Mixed formulations for fluid-poroelastic structure interaction
Thursday, March 4, 2021
3:30PM – 5PM
The interaction between a free fluid and a flow in deformable poroelastic medium, referred as fluid-poroelastic structure interaction (FPSI), is a challenging multiphysics problem motivated by a wide range of applications in petroleum engineering, hydrology, environmental sciences, and biomechanical engineering. For this kind of physical phenomenon, the free fluid region can be modeled by the Stokes (or Navier–Stokes) equations, while the flow through the deformable porous medium is modeled by the Biot system of poroelasticity. The two regions are coupled via dynamic and kinematic interface conditions. In this talk, we will introduce the design, analysis and numerical implementation of mixed finite element methods for FPSI problems, focusing on a new mixed elasticity formulation for the Stokes-Biot model and a finite element method for its numerical solution.
Tongtong Li is a PhD candidate at University of Pittsburgh in the Department of Mathematics, under the supervision of Ivan Yotov. She is interested in the numerical analysis and solution of partial differential equations (PDEs) with an emphasis on the development, theoretical analysis and computer implementation of numerical methods to approximate solutions of PDEs. Her current research has been on the study of mixed finite element methods for the coupled problem arising in the interaction between free fluid flow and flow in deformable poroelastic medium, referred to as fluid-poroelastic structure interaction (FPSI).