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Multiscale Systems for Flow and Transport

Presented by: 
Ralph Showalter Oregon State University
Thursday 14th April 2016 - 11:30 to 12:30
INI Seminar Room 1
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons