We present a possible framework for the numerical simulation of flow in fractured porous media that couples mimetic finite differences for the porous matrix with a finite volume scheme for the flow in the fractures. The resulting method is theoretically analyzed in the case of a single fracture. Moreover, several numerical experiments show the capability of the method to deal also with complicated networks of fractures. Thanks to the implementation of rather general coupling conditions, it encompasses both “conductive fractures”, i.e., fractures with high permeability and “sealed fractures”, i.e., fractures with low permeability which act as a flow barrier.
DOI : 10.1051/m2an/2015087
Mots-clés : Mimetic finite differences, flow in fractured porous media
@article{M2AN_2016__50_3_809_0,
author = {Antonietti, Paola F. and Formaggia, Luca and Scotti, Anna and Verani, Marco and Verzott, Nicola},
title = {Mimetic finite difference approximation of flows in fractured porous media},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {809--832},
publisher = {EDP-Sciences},
volume = {50},
number = {3},
year = {2016},
doi = {10.1051/m2an/2015087},
mrnumber = {3507274},
zbl = {1381.76231},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015087/}
}
TY - JOUR AU - Antonietti, Paola F. AU - Formaggia, Luca AU - Scotti, Anna AU - Verani, Marco AU - Verzott, Nicola TI - Mimetic finite difference approximation of flows in fractured porous media JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 809 EP - 832 VL - 50 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015087/ DO - 10.1051/m2an/2015087 LA - en ID - M2AN_2016__50_3_809_0 ER -
%0 Journal Article %A Antonietti, Paola F. %A Formaggia, Luca %A Scotti, Anna %A Verani, Marco %A Verzott, Nicola %T Mimetic finite difference approximation of flows in fractured porous media %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 809-832 %V 50 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015087/ %R 10.1051/m2an/2015087 %G en %F M2AN_2016__50_3_809_0
Antonietti, Paola F.; Formaggia, Luca; Scotti, Anna; Verani, Marco; Verzott, Nicola. Mimetic finite difference approximation of flows in fractured porous media. ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 809-832. doi : 10.1051/m2an/2015087. http://www.numdam.org/articles/10.1051/m2an/2015087/
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