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Multiscale Model Reduction of the Unsaturated Flow Problem in Heterogeneous Porous Media with Rough Surface Topography

Author

Listed:
  • Denis Spiridonov

    (Multiscale Model Reduction Laboratory, North-Eastern Federal University, 677980 Yakutsk, Russia)

  • Maria Vasilyeva

    (Multiscale Model Reduction Laboratory, North-Eastern Federal University, 677980 Yakutsk, Russia
    Department of Mathematics, Texas A&M University, College Station, TX 77843, USA)

  • Eric T. Chung

    (Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China)

  • Yalchin Efendiev

    (Department of Mathematics, Texas A&M University, College Station, TX 77843, USA)

  • Raghavendra Jana

    (Center for Computational and Data-Intensive Science and Engineering, Skolkovo Institute of Science and Technology, 121205 Moscow, Russia)

Abstract

In this paper, we consider unsaturated filtration in heterogeneous porous media with rough surface topography. The surface topography plays an important role in determining the flow process and includes multiscale features. The mathematical model is based on the Richards’ equation with three different types of boundary conditions on the surface: Dirichlet, Neumann, and Robin boundary conditions. For coarse-grid discretization, the Generalized Multiscale Finite Element Method (GMsFEM) is used. Multiscale basis functions that incorporate small scale heterogeneities into the basis functions are constructed. To treat rough boundaries, we construct additional basis functions to take into account the influence of boundary conditions on rough surfaces. We present numerical results for two-dimensional and three-dimensional model problems. To verify the obtained results, we calculate relative errors between the multiscale and reference (fine-grid) solutions for different numbers of multiscale basis functions. We obtain a good agreement between fine-grid and coarse-grid solutions.

Suggested Citation

  • Denis Spiridonov & Maria Vasilyeva & Eric T. Chung & Yalchin Efendiev & Raghavendra Jana, 2020. "Multiscale Model Reduction of the Unsaturated Flow Problem in Heterogeneous Porous Media with Rough Surface Topography," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:904-:d:366672
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    Cited by:

    1. Sergey I. Fomenko & Raghavendra B. Jana & Mikhail V. Golub, 2023. "Numerical Modeling of Elastic Wave Propagation in Porous Soils with Vertically Inhomogeneous Fluid Contents Due to Infiltration," Mathematics, MDPI, vol. 11(19), pages 1-17, September.

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