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Issue ESAIM: Proc.
Volume 14, 2005
CEMRACS 2004 - Mathematics and applications to biology and medicine
Page(s) 201 - 212
DOI http://dx.doi.org/10.1051/proc:2005015

ESAIM: Proc., September 2005, Vol. 14, pp. 201-212
DOI: 10.1051/proc:2005015

Outlet Dissipative conditions for air flow in the bronchial tree

B. Maury1, N. Meunier2, A. Soualah1 and L. Vial2

1  Laboratoire de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France; .
2  Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Boîte courrier 187, 75252 Paris Cedex 05, France ; .

Bertrand.Maury@math.u-psud.fr
Assia.Soualah@math.u-psud.fr
meunier@ann.jussieu.fr
vial@ann.jussieu.fr

Abstract
We propose inflow and outflow boundary conditions to handle the airflow through the upper part of bronchial tree-like domains. This approach is based on a condensation of the part of the domain which is geometrically complex by using the linearity of the flow through a net of ducts with small diameters with respect to the pressure jumps. We show that the boundary conditions we obtain lead to a well-posed problem, and we present some numerical tests where the results with those new conditions are compared with the results obtained by simulating the flow over the full (non-condensed) domain.


Mathematics Subject Classification. 92B05, 76Z05, 65M60

Key words: Lungs, Navier-Stokes equations, boundary conditions, Finite Element Method


© EDP Sciences, ESAIM 2005


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