Multiscale Model Reduction of the Flow Problem in Fractured Porous Media Using Mixed Generalized Multiscale Finite Element Method

Mathematical modeling of a flow in fractured porous media is important problem in subsurface simulations. Therefore, the development of mathematical models and efficient computational algorithms for numerical modeling of such processes is an actual problem. The mathematical model should take into account the entire complex of complicated, multiscale processes occurring in fractured porous media. In this work, we construct a coupled mixed dimensional model for simulation of the flow process in the fractured porous media with dual continuum background model. Mathematically the problem is described by a coupled system of equations consisting a d-dimensional equation for flow in porous matrix and a (d - 1)-dimensional equation for fracture networks with a specific exchange term for coupling them. In order to reduce size of the system and efficient solution of the presented problem, we construct coarse grid approximation using Mixed Generalized Multiscale Finite Element method. We present results of the numerical simulations for two-dimensional model problem.