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Performances of the Mixed Virtual Element Method on Complex Grids for Underground Flow

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Polyhedral Methods in Geosciences

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

Abstract

The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The development of approximation schemes has recently focused on the overcoming of such difficulties with the objective of obtaining numerical schemes with good approximation properties. In this work we carry out a numerical study on the performance of the Mixed Virtual Element Method (MVEM) for the solution of a single-phase flow model in fractured porous media. This method is able to handle grid cells of polytopal type and treat hybrid dimensional problems. It has been proven to be robust with respect to the variation of the permeability field and of the shape of the elements. Our numerical experiments focus on two test cases that cover several of the aforementioned critical aspects.

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Acknowledgements

We acknowledge the PorePy development team: Eirik Keilegavlen, Runar Berge, Michele Starnoni, Ivar Stefansson, Jhabriel Varela, Inga Berre.

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Authors and Affiliations

  1. MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, via Bonardi 9, 20133, Milan, Italy

    Alessio Fumagalli, Anna Scotti & Luca Formaggia

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  1. Alessio Fumagalli
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  2. Anna Scotti
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  3. Luca Formaggia
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Correspondence to Anna Scotti .

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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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Fumagalli, A., Scotti, A., Formaggia, L. (2021). Performances of the Mixed Virtual Element Method on Complex Grids for Underground Flow. 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_8

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