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.
翻译:离散断裂模型(DFM)已被广泛用于模拟断裂多孔介质的流体流动。传统DFM使用所谓的混合维度方法,将骨折作为基质细胞界面中的低维条目(如2D介质的线条条目和3D介质的面条条目)处理,然后将基质断裂模型和断裂流系统根据叠加原则与用作立体同质系数的断裂厚度比对齐。由于这一方法,DFM被认为仅限于符合 meshes,因此在生成高品质的不结构间歇时可能会带来困难。在本文件中,我们澄清DFMFM实际上可以扩展至不兼容的模项,而没有任何基本变化。为了清楚地显示,我们基于混合维表示的渗透性抗光度变异度,DFMFM将骨折模型描述为单维线Dirac 三角曲线功能,因此,由于骨折质断裂的精度不精度不精度不精确度模型生成,由于骨质对骨质结构的精确度流适用,因此,DFMFMFMFM计划在不连续测试中会自动地分析中也显示。