Numerical analysis and modeling of multiscale Forchheimer–Forchheimer coupled model for compressible fluid flow in fractured media aquifer system

A multiscale coupled model is developed to simulate the compressible fluid flow in fractured media aquifer system, where the flow is governed by Forchheimer's law in the fracture and continuum porous medium. Due to the fact that the thickness of fracture is much smaller than characteristic diameters of surrounding porous medium, the fracture is reduced to a lower dimensional interface and a more complicated transmission condition is derived on the fracture-interface. The coupled model is numerically solved by the finite difference method with an implicit iteration procedure. The fewest nodal points are used to construct the optimal scheme for approximating the multiscale Forchheimer–Forchheimer coupled model. Different degrees of freedom are located on both sides of fracture-interface in order to capture the jump of velocity. Second-order error estimates in discrete norms are derived on nonuniform staggered grids for both pressure and velocity. The proposed scheme can also be extended to high dimensional model without loss of accuracy. Numerical experiments are performed to demonstrate the efficiency and accuracy of the numerical method.