The Virtual Element Method for Discrete Fracture Network Flow and Transport Simulations

Abstract

Abstract. We discuss several issues concerning the application of the Virtual Element Method (VEM) to the flow in fractured media modeled by the Discrete Fracture Network (DFN) model. Due to the stochastic nature of the computational domains, several geometrical complexities make the computations very challenging. The geometrical flexibility provided by the Virtual Element Method can be exploited to mutually couple local problems, either by resorting to a Mortar approach, or by allowing for the global conformity of the local meshes, while keeping the computational cost under control. We describe these two approaches in detail and we test them on a realistic test case, showing the viability of the two approaches.

Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations

“…For our study, the resulting numerical schemes will be termed vem-m (mortar VEM in primal formulation) of order n = 1, 2. Details can be found in [7,9].…”

“…This indicates that the additional basis functions are able to capture the desired irregular behavior across the traces. Finally, the convergence curves of the methods vem-m and vem-c of both order 1 and 2 are almost overlapped, since the two matching strategies (Lagrange multipliers and mortaring, re- spectively) have intrinsically a similar nature, with a different definition of the space of the multipliers [9].…”

“…The resulting schemes are termed vem-c (VEM in primal formulation with conforming mesh) of order n = 1, 2. Details can be found in [11,9]. This approach can be seen as conforming method where the potentialities of the numerical scheme are exploited at best.…”