Particle methods for 3D biological flows with variable density and viscosity

Robin Chatelin (1) , Philippe Poncet (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

This work is investigating a mechanical dysfunction of human lungs: Mucociliary clearance. The goal is to understand how diseases like cystic fibrosis impact mucus motion (by altering mucus viscosity, cilia vibrations, respiration cycle...) and to identify stagnation situations where pathogens proliferate. Strategies for computation of mucus flow around an epithelium ciliated cell are presented. Governing equations are proposed to take into account this complex geometry in motion in the surrounding highly viscous fluid. The characteristic Reynolds number of the flow is very small and mucus is modelled by Stokes problem with both variable viscosity and density. Epithelium displacement is taken into account using a penal-ization method. As density and viscosity follow a convection equation, these assumptions lead to an elliptic/hyperbolic coupling and non-linear equations. Numerical implementations are discussed to get a fast, robust and accurate algorithm in three dimension based on fast elliptic solvers and Lagrangian methods.

Mots clés: Variable density flows; Variable viscosity flows; Biological flows; Lung pathologies; Particle methods; Three-dimensional flows; Stokes equations; Complex geometry

Domaines: Analyse numérique [math.NA]; Modélisation et simulation

Robin Chatelin, Philippe Poncet. Particle methods for 3D biological flows with variable density and viscosity. European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Sep 2012, Vienna, Austria. ⟨hal-02011145⟩