The HADES seminar on Tuesday, April 23rd, will be at 3:30pm in Room 939.

Speaker: Andrew Scharf

Abstract: Multilayered poroelastic structures are found in many biological tissues, such as cartilage and the cornea, and find use in the design of bioartificial organs and other bioengineering applications. Motivated by these applications, we analyze the interaction of a free fluid flow modeled by the time-dependent Stokes equation and a multilayered poroelastic structure consisting of a thick Biot layer and a thin, linear, poroelastic membrane separating it from the Stokes flow. The resulting equations are linearly coupled across the thin structure domain through physical coupling conditions such as the Beavers-Joseph-Saffman condition. I will discuss previous work in which weak solutions were shown to exist by constructing approximate solutions using Rothe’s method. While a number of partitioned numerical schemes have been developed for the interaction of Stokes flow with a thick Biot structure, the existence of an additional thin poroelastic plate in the model presents new challenges related to finite element analysis on multiscale domains. As an important step toward an efficient numerical scheme for this model, we develop a novel, fully discrete partitioned method for the multilayered poroelastic structure problem based on the fixed strain Biot splitting method. This work is carried out jointly with Sunčica Čanić and Jeffrey Kuan at the University of California, Berkeley and Martina Bukač at the University of Notre Dame.