Online Meshfree Generalized Multiscale Finite Element Method for Flows in Fractured Media

Modeling fracture systems in porous media requires a specialized approach due to the high permeability of fractures, which significantly influences transport and flow processes. Fracture systems can exist at various scales and differ in their origins, complicating their modeling. This paper presents a generalized multiscale finite element method (GMsFEM) utilizing a meshfree approach for constructing the coarse grid. We develop a methodology for creating online multiscale basis functions computed during the solution of non-stationary problems, which account for changes in local subdomains. This approach reduces the number of offline basis functions required to achieve high accuracy. Comparative studies demonstrate the advantages of the online approach over traditional finite element methods on detailed grids. The online multiscale approach proves effective for problems in fractured porous media, albeit requiring additional computational resources.