Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 147, pp. 1-30.

Title: Multiscale elliptic-parabolic systems for flow and transport

Authors: Malgorzata Peszynska (Oregon State Univ., Corvallis, OR, USA)
         Ralph E. Showalter   (Oregon State Univ., Corvallis, OR, USA)

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 05, 2007. Published November 05, 2007.
Math Subject Classifications: 76S05, 35B27, 74Q15, 35R10.
Key Words: Upscaled porous media; double porosity models; 
           multiscale flow and transport; nonlocal dispersion