Modeling and numerical analysis of compressible Darcy–Brinkman fluid flow in fractured media with finite volume method on non-matching grids

Abstract

In this paper, a hybrid-dimensional coupled model of compressible fluid flow in fractured porous media is studied from theoretical and numerical points of view, in which the flow is governed by Brinkman model in fracture and Darcy model in surrounding porous media. A finite volume scheme with the fewest nodal points is constructed for solving the hybrid-dimensional coupled model on non-matching grids. The second-order error estimates with respect to different meshsizes are derived for both pressure and velocity in corresponding discrete norms. Numerical experiments are performed to verify the efficiency and accuracy of the proposed method. The effects of some parameters, such as the permeability, width and effective viscosity in fracture, together with the integration parameter introduced by the mathematical model, are investigated on the property of fluid flow in fractured system.