Mimetic finite difference approximation of flows in fractured porous media

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. Mor...

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Bibliographic Details
Published inESAIM. Mathematical modelling and numerical analysis Vol. 50; no. 3; pp. 809 - 832
Main Authors Antonietti, Paola F., Formaggia, Luca, Scotti, Anna, Verani, Marco, Verzott, Nicola
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.05.2016
Subjects
35Q86
65N30
76S05
Computer simulation
Finite difference method
flow in fractured porous media
Fractures
Mimetic finite differences
Permeability
Porous media
Simulation
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Summary: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.
Bibliography:Paola F. Antonietti, Anna Scotti and Marco Verani have been partially funded by INdAM - GNCS Project 2015 “Non-standard numerical methds for geophysics”. Paola F. Antonietti has been also partially supported by SIR Project No. RBSI14VT0S “PolyPDEs: Non-conforming polyhedral finite element methods for the approximation of partial differential equations” funded by MIUR. The fourth author has been also partially supported by the Italian research Grant Prin 2012 2012HBLYE4 “Metodologie innovative nella modellistica differenziale numerica”.
paola.antonietti@polimi.it; anna.scotti@polimi.it; marco.verani@polimi.it; nicola.verzotti@gmail.com
publisher-ID:m2an150077
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PII:S0764583X15000874
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content type line 14
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2015087