PARTICLE METHODS FOR 3D BIOLOGICAL FLOWS WITH VARIABLE DENSITY AND VISCOSITY

International audienceThis 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