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.
Highlights
Prediction of flows in unsaturated media is an important problem in many areas of science and engineering
We consider the problem in heterogeneous porous media with rough surface topography
Unsaturated flow conditions occur below the surface, the surface topography plays an important role in determining the flow process
Summary
Prediction of flows in unsaturated media is an important problem in many areas of science and engineering. We consider the problem in heterogeneous porous media with rough surface topography. These problems occur in many applications related to the vadose (or unsaturated) zone. Typical surface topography includes micro-scale features, such as roughness, as well as macro-scale features, such as hills, slopes, and valleys It has been shown by previous studies on hydrological processes (e.g., [1,2,3]) that the surface topography exerts varying control over soil hydrological processes at different spatial scales.
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