Outlet Dissipative Conditions for Air Flow in the Bronchial Tree

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.