On a PDE-Constrained Optimization Approach for Flow Simulations in Fractured Media

In the present work we consider the problem of performing underground flow simulations in fractured media, following the Discrete Fracture Network (DFN) model. We will focus on a quite recent approach to the problem, based on a PDE-constrained optimization formulation, which allows for the use of totally non-conforming meshes on the network. In this way arbitrarily complex DFNs can be effectively tackled, without requiring any modification of the geometry of the network. Extended numerical simulations are reported demonstrating the performances of the proposed method, and highlighting its robustness in handling networks with hard-to-mesh configurations, such as extremely narrow angles between intersecting fractures. The problem of advection-diffusion of pollutant species in networks of fractures is also addressed in a time-dependent framework, using the optimization-based approach both to derive the Darcy velocity and to solve the transport problem at each time frame.