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Implementation of Mixed-Dimensional Models for Flow in Fractured Porous Media

  • Eirik KeilegavlenEmail author
  • Alessio Fumagalli
  • Runar Berge
  • Ivar Stefansson
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and their intersections form a hierarchy of interacting subdomains. We discuss the implementation of a simulation framework, with an emphasis on reuse of existing discretization tools for mono-dimensional problems. The key ingredients are the representation of the mixed-dimensional geometry as a graph, which allows for convenient discretization and data storage, and a non-intrusive coupling of dimensions via boundary conditions and source terms. This approach is applicable for a wide class of mixed-dimensional problems. We show simulation results for a flow problem in a three-dimensional fracture geometry, applying both finite volume and virtual finite element discretizations.

Notes

Acknowledgements

We acknowledge financial support from the Research Council of Norway, project no. 244129/E20 and 250223.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Eirik Keilegavlen
    • 1
    Email author
  • Alessio Fumagalli
    • 1
  • Runar Berge
    • 1
  • Ivar Stefansson
    • 1
  1. 1.University of BergenDepartment of MathematicsBergenNorway

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