Advertisement

The Virtual Element Method for the Transport of Passive Scalars in Discrete Fracture Networks

  • S. Berrone
  • M. F. Benedetto
  • Andrea BorioEmail author
  • S. Pieraccini
  • S. Scialò
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)

Abstract

Simulation of physical phenomena in networks of fractures is a challenging task, mainly as a consequence of the geometrical complexity of the resulting computational domains, typically characterized by a large number of interfaces, i.e. the intersections among the fractures. The use of numerical strategies that require a mesh conforming to the interfaces is limited by the difficulty of generating such conforming meshes, as a consequence of the large number of geometrical constraints. Here we show how this issue can be effectively tackled by resorting to the Virtual Element Method on polygonal grids. Advection-diffusion-reaction phenomena are considered, also in advection-dominated flow regimes.

Notes

Acknowledgements

This work has been partially supported by INdAM-GNCS and by Politecnico di Torino through project Starting Grant RTD. Computational resources were partially provided by HPC@POLITO (http://hpc.polito.it).

References

  1. 1.
    M. Benedetto, S. Berrone, A. Borio, S. Pieraccini, S. Scialò, A hybrid mortar virtual element method for discrete fracture network simulations. J. Comput. Phys. 306, 148–166 (2016)MathSciNetCrossRefGoogle Scholar
  2. 2.
    M. Benedetto, S. Berrone, A. Borio, S. Pieraccini, S. Scialò, Order preserving SUPG stabilization for the virtual element formulation of advection-diffusion problems. Comput. Methods Appl. Mech. Eng. 311, 18–40 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    M. Benedetto, S. Berrone, S. Scialò, A globally conforming method for solving flow in discrete fracture networks using the virtual element method. Finite Elem. Anal. Des. 109, 23–36 (2016)CrossRefGoogle Scholar
  4. 4.
    S. Berrone, A. Borio, Orthogonal polynomials in badly shaped polygonal elements for the Virtual Element Method. Finite Elem. Anal. Des. 129, 14–31 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    L. Beirão Da Veiga, F. Brezzi, L.D. Marini, A. Russo, The hitchhiker’s guide to the virtual element method. Math. Models Methods Appl. Sci 24(8), 1541–1573 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    L. Beirão da Veiga, F. Brezzi, L.D. Marini, A. Russo, Virtual element methods for general second order elliptic problems on polygonal meshes. Math. Models Methods Appl. Sci. 26(4), 729–750 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • S. Berrone
    • 1
  • M. F. Benedetto
    • 2
  • Andrea Borio
    • 1
    Email author
  • S. Pieraccini
    • 1
  • S. Scialò
    • 1
  1. 1.Politecnico di TorinoTurinItaly
  2. 2.Universidad de Buenos AiresCiudad de Buenos AiresArgentina

Personalised recommendations