Geodesic
Mimetic finite difference approximation of flows in fractured porous media
Antonietti, Paola F.1  ; Formaggia, Luca1  ; Scotti, Anna1 ; Verani, Marco1  ; Verzott, Nicola1
1 MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue – Polyhedral discretization for PDE, Tome 50 (2016) no. 3, pp. 809-832

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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.

Reçu le :
DOI : 10.1051/m2an/2015087
Classification : 65N30, 35Q86, 76S05
Keywords: Mimetic finite differences, flow in fractured porous media

Antonietti, Paola F. 1 ; Formaggia, Luca 1 ; Scotti, Anna 1 ; Verani, Marco 1 ; Verzott, Nicola 1

1 MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy 
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     title = {Mimetic finite difference approximation of flows in fractured porous media},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {809--832},
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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

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