SimTech Colloquium: Mathematical and computational modeling of fluid-poroelastic structure interaction

Date: 10 May 2023
Place: PWR7, V7.01
Time: 4pm

In this lecture series, leading researchers and promising young scientists report on their latest findings in the field of simulation science. We place particular emphasis on the interdisciplinary variety of contributions. We invite all interested parties to our colloquium.

Mathematical and computational modeling of fluid-poroelastic structure interaction

We present 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.

CV

Ivan Yotov is Professor in the Department of Mathematics at University of Pittsburgh. His research interests are in numerical analysis of partial differential equations and large scale scientific computing with applications to flow in porous media, computational fluid dynamics, and biomedical problems. His recent work spans multiscale modeling of multiphysics systems of coupled flow and mechanics, advanced finite element and finite volume discretizations, scalable parallel solvers and preconditioners, stochastic modeling, uncertainty quantification, and parameter estimation. Professor Yotov obtained his Ph.D. in Computational and Applied Mathematics from Rice University. He held a postdoctoral position at the Institute for Computational Engineering and Sciences at The University of Texas at Austin before joining University of Pittsburgh. He is an author of more than 100 scientific papers. He is Editor in Chief of Computational Geosciences and has served as Associate Editor of SIAM Journal on Numerical Analysis, Numerical Linear Algebra with Applications, and The Modeling and Computation for Flow and Transport. He is a recipient of the Ralph E. Powe Junior Faculty Enhancement Award from Oak Ridge Associated Universities, Distinguished TICAM Faculty Research Fellowship and J.T. Oden Faculty Fellowship at The University of Texas at Austin, Simons Visiting Professor to Oberwolfach, Inria Invited Professor at Inria Paris, and SFB 1313 Visiting Professor and Mercator Fellowship Visiting Professor at University of Stuttgart.