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Meshfree Multiscale Method for Richards’ Equation in Fractured Media

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Abstract

In this paper, we develop a meshfree multiscale method for solving the unsaturated filtration problem in fractured media described by Richards’ equation. This approach is based on Generalized Multiscale Finite Element Method (GMsFEM). Multiscale basis functions are constructed in the offline stage via local spectral problems. Meshfree method is used to solve the coarse-grid system. On the fine grid, the standard Finite Element Method (FEM) is used. To represent the fractures on the fine grid, we use Discrete Fracture Model (DFM). The results of comparing the solution on the coarse grid with the solution on the fine grid are shown numerically. In this work, we discuss handling nonlinearities within meshfree GMsFEM. Our numerical results show a good agreemenet between coarse and fine grids solutions.

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Funding

The D.Y.N.’s work is supported by the Ministry of science and Higher Education of the Russian Federation, agreement no. 075-02-2023-947, February 16, 2023 and Ministry of Science and Higher Education of the Russian Federation (Grant no. FSRG-2023-0025). The research of YY is supported by the National Natural Science Foundation of China Project (12261131501).

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Authors and Affiliations

  1. North-Eastern Federal University, 677000, Yakutsk, Russia

    D. Y. Nikiforov

  2. School of Mathematics and Computational Science, Xiangtan University, National Center for Applied Mathematics in Hunan, Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Xiangtan, 411105, Hunan, China

    Y. Yang

Authors
  1. D. Y. Nikiforov
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  2. Y. Yang
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Correspondence to D. Y. Nikiforov or Y. Yang.

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Nikiforov, D.Y., Yang, Y. Meshfree Multiscale Method for Richards’ Equation in Fractured Media. Lobachevskii J Math 44, 4135–4142 (2023). https://doi.org/10.1134/S1995080223100293

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  • DOI: https://doi.org/10.1134/S1995080223100293

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