et directement dans la plupart des logiciels utilisant la méthode des éléments finis, en particulier FreeFEM++ [11]. L'objectif ici, est d'apporter une méthode de résolution implémentable dans tout logiciel EFM. Après une description de la méthode, nous l'illustrerons par des simulations 2D.



© EDP Sciences, ESAIM 2009


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