Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Heterogeneous Medium

Abstract

We consider a mathematical model for simulation of the unsaturated flow problems in heterogeneous porous medium that describes by the Richards equation. To resolve all heterogeneity, we construct fine grid and construct finite element approximation. For dimension reduction of the discrete system, we construct multiscale solver for coarse grid solution using Generalized Multiscale Finite Element Method (GMsFEM). We generate multiscale basis functions by solution of the local spectral problems. We present numerical result and compare relative error for different number of the multiscale basis functions for 2D and 3D model problems.