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

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
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