Electron. J. Diff. Eqns., Vol. 2007(2007), No. 147, pp. 1-30.

Multiscale elliptic-parabolic systems for flow and transport

Malgorzata Peszynska, Ralph E. Showalter

Abstract:
An upscaled elliptic-parabolic system of partial differential equations describing the multiscale flow of a single-phase incompressible fluid and transport of a dissolved chemical by advection and diffusion through a heterogeneous porous medium is developed without the usual assumptions of scale separation. 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. The resulting model is mass conserving and contains the effects of local advective transport as well as diffusion, it includes non-Fickian models of dispersion and works over a broad range of contrast cases.

Submitted October 5, 2007. Published November 5, 2007.
Math Subject Classifications: 76S05, 35B27, 74Q15, 35R10.
Key Words: Upscaled porous media; double porosity models; multiscale flow and transport; nonlocal dispersion

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Malgorzata Peszynska
Department of Mathematics
Oregon State University, Corvallis, OR 97331, USA
email: mpesz@math.oregonstate.edu
Ralph E. Showalter
Department of Mathematics
Oregon State University, Corvallis, OR 97331, USA
email: show@math.oregonstate.edu

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