The virtual element method for underground flow simulations in fractured media

We focus on the problem of performing underground flow simulations in fractured media. The medium is modelled by means of the so-called Discrete Fracture Network (DFN) model. Within this framework, we discuss about the use of the Virtual Element Method (VEM) in performing simulations, and about its role in facilitating the meshing process. DFN models are characterized by a large number of planar fractures stochastically generated and placed in a 3D reference system starting from given probabilistic distribution of space position, dimension, aspect ratio, orientation and hydrogeological properties. For these reasons, realistic DFNs are usually characterized by the presence of very complex geometrical configurations on which it is very difficult to obtain a good quality Finite Element mesh. In particular, in order to circumvent these difficulties, we consider two different VEM approaches: an approach based on a totally conforming polygonal mesh obtained starting from a triangular mesh independently generated on the different fractures of the system and an approach based on a partially conforming mesh in which the connection between the fracture meshes is imposed through a mortaring approach borrowed from the classical domain decomposition methods. Concerning these two approaches, we discuss their relative advantages and present numerical results aimed at comparing them.