Transport in Porous Media

, Volume 124, Issue 2, pp 439–462 | Cite as

Finite-Volume Discretisations for Flow in Fractured Porous Media

  • Ivar Stefansson
  • Inga Berre
  • Eirik Keilegavlen


Over the last decades, finite-volume discretisations for flow in porous media have been extended to handle situations where fractures dominate the flow. Successful discretisations have been based on the discrete fracture-matrix models to yield mass conservative methods capable of explicitly incorporating the impact of fractures and their geometry. When combined with a hybrid-dimensional formulation, two central concerns are the restrictions arising from small cell sizes at fracture intersections and the coupling between fractures and matrix. Focusing on these aspects, we demonstrate how finite-volume methods can be efficiently extended to handle fractures, providing generalisations of previous work. We address the finite-volume methods applying a general hierarchical formulation, facilitating implementation with extensive code reuse and providing a natural framework for coupling of different subdomains. Furthermore, we demonstrate how a Schur complement technique may be used to obtain a robust and versatile method for fracture intersection cell elimination. We investigate the accuracy of the proposed elimination method through a series of numerical simulations in 3D and 2D. The simulations, performed on fractured domains containing permeability heterogeneity and anisotropy, also demonstrate the flexibility of the hierarchical framework.


Fractures Hybrid-dimensional discretisation Finite volumes 



The work has partly been funded by the Research Council of Norway through Grant Number 267908.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.Christian Michelsen ResearchBergenNorway

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