Multiscale Systems for Flow and Transport

MIMW02 - From the grain to the continuum: two phase dynamics of a partially molten, polycrystalline aggregate

An elliptic-parabolic system of partial differential equations describes the flow of a single-phase incompressible fluid and the transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium.  The objective is to develop an upscaled model of this system which represents the full range of scales observed.  After a review of homogenization results for the traditional low contrast and the $\epsilon^2$-scaled high contrast cases, the new discrete upscaled model based on local affine approximations is constructed. It reproduces the full range of scale contrasts observed in experiments.

This talk is part of the Isaac Newton Institute Seminar Series series.