A block-centered finite difference method for an unsteady asymptotic coupled model in fractured media aquifer system

A block-centered finite difference method is proposed for solving an unsteady asymptotic coupled model, in which the flow is governed by Darcy's law both in the one-dimensional fracture and two-dimensional porous media. The second-order error estimates in discrete norms are derived on nonuniform rectangular grids for both pressure and velocity. The numerical scheme can be extended to nonmatching spatial and temporal grids without loss of accuracy. Numerical experiments are performed to verify the efficiency and accuracy of the proposed method. It is shown that the pressure and velocity are discontinuous across the fracture-interface and the fracture indeed acts as the fast pathway or geological barrier in the aquifer system.