A family of methods with arbitrary meshes for DFN flow simulations

A new approach for the simulation of the steady-state flow in discrete fracture networks is presented, along with new numerical results on complex configurations. The networks considered may have an arbitrary number of planar polygonal fractures with random spatial orientation, size and hydrological properties. The method is based on the minimization of a proper functional to enforce matching conditions at fracture intersections; the solution of the flow equations on each fracture of the network is carried on independently from the solution on the other fractures. Non-conforming Finite Element meshes on the fractures are allowed. Different discretization strategies can be used and mixed in order to improve approximation properties and provide high levels of accuracy. Extended Finite Elements and Virtual Elements have been successfully explored, thus a great flexibility is ensured when dealing with complex DFN configurations. The process for generating a suitable mesh is independently performed for each fracture, without requiring conformity at intersections, thus being extremely reliable and computationally inexpensive. The overall method is parallel oriented, thus providing an efficient handling of problem size and complexity. This is of paramount importance for massive simulations for uncertainty quantification in stochastically generated networks, or in the resolution of networks at very large scale and/or composed of even millions of fractures. The modular structure of the algorithm can easily embody other physical models for the description of flow regimes of increasing complexity