Advanced computation of steady-state fluid flow in discrete fracture-matrix models: FEM-BEM and VEM-VEM fracture-block coupling

In this note the issue of fluid flow computation in a Discrete Fracture-Matrix (DFM) model is addressed. In such a model, a network of percolative fractures delimits porous matrix blocks. Two frameworks are proposed for the coupling between the two media. First, a FEM-BEM technique is considered, in which finite elements on non-conforming grids are used on the fractures, whereas a boundary element method is used on the blocks; the coupling is pursued by a PDE-constrained optimization formulation of the problem. Second, a VEM-VEM technique is considered, in which a 2D and a 3D virtual element method are used on the fractures and on the blocks, respectively, taking advantage of the flexibility of VEM in using arbitrary meshes in order to ease the meshing process and the consequent enforcement of the matching conditions on fractures and blocks.