Finite element simulation of fluid dynamics and CO 2 gas exchange in the alveolar sacs of the human lung

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Caucha L.J.
Frei S.
Rubio O.
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Springer Science and Business Media, LLC
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In this article, we present a numerical framework based on continuum models for the fluid dynamics and the CO2 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.
We gratefully acknowledge financial support by CONCYTEC Peru within the program Programa nacional de innovación para la competitividad y productividad (PNICP, 361-PNICP-PIBA-2014) as well as travel support by the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences (HGS MathComp). The second author was supported by the DFG Research Scholarship FR3935/1-1.
Palabras clave
Método arbitrario Lagrangiano-Euleriano (ALE), Dinámica de gases alveolares, Estabilización de presión anisotrópica, Condiciones de contorno artificiales, Estabilización de proyección local, Estabilización de penalti interior