Second-order numerical method for coupling of slightly compressible Brinkman flow with advection-diffusion system in fractured media

This paper considers a coupling of slightly compressible Darcy-Brinkman-transport problem in fractured media with higher Reynolds numbers, involving Brinkman flow in the fractures with advection-diffusion transport in the whole considered media. A new two-layer reduced coupled model is introduced by treating the fracture as hyperplane. The finite difference method with second-order backward differentiation formula and modified upwind scheme by using the fewest nodal points is constructed to solve the new reduced coupled model on staggered nonuniform grids. Based on error derivation of the coupling term, the uniqueness and existence of solutions and second-order convergence rate of numerical method are derived in the mixed forms under the mass conservative transmission and Beavers-Joseph-Saffman conditions. Some experiments are provided to testify the accuracy and efficiency of the numerical method. The numerical analysis of new two-layer reduced model is illustrated to show the behavior of fluid flow and solute transport in the media with intersected, embedded and L-shaped fractures.