Electron. J. Diff. Equ., Vol. 2014 (2014), No. 189, pp. 1-21.

Homogenization of geological fissured systems with curved non-periodic cracks

Fernando A. Morales

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.

Submitted September 7, 2013. Published September 11, 2014.
Math Subject Classifications: 35F15, 80M40, 76S99, 35B25.
Key Words: Fissured media; tangential flow; interface geometry; coupled Darcy flow system; upscaling; mixed formulation.

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Fernando A. Morales
Escuela de Matemáticas
Universidad Nacional de Colombia
Sede Medellín, Colombia
email: famoralesj@unal.edu.co

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