Applied Mathematics Colloquium: Dr Ivan Yotov
University of Pittsburgh
Friday, April 1, 2022 · 2 - 3 PM
Title: Stokes-Biot modeling of fluid-poroelastic structure interaction
Abstract: 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 flows in fractured poroelastic media, coupling of
surface and subsurface flows, and arterial flows. 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.
Abstract: 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 flows in fractured poroelastic media, coupling of
surface and subsurface flows, and arterial flows. 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.
