Geodesic
Modeling flow in porous media with fractures; discrete fracture models with matrix-fracture exchange
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 2, pp. 197-204

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This article is concerned with a numerical model for flow in a porous medium containing fractures. The fractures are modeled as $(d-1)$-dimensional surfaces inside the $d$-dimensional matrix domain, and a mixed finite element method containing both $d$ and $(d-1)$ dimensional elements is used. The method allows for fluid exchange between the fractures and the matrix. The method is defined for single-phase Darcy flow throughout the domain and for Forchheimer flow in the fractures. We also consider the case of two-phase flow in a domain in which the fractures and the matrix are of different rock type. 
@article{SJVM_2012_15_2_a9,
     author = {J. Jaffr\'e and J. E. Roberts},
     title = {Modeling flow in porous media with fractures; discrete fracture models with matrix-fracture exchange},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {197--204},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a9/}
}
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J. Jaffré; J. E. Roberts. Modeling flow in porous media with fractures; discrete fracture models with matrix-fracture exchange. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 2, pp. 197-204. http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a9/