An Online Generalized Multiscale Method for Embedded Discrete Fracture Model

This study concerns an online generalized multiscale method for flow in fractured porous media that is based on an embedded discrete fracture model. We first convert a two-point flux-approximation scheme into an equivalent discrete weak formulation that results in the same linear algebraic system for the unknown pressure. Then, by the use of a suitable local snapshot space and a well-designed spectral decomposition, we compute offline basis functions to capture local heterogeneity information on account of the presence of various fractures in each coarse cell. After that, we compute residual-based online basis functions that contain global multiscale information to enrich the multiscale space and thus achieve higher accuracy of the multiscale solution. Meanwhile, theoretical analyses are conducted to show the convergence behavior, and a number of numerical tests with different fracture configurations are performed to investigate the performance of online enrichment.