Meshfree Multiscale Method for Richards’ Equation in Fractured Media
Djulustan Nikiforov, Yin Yang · Lobachevskii Journal of Mathematics · 2023
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.