Multiscale elliptic-parabolic systems for flow and transport. (English) Zbl 1137.76064

Peszynska, Malgorzata; Showalter, Ralph E.

Electron. J. Differ. Equ. 2007, Paper No. 147, 30 p. (2007).

Summary: Without usual assumptions of scale separation, we develop an upscaled elliptic-parabolic system of partial differential equations describing the multiscale flow of single-phase incompressible fluid and transport of dissolved chemical by advection and diffusion through a heterogeneous porous medium. After a review of homogenization results for the traditional low contrast and the \(\varepsilon^2\)-scaled high contrast cases, we construct new discrete upscaled model based on local affine approximations. The resulting model is mass-conserving and contains the effects of local advective transport as well as diffusion; additionally, it includes non-Fickian models of dispersion and works over a broad range of contrast cases.

MSC:

76S05	Flows in porous media; filtration; seepage
76M50	Homogenization applied to problems in fluid mechanics
76R50	Diffusion

Keywords:

nonlocal dispersion; heterogeneous porous medium; homogenization; diffusion