Séminaire des équipes de recherche
Séminaire SERENA : A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media
- Date : 27/09/2019
- Lieu : Salle A415, bâtiment A -15h
- Intervenant(s) : Ivan Yotov
A nonlinear model is developed for fluid-poroelastic structure interaction with quasi-Newtonian fluids that exhibit a shear-thinning property.
The flow in the fluid region is described by the Stokes equations and in the poroelastic medium by the quasi-static Biot model. Equilibrium and kinematic conditions are imposed on the interface. A mixed Darcy formulation is employed, resulting in continuity of flux condition of essential type, which is weakly enforced through a Lagrange multiplier.
We establish existence and uniqueness of the solution of the weak formulation using non-Hilbert spaces. A stability and error analysis is performed for the semi-discrete continuous-in-time and the fully discrete formulations.
The model is further coupled with an advection-diffusion equation for modeling transport of chemical species within the fluid.Applications to hydraulic fracturing and arterial flows are presented.