  The discrete fracture model (DFM) has been widely used in the simulation of
fluid flow in fractured porous media. Traditional DFM uses the so-called
hybrid-dimensional approach to treat fractures explicitly as low-dimensional
entries (e.g. line entries in 2D media and face entries in 3D media) on the
interfaces of matrix cells and then couple the matrix and fracture flow systems
together based on the principle of superposition with the fracture thickness
used as the dimensional homogeneity factor. Because of this methodology, DFM is
considered to be limited on conforming meshes and thus may raise difficulties
in generating high quality unstructured meshes due to the complexity of
fracture's geometrical morphology. In this paper, we clarify that the DFM
actually can be extended to non-conforming meshes without any essential
changes. To show it clearly, we provide another perspective for DFM based on
hybrid-dimensional representation of permeability tensor to describe fractures
as one-dimensional line Dirac delta functions contained in permeability tensor.
A finite element DFM scheme for single-phase flow on non-conforming meshes is
then derived by applying Galerkin finite element method to it. Analytical
analysis and numerical experiments show that our DFM automatically degenerates
to the classical finite element DFM when the mesh is conforming with fractures.
Moreover, the accuracy and efficiency of the model on non-conforming meshes are
demonstrated by testing several benchmark problems. This model is also
applicable to curved fracture with variable thickness.
