Discontinuous finite volume element method for Darcy flows in fractured porous media

This paper presents a numerical simulation of the single phase Darcy flow model in two-dimensional fractured porous media. Under some physically consistent coupling conditions, the model can be described as a reduced problem by coupling the bulk problem in porous matrix and the fracture problem in fractures. Flows are governed by the primal form of the Darcy's equations for both the bulk and fractures. The coupled discontinuous finite volume element methods and conforming finite element method are adopted to solve the bulk problem and fracture problem, respectively. We theoretically analyze the well-posedness of the discrete problem, and derive optimal error estimates in standard L-2 error and broken H-1 error. Numerical experiments include not only the fractures with high permeability as the prior flow conduit, but also the fractures with low permeability as the flow barrier, which demonstrate the accuracy, flexibility and robustness of our discrete formulation for complicated networks of fractures in porous media domain. (C) 2020 Elsevier B.V. All rights reserved.