Mimetic finite difference approximation of flows in fractured porous media∗
MOX-Laboratory for Modeling and Scientific Computing, Dipartimento
di Matematica, Politecnico di
Milano, Piazza Leonardo da Vinci 32, 20133
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Received: 15 April 2015
Revised: 19 October 2015
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.
Mathematics Subject Classification: 65N30 / 35Q86 / 76S05
Key words: Mimetic finite differences / flow in fractured porous media
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”.
© EDP Sciences, SMAI 2016
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