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

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Abstract

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.

Keywords

Karst aquifers
Block-centered finite difference method
Reduced coupled model

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The work is supported by the National Natural Science Foundation of China Grant No. 11401289, Shandong Province Higher Educational Science and Technology Program No. J16LI05, and in part by The Hong Kong Polytechnic University AMSS-PolyU Joint Research Institute (JRI) 1-ZVA8.

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