Development and analysis of a novel optimization approach for the simulation of the flow in large scale discrete fracture networks with non-conforming finite elements / Sviluppo ed analisi di un nuovo approccio per la simulazione del flusso in network discreti di fratture su larga scala basato su un metodo di ottimizzazione ed elementi finiti su griglie non conformi

The present Thesis reports the description of a new numerical model for the definition of the hydraulic head distribution in Discrete Fracture Networks (DFNs). The solution to the DFN problem is obtained through a PDE constrained minimization approach. The problem on the whole DFN can be split in many small sub-problems on the fractures that can be solved independently from each other, and resorting to the minimization of a cost functional to enforce the compatibility conditions at fracture intersections. In such a way the complexity of the initial problem can be handled more efficiently in parallel computers in an easy and straightforward way, and the meshing process can be performed independently on each fracture and is therefore fast and reliable. Different discretization strategies are investigated to improve the representation of the solution on non-conformng meshes with respect to standard finite elements: the eXtended Finite Elements or th Virtual Finite Elements. Within the proposed approach a mixing of these discretization strategies is possible, improving fexibility in dealing with complex DFN configurations. A large set of numerical results are reported to highlight effectiveness and performances of the method.