The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place next Monday (November 19, 2018) in K3 from 9:00 till 10:30. The talk will be given by Eduard Rohan. Please see the details below.
Speaker: Eduard Rohan
Title: Homogenization of hierarchically arranged porous media
The talk is aimed as an itroduction to the homogenization-based modelling of the so-called double-porosity media. Two situations can be distinguished: A) media described by the Biot-Darcy system of equations with highly heterogeneous permeability coefficients and other poroelastic coefficients, or B) media constituted by nested periodic structures. We focus on the second type of porous media formed by a microporous elastic skeleton with mesoscopic channels (cracks, or fissures). At the microscale level, the linearized fluid-structure interaction problem is treated, so that the first level of homogenization leads to the Biot continuum model describing the mesoscopic matrix coupled with the Stokes flow in the channels. The second step of the homogenization leads to a macroscopic model describing flow at the micro and meso-scopic pores coupled with the overall equilibrium equation respecting the hierarchical structure of the two-phase medium. Applications in the tissue perfusion modelling are shown.