Professor Yang Yang, Michigan Tech University
Title: A Discrete Fracture Model for Single-phase Flow on Non-conforming Meshes
Abstract: The discrete fracture model (DFM) has been widely used in the simulation of fluid flow in fractured porous media. Traditional DFM use 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 to avoid local grid refinements in fractured region 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 qualified unstructured meshes due to the complexity of fracture’s geometrical morphology. In this paper, we clarify that the discrete fracture model 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 modified from the comb model 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 scheme 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 is demonstrated by testing several benchmark problems. This model is also applicable to curved fracture with variable thickness.