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Polyhedral Methods in Geosciences pp 227–258Cite as

A Hybrid High-Order Method for Multiple-Network Poroelasticity

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Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 27))

Abstract

We develop Hybrid High-Order methods for multiple-network poroelasticity, modelling seepage through deformable fissured porous media. The proposed methods are designed to support general polygonal and polyhedral elements. This is a crucial feature in geological modelling, where the need for general elements arises, e.g., due to the presence of fracture and faults, to the onset of degenerate elements to account for compaction or erosion, or when nonconforming mesh adaptation is performed. We use as a starting point a mixed weak formulation where an additional total pressure variable is added, that ensures the fulfilment of a discrete inf-sup condition. A complete theoretical analysis is performed, and the results are demonstrated on a panel of numerical tests.

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Acknowledgements

M. Botti acknowledges funding from the European Commission through the H2020-MSCA-IF-EF project PDGeoFF, Polyhedral Discretisation Methods for Geomechanical Simulation of Faults and Fractures in Poroelastic Media (Grant no. 896616).

Author information

Authors and Affiliations

  1. Department of Engineering and Applied Sciences, University of Bergamo, Bergamo, Italy

    Lorenzo Botti

  2. MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Milan, Italy

    Michele Botti

  3. IMAG, University of Montpellier, CNRS, Montpellier, France

    Daniele A. Di Pietro

Authors
  1. Lorenzo Botti
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  2. Michele Botti
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  3. Daniele A. Di Pietro
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Corresponding author

Correspondence to Daniele A. Di Pietro .

Editor information

Editors and Affiliations

  1. Institut Montpelliérain Alexander Grothendieck, University of Montpellier, Montpellier, France

    Daniele Antonio Di Pietro

  2. MOX-Laboratory for Modeling and Scientific Computing Dipartimento di Matematica, Politecnico di Milano, Milan, Italy

    Luca Formaggia

  3. Laboratoire de Mathématiques J. A. Dieudonné, Université Côte d’Azur, Nice, France

    Roland Masson

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Botti, L., Botti, M., Di Pietro, D.A. (2021). A Hybrid High-Order Method for Multiple-Network Poroelasticity. In: Di Pietro, D.A., Formaggia, L., Masson, R. (eds) Polyhedral Methods in Geosciences. SEMA SIMAI Springer Series, vol 27. Springer, Cham. https://doi.org/10.1007/978-3-030-69363-3_6

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