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Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model

Author

Listed:
  • Denis Spiridonov

    (Multiscale Model Reduction Laboratory, North-Eastern Federal University, 677980 Yakutsk, Republic of Sakha (Yakutia), Russia)

  • Jian Huang

    (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
    Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan 411105, China
    Key Laboratory of Intelligent Computing Information Processing of Ministry of Education, Xiangtan 411105, China)

  • Maria Vasilyeva

    (Institute for Scientific Computation, Texas A&M University, College Station, TX 77843-3368, USA
    Department of Computational Technologies, North-Eastern Federal University, 677980 Yakutsk, Republic of Sakha (Yakutia), Russia)

  • Yunqing Huang

    (School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
    Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan 411105, China
    Key Laboratory of Intelligent Computing Information Processing of Ministry of Education, Xiangtan 411105, China)

  • Eric T. Chung

    (Department of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong, China)

Abstract

In this paper, the solution of the Darcy-Forchheimer model in high contrast heterogeneous media is studied. This problem is solved by a mixed finite element method (MFEM) on a fine grid (the reference solution), where the pressure is approximated by piecewise constant elements; meanwhile, the velocity is discretized by the lowest order Raviart-Thomas elements. The solution on a coarse grid is performed by using the mixed generalized multiscale finite element method (mixed GMsFEM). The nonlinear equation can be solved by the well known Picard iteration. Several numerical experiments are presented in a two-dimensional heterogeneous domain to show the good applicability of the proposed multiscale method.

Suggested Citation

  • Denis Spiridonov & Jian Huang & Maria Vasilyeva & Yunqing Huang & Eric T. Chung, 2019. "Mixed Generalized Multiscale Finite Element Method for Darcy-Forchheimer Model," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1212-:d:296030
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    Cited by:

    1. Shan Jiang & Yue Cheng & Yao Cheng & Yunqing Huang, 2023. "Generalized Multiscale Finite Element Method and Balanced Truncation for Parameter-Dependent Parabolic Problems," Mathematics, MDPI, vol. 11(24), pages 1-14, December.

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