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Homogenization of secondary-flux models of partially fissured media. (English) Zbl 1165.76051

Summary: Fully-saturated and partially fissured media, in which supplementary flow and transport arise from direct cell-to-cell diffusion paths, have been described accurately over a wide range of scales by discrete secondary-flux models. These models were constructed as an extension of classical double-porosity models for totally fissured media by two-scale modeling considerations. There is some substantial literature on the analysis of continuously distributed secondary-flux models, and the corresponding discrete models have been proven to give efficient and accurate simulations when compared to recently available experimental data. These are particularly effective in the presence of advection. In this note, a summary description is given for the two-scale convergence of the discrete secondary-flux model to the corresponding continuous double-porosity secondary-flux model.

MSC:

76S05 Flows in porous media; filtration; seepage
76M50 Homogenization applied to problems in fluid mechanics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
86A05 Hydrology, hydrography, oceanography
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