Finite element simulation of fluid dynamics and CO$_2$ gas exchange in the alveolar sacs of the human lung
This work provides a computational tool for studying gas exchange in lung alveoli, but it is incremental as it applies known methods to a specific physiological problem with simplified geometry.
The authors developed a finite element framework to simulate fluid dynamics and CO2 gas exchange in alveolar sacs, incorporating moving geometry via the ALE method and novel pressure stabilization techniques. Numerical results on a 2D geometry demonstrate the influence of different boundary conditions and stabilization methods.
In this article we present a numerical framework based on continuum models for the fluid dynamics and the CO$_2$ gas distribution in the alveolar sacs of the human lung during expiration and inspiration, including the gas exchange to the cardiovascular system. We include the expansion and contraction of the geometry by means of the Arbitrary Lagrangian Eulerian (ALE) method. For discretisation, we use equal-order finite elements in combination with pressure-stabilisation techniques based on local projections or interior penalties. We derive formulations for both techniques that are suitable on arbitrarily anisotropic meshes. These formulations are novel within the ALE method. Moreover, we investigate the effect of different boundary conditions, that vary between inspiration and expiration. We present numerical results on a simplified two-dimensional alveolar sac geometry and investigate the influence of the pressure stabilisations as well as the boundary conditions