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Comparison of linear reconstructions for second-order finite volume schemes on polyhedral grids


Improved and enhanced oil recovery methods require sophisticated simulation tools to predict the injected flow pass together with the chemical reactions inside it. One approach is application of higher-order numerical schemes to avoid excessive numerical diffusion that is very typical for transport processes. In this work, we provide a first step towards higher-order schemes applicable on general polyhedral and corner-point grids typically used in reservoir simulation. We compare three possible approaches of linear reconstruction and slope limiting techniques on a variety of different meshes in two and three spatial dimensions and discuss advantages and disadvantages.

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Robert Klöfkorn and Anna Kvashchuk thank the Research Council of Norway and the industry partners—ConocoPhillips Skandinavia AS, BP Norge AS, Det Norske Oljeselskap AS, Eni Norge AS, Maersk Oil Norway AS, DONG Energy AS Denmark, Statoil Petroleum AS, ENGIE E&P NORGE AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall and Norge AS—of The National IOR Centre of Norway for the financial support.

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Correspondence to Robert Klöfkorn.

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Klöfkorn, R., Kvashchuk, A. & Nolte, M. Comparison of linear reconstructions for second-order finite volume schemes on polyhedral grids. Comput Geosci 21, 909–919 (2017).

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  • Second-order finite volume
  • Linear reconstruction
  • Polyhedral grids
  • DUNE
  • OPM