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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 5
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Research Article

Intersecting fractures in porous media: mathematical and numerical analysis

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Pages 1312-1334 | Received 15 Feb 2021, Accepted 10 Sep 2021, Published online: 04 Oct 2021
 

Abstract

This paper studies a model for flow in a fractured porous medium with intersecting fractures. The fractures are treated as lower-dimensional manifolds and then physical transmission conditions express the pressure jump and the continuity of the flux across the fractures. Specific attention is borne to the conditions when several fractures intersect. The resulting system is discretized with mixed finite element, and the well-posedness of both the continuous and the discrete problems are proved. Then a domain decomposition method is formulated, so that the problem is reduced to the set of fractures, and a simple preconditioner is proposed. Numerical results exemplify the performance of the method.

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Disclosure statement

No potential conflict of interest was reported by the author(s).

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