Multiscale model reduction of the unsaturated flow problem in heterogeneous porous media with rough surface topography

Denis Spiridonov, Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev, Raghavendra Jana

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Article number904
JournalMathematics
Volume8
Issue number6
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • Generalized multiscale finite element method
  • Unsaturated flow

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