Outlet Dissipative conditions for air flow in the bronchial tree

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 ; .

Corresponding authors: 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.