A block-centered finite difference method for reduced fracture model in Karst aquifer system

A block-centered finite difference scheme is given for the approximation of reduced coupled model in the fractured media aquifer system. The fluid flow of aquifer system is governed by Darcy's law in both fracture and surrounding porous media. The degrees of freedom are given separately on both sides of fracture to capture the discontinuity of pressure and velocity. Optimal error estimates in discrete L2 norms are obtained. Numerical experiments are provided to verify the second-order accuracy of presented method. It is demonstrated whether the fracture acts as a fast pathway or geological barrier is totally determined by the value of its permeability tensor.