Algebraic dynamic multilevel method for embedded discrete fracture model (F-ADM)

•Algebraic dynamic multilevel method for multiphase flow in heterogeneous fractured porous media (F-ADM) is developed.•F-ADM generates an automatic framework to accurately represent discrete fractures at multiple scales, based on multilevel operators.•F-ADM develops multi-level embedded discrete fracture model, i.e., independent grids are used at all levels for fractures and matrix.•F-ADM is directly applicable to heterogeneous fractured media with no dependency on upscaled quantities.•F-ADM is a scalable and stable (fully-implicit) multiscale method for multiphase flow simulations in large-scale fractured media.