A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media
A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media
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DOI：
10.1016/j.advwatres.2022.104129
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发表时间：
2021-11
期刊：
影响因子：
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通讯作者：
G. Fu;Yang Yang-Yang
中科院分区：
文献类型：
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作者：
G. Fu;Yang Yang-Yang
我们提出了一种混合有限元方法，用于裂缝多孔介质中单相达西流的新型混合维度模型。在该模型中，裂缝被视为 d 维裂缝多孔域内的 (d−1) 维界面，其中 d= 2, 3。根据裂缝与其周围介质之间的渗透率大小比来区分两类裂缝：当裂缝中的渗透率（显着）大于其周围介质时，它被认为是传导裂缝；当裂缝中的渗透率（显着）小于其周围介质的渗透率时，它被认为是阻塞裂缝。传导裂缝采用经典的界面模型混合维方法进行处理，其中假设压力在裂缝界面上是连续的，而阻塞裂缝则使用最近的狄拉克-δ函数方法进行处理，其中假设达西速度的法向分量在界面上是连续的。由于使用 Dirac-δ 函数方法来处理阻塞裂缝，我们的数值方案允许使用与阻塞裂缝有关的不整合网格。这是我们的模型和数值离散化的主要新颖之处。此外，我们的数值方案产生局部保守的速度近似，并导致仅涉及网格骨架上的压力自由度的对称正定线性系统。作为一个应用程序，我们将这个想法扩展到一个简单的传输模型。所提出方法的性能通过二维和三维的各种基准测试用例得到证明。数值结果表明，所提出的方案与文献中现有的方法相比具有很强的竞争力
We present a hybrid-mixed finite element method for a novel hybrid-dimensional model of single-phase Darcy flow in a fractured porous media. In this model, the fracture is treated as a (d− 1)-dimensional interface within the d-dimensional fractured porous domain, for d= 2, 3. Two classes of fracture are distinguished based on the permeability magnitude ratio between the fracture and its surrounding medium: when the permeability in the fracture is (significantly) larger than in its surrounding medium, it is considered as a conductive fracture; when the permeability in the fracture is (significantly) smaller than in its surrounding medium, it is considered as a blocking fracture. The conductive fractures are treated using the classical hybrid-dimensional approach of the interface model where pressure is assumed to be continuous across the fracture interfaces, while the blocking fractures are treated using the recent Dirac-δ function approach where normal component of Darcy velocity is assumed to be continuous across the interface. Due to the use of Dirac-δ function approach for the blocking fractures, our numerical scheme allows for nonconforming meshes with respect to the blocking fractures. This is the major novelty of our model and numerical discretization. Moreover, our numerical scheme produces locally conservative velocity approximations and leads to a symmetric positive definite linear system involving pressure degrees of freedom on the mesh skeleton only. As an application, we extend the idea to a simple transport model. The performance of the proposed method is demonstrated by various benchmark test cases in both two-and three-dimensions. Numerical results indicate that the proposed scheme is highly competitive with existing methods in the literature