A Three-field Based Optimization Formulation for Flow Simulations in Networks of Fractures on Nonconforming Meshes

Abstract

A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field domain decomposition framework in which independent variables are introduced at the interfaces generated in the process of decoupling the original problem on the whole network into a set of fracture-local problems. A PDE-constrained formulation is then used to enforce compatibility conditions at the interfaces. The combination of the three-field domain decomposition and of the optimization-based coupling strategy results in a novel method which can handle nonconforming meshes, independently built on each geometrical object of the computational domain, and ensures a local mass conservation property at fracture intersections, which is of paramount importance for hydrogeological applications. An iterative solver is devised for the method, suitable for parallel implementation on parallel computing architectures.