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Generalized Multiscale Finite Element Method for Poroelasticity Problems in Heterogeneous Media

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Finite Difference Methods. Theory and Applications (FDM 2018)

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Abstract

In this work, we consider the poroelasticity problems in heterogeneous porous media. Mathematical model contains coupled system of the equations for pressure and displacements. For the numerical solution, we present a Generalized Multiscale Finite Element Method (GMsFEM). This method solves a problem on a coarse grid by construction of the local multiscale basic functions. The procedure begins with construction of multiscale bases for both displacement and pressure in each coarse block. Using a snapshot space and local spectral problems, we construct a basis of reduced dimension. Finally, after multiplying by a multiscale partitions of unity, the multiscale basis is constructed in the online phase and the coarse grid problem then can be solved for arbitrary forcing and boundary conditions. We compare the solutions by choosing different numbers of multiscale basis functions. The results show that GMsFEM can provide good accuracy for two and three dimensional problems in heterogeneous domains.

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Acknowledgments

Work is supported by the grant of the Russian Scientific Found (N 17-71-20055).

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Authors and Affiliations

  1. Multiscale Model Reduction Laboratory, North-Eastern Federal University, Yakutsk, Russia

    A. Tyrylgin & M. Vasilyeva

  2. Institute for Scientific Computation, Texas A&M University, College Station, TX, USA

    M. Vasilyeva

  3. School of Mathematical Sciences, GeoEnergy Research Center, The University of Nottingham, Nottingham, UK

    D. Brown

Authors
  1. A. Tyrylgin
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  2. M. Vasilyeva
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  3. D. Brown
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Corresponding author

Correspondence to A. Tyrylgin .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Tyrylgin, A., Vasilyeva, M., Brown, D. (2019). Generalized Multiscale Finite Element Method for Poroelasticity Problems in Heterogeneous Media. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_66

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_66

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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