Computational Geosciences

, Volume 22, Issue 4, pp 993–1007 | Cite as

A finite-volume discretization for deformation of fractured media

  • Eren UcarEmail author
  • Eirik Keilegavlen
  • Inga Berre
  • Jan Martin Nordbotten
Original paper


Simulating the deformation of fractured media requires the coupling of different models for the deformation of fractures and the formation surrounding them. We consider a cell-centered finite-volume approach, termed the multi-point stress approximation (MPSA) method, which is developed in order to discretize coupled flow and mechanical deformation in the subsurface. Within the MPSA framework, we consider fractures as co-dimension one inclusions in the domain, with the fracture surfaces represented as line pairs in 2D (face pairs in 3D) that displace relative to each other. Fracture deformation is coupled to that of the surrounding domain through internal boundary conditions. This approach is natural within the finite-volume framework, where tractions are defined on surfaces of the grid. The MPSA method is capable of modeling deformation, considering open and closed fractures with complex and nonlinear relationships governing the displacements and tractions at the fracture surfaces. We validate our proposed approach using both problems, for which analytical solutions are available, and more complex benchmark problems, including comparison with a finite-element discretization.


Deformation Fracture mechanics Geomechanics Finite-volume method 


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The work was funded by the Research Council of Norway through grants no. 228832/E20, 267908/E20 and 250223 and Statoil ASA through the Akademia agreement.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.Christian Michelsen ResearchBergenNorway
  3. 3.Department of Civil and Environmental EngineeringPrinceton UniversityPrincetonUSA

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