  Over the last decade, finite volume discretizations for flow in porous media
have been extended to handle situations where fractures dominate the flow.
These discretizations have successfully been combined with the discrete
fracture-matrix models to yield mass conservative methods capable of explicitly
incorporating the impact of fractures and their geometry. When combined with a
hybrid-dimensional formulation, two central concerns are the restrictions
arising from small cell sizes at fracture intersections and the coupling
between fractures and matrix. Focusing on these aspects, we demonstrate how
finite volume methods effectively can be extended to handle fractures,
providing generalizations of previous work. We address the finite volume
methods applying a general hierarchical formulation, facilitating
implementation with extensive code reuse and providing a natural framework for
coupling of different subdomains. Furthermore, we demonstrate how a Schur
complement technique may be used to obtain a robust and versatile method for
fracture intersection cell elimination. We investigate the accuracy of the
proposed elimination method through a series of numerical simulations in 3D and
2D. The simulations, performed on fractured domains containing permeability
heterogeneity and anisotropy, also demonstrate the flexibility of the
hierarchical framework.
