DMS Colloquium: Ivan Yotov

Speaker: Ivan Yotov (University of Pittsburgh, http://www.math.pitt.edu/~yotov/)

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.

Brief Bio: 

Dr. Ivan Yotov is a Professor in the Department of Mathematics at the University of Pittsburgh. He received his Ph.D. in 1996 from Rice University. Dr. Yotov’s research interests are in the numerical analysis and solution of partial differential equations and large scale scientific computing with applications to fluid flow and transport. His current research focus is on the design and analysis of accurate multiscale adaptive discretization techniques (mixed finite elements, finite volumes, finite differences) and efficient linear and nonlinear iterative solvers (domain decomposition, multigrid, Newton-Krylov methods) for massively parallel simulations of coupled multiphase porous media and surface flows. Other areas of research interest include estimation of uncertainty in stochastic systems and mathematical and computational modeling for biomedical applications. Dr. Yotov is also an adjunct faculty at the McGowan Institute for Regenerative Medicine.

Faculty host: Thi-Thao-Phuong Hoang

Zoom link: https://auburn.zoom.us/j/84763379682