The virtual element method for discrete fracture network simulations

In this work, an optimization based approach presented in previous work of the authors for Discrete Fracture Network simulations is coupled with the Virtual Element Method (VEM) for the space discretization of the underlying Darcy law. The great flexibility of the VEM in allowing rather general polygonal elements, allow to easily describe irregular solutions starting from a general triangulation which can be built independently of the mesh on other fractures. Only a partial conformity is in fact obtained with this approach. Numerical results performed on several DFN configurations confirm the viability and efficiency of the resulting method.