A PDE-Constrained Optimization Formulation for Discrete Fracture Network Flows

We investigate a new numerical approach for the computation of the threedimensional flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex three-dimensional systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersections. An independent meshing process within each fracture is a very important issue for practical large-scale simulations, making mesh generation easier. Some numerical simulations are given to show the viability of the method. The resulting approach can be naturally parallelized for dealing with systems with a huge number of fractures.