University of Pittsburgh
Colloquium Tea held at 4:00 pm in 101A Crowley Hall
Mathematical and computational modeling of fluid-poroelastic structure interaction
We study mathematical models and their finite element approximations for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic material. Applications of interest include arterial flows, flows in fractured poroelastic media, coupling of surface and subsurface flows, and flows through industrial filters. The free fluid flow is governed by the Navier-Stokes or Stokes/Brinkman equations, while the poroelastic material is modeled using the Biot system of poroelasticity. The two regions are coupled via dynamic and kinematic interface conditions, including balance of forces, continuity of normal velocity, and no-slip or slip with friction tangential velocity condition. Well posedness of the weak formulations is established using techniques from semigroup theory for evolution PDEs with monotone operators. Mixed finite element methods are employed for the numerical approximation. Solvability, stability, and accuracy of the methods are analyzed with the use of suitable discrete inf-sup conditions. Numerical results will be presented to illustrate the performance of the methods, including their flexibility and robustness for several applications of interest.