An Online Generalized Multiscale Finite Element Method for Unsaturated Filtration Problem in Fractured Media

In this paper, we present a multiscale model reduction technique for unsaturated filtration problem in fractured porous media using an Online Generalized Multiscale finite element method. The flow soils is described by the Richards equation. To approximate fractures use Discrete Fracture Model (DFM). Complex geometric features of computational domain requires construction fine grid that explicitly resolves heterogeneities such as fractures. This approach leads to systems with large number unknowns, which require costs. order develop more efficient numerical scheme, propose procedure based on Finite method (GMsFEM). GMsFEM allows solving problems very coarse basis functions can capture heterogeneities. GMsFEM, there are offline and online stages. stage, construct snapshot spaces solve local spectral obtain functions. These defined space each domain. improve accuracy method, add stage. residuals. bases will allow us get significant improvement We results different multisacle compare all reference solution. Our show proposed able achieve high small cost.