Multiscale elliptic-parabolic systems for flow and transport

Peszynska, Malgorzata
Showalter, Ralph
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Texas State University-San Marcos, Department of Mathematics
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 ɛ2-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.
Upscaled porous media, Double porosity models, Multiscale flow and transport, Nonlocal dispersion
Peszynska, M., & Showalter, R. E. (2007). Multiscale elliptic-parabolic systems for flow and transport. <i>Electronic Journal of Differential Equations, 2007</i>(147), pp. 1-30.