September 27 – Ivan Yotov: A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media

Ivan Yotov: Friday 27 September at 15:00, A415 Inria Paris.

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.

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