Geodesic
Numerical method for the 2D simulation of the respiration.
A. Devys1, 2 ; C. Grandmont3 ; B. Grec4 ; B. Maury5 ; 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;
ESAIM. Proceedings, Tome 28 (2009), pp. 162-181.

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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.
DOI : 10.1051/proc/2009045

A. Devys 1, 2 ; C. Grandmont 3 ; B. Grec 4 ; B. Maury 5 ; D. Yakoubi 3

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; 
@article{EP_2009_28_a10,
     author = {A. Devys and C. Grandmont and B. Grec and B. Maury and D. Yakoubi},
     title = {Numerical method for the {2D} simulation of the respiration.},
     journal = {ESAIM. Proceedings},
     pages = {162--181},
     publisher = {mathdoc},
     volume = {28},
     year = {2009},
     doi = {10.1051/proc/2009045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009045/}
}
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A. Devys; C. Grandmont; B. Grec; B. Maury; D. Yakoubi. Numerical method for the 2D simulation of the respiration.. ESAIM. Proceedings, Tome 28 (2009), pp. 162-181. doi : 10.1051/proc/2009045. http://geodesic.mathdoc.fr/articles/10.1051/proc/2009045/

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