Homogenization of geological fissured systems with curved non-periodic cracks

We analyze the steady fluid flow in a porous medium containing a network of thin fissures of width $\mathcal{O}(\epsilon)$, generated by the rigid translation of continuous piecewise $C^{1}$ functions in a fixed direction. The phenomenon is modeled in mixed variational formulation, using the station...

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Bibliographic Details
Published in:Electronic journal of differential equations 2014-09, Vol.2014 (189), p.1-21
Main Author: Fernando A. Morales
Format: Article
Language:English
Subjects:
coupled Darcy flow system
Fissured media
interface geometry
mixed formulation
tangential flow
upscaling
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Summary:We analyze the steady fluid flow in a porous medium containing a network of thin fissures of width $\mathcal{O}(\epsilon)$, generated by the rigid translation of continuous piecewise $C^{1}$ functions in a fixed direction. The phenomenon is modeled in mixed variational formulation, using the stationary Darcy's law and coefficients of low resistance $\mathcal{O}(\epsilon)$ on the network. The singularities are removed by asymptotic analysis as $\epsilon \to 0$ which yields an analogous system hosting only tangential flow in the fissures. Finally the fissures are collapsed into two dimensional manifolds.
ISSN:1072-6691