  Discrete Fracture and Matrix (DFM) models describe fractured porous media as
complex sets of 2D planar polygons embedded in a 3D matrix representing the
surrounding porous medium. The numerical simulation of the flow in a DFM
requires the discretization of partial differential equations on the three
dimensional matrix, the planar fractures and the one dimensional fracture
intersections, and suitable coupling conditions between entities of different
dimensionality need to be added at the various interfaces to close the problem.
The present work proposes an arbitrary order implementation of the Virtual
Element method in mixed formulation for such multidimensional problems. Details
on effective strategies for mesh generation are discussed and implementation
aspects are addressed. Several numerical results in various contexts are
provided, which showcase the applicability of the method to flow simulations in
complex multidimensional domains.
