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A Double-Layer Reduced Model for Fault Flow on Slipping Domains with an Hybrid Finite Volume Scheme

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Abstract

In this work we are interested in single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than other characteristic sizes, can allow one part of the domain to slide past to the other. We propose a mathematical scheme where a reduced model for the fault flows is employed yielding a problem of co-dimension one. The hybrid finite volume method is used to obtain the discretized problem, which uses two different meshes on each side of the fault. These two meshes can move with the corresponding domain, resulting in non-matching grids between the two parts of the fault. In an earlier paper a mathematical scheme was proposed where the numerical discretization considers the hybrid finite volume method. In this paper we focus on the well-posedness of the continuous problem, the convergence of the discretized problem, and we support the theoretical findings with several numerical tests.

Keywords

Porous media Reduced model Faults Finite volume Non-matching grids 

Mathematics Subject Classification

76S05 65N08 86A60 

Notes

Acknowledgements

The authors warmly thank Jérôme Jaffré and Jean E. Roberts for many fruitful discussions. They also wish to thank the anonymous reviewers for their valuable comments and suggestions, which allowed them to improve the quality of the paper.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universitetet i BergenBergenNorway

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