Mixed Virtual Elements for discrete fracture network simulations

The present work deals with the simulation of the flow in Discrete Fracture Networks (DFN), using the mixed formulation of the Virtual Element Method (VEM) on polygonal conforming meshes. The flexibility of the VEM in handling polygonal meshes is used to easily generate a conforming mesh even in the case of intricate DFNs. Mixed Virtual Elements of arbitrary polynomial accuracy are then used for the discretization of the velocity field. The well posedness of the resulting discrete problem is shown. Numerical results on simple problems are proposed to show convergence properties of the method with respect to known analytic solutions, whereas some tests on fairly complex networks are also reported showing its applicability and effectiveness.