New strategies for the simulation of the flow in three dimensional poro-fractured media

Two novel approaches are presented for dealing with three dimensional flow simulations in porous media with fractures: one method is based on the minimization of a cost functional to enforce matching conditions at the interfaces, thus allowing for non conforming grids at the interfaces; the other, instead, takes advantage of the new Virtual Elements to easily build conforming polygonal grids at the fracture-porous matrix interfaces. Both methods are designed to minimize the effort in mesh generation process for problems characterized by complex geometries. The methods are described in their simplest fashion in order to keep the notation as compact and simple as possible.