Homogenization of one phase flow in a highly heterogeneous porous medium including a thin layer

Amaziane, Brahim; Pankratov, Leonid; Prytula, Vladyslav

doi:10.3233/asy-2010-1005

Cited by 7 publications

(6 citation statements)

References 28 publications

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“…The asymptotic analysis is based on weak and strong two-scale convergence results for sequences of functions defined on thin heterogeneous layers. More recently, in [4], Amaziane et al study a flow problem in a domain that contains small structures. The flow is modeled by a linear parabolic equation with an x-dependent permeability coefficient K(x) in an elliptic operator in divergence form.…”

Section: Introductionmentioning

confidence: 99%

On the non‐stationary non‐Newtonian flow through a thin porous medium

Anguiano

2017

Z Angew Math Mech

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Section: Introductionmentioning

confidence: 99%

On the non‐stationary non‐Newtonian flow through a thin porous medium

Anguiano

2017

Z Angew Math Mech

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“…Relying on the estimates obtained here, we hope to be able to deal at a later stage with the boundary layers occurring during the simultaneous homogenization-dimension reduction procedure. We expect that the concept of two-scale convergence for thin heterogeneous layers (see [36]) and appropriate scaling arguments, somewhat similar to the spirit of [5,10], are applicable. A similar strategy would be to use a periodic unfolding operator depending on two parameters [14].…”

mentioning

confidence: 99%

Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers

Fatima¹,

Ijioma²,

Ogawa³

et al. 2014

Networks &Amp; Heterogeneous Media

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“…and the upscaling of reaction, diffusion, and flow processes in porous media with thin fissures (cf. [4,32], e.g. ).…”

Section: Background Motivationmentioning

confidence: 99%

Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure

et al. 2020

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We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift. Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving the upscaled model equations as well as the effective transport coefficients for suitable scalings in terms of both the inherent thickness at the strip and the typical length scales of the microscopic heterogeneities. Aiming at computable scenarios, we consider that the heterogeneity of the strip is made of an array of periodically arranged impenetrable solid rectangles and identify two scaling regimes what concerns the small asymptotics parameter for the upscaling procedure: the characteristic size of the microstructure is either significantly smaller than the thickness of the thin obstacle or it is of the same order of magnitude. We scale up the diffusion–polynomial drift model and list computable formulas for the effective diffusion and drift tensorial coefficients for both scaling regimes. Our upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We illustrate numerically the concentration profile of the chemical species passing through the upscaled strip in the finite thickness regime and point out that trapping of concentration inside the strip is likely to occur in at least two conceptually different transport situations: (i) full diffusion/dispersion matrix and nonlinear horizontal drift, and (ii) diagonal diffusion matrix and oblique nonlinear drift.

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Homogenization of one phase flow in a highly heterogeneous porous medium including a thin layer

Cited by 7 publications

References 28 publications

On the non‐stationary non‐Newtonian flow through a thin porous medium

On the non‐stationary non‐Newtonian flow through a thin porous medium

Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers

Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure

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