Unsteady advection-diffusion simulations in complex Discrete Fracture Networks with an optimization approach

It is widely recognized that the prediction of transport of contaminants in a fractured rock mass requires models that preserve several distinctive features of the inner fracture network, like heterogeneity and directionality; in this respect, Discrete Fracture Networks (DFNs) play a significant role. The solution of the associated equations would claim a high computational demand, that could be met only by using agile and robust numerical techniques. In this note a new numerical technique, fully validated from a mathematical standpoint, is applied to engineering problems, also introducing dispersion models for the description of non-stationary transport phenomena. The method results in a fast and scalable resolution tool, based on a PDE-constrained optimization approach designed to avoid mesh generation problems and allowing for transport simulations with an Eulerian approach. Examples are reported to show the quality of the solution obtained, even by using relatively coarse meshes and quite geometrically complex DFNs.