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Conservative numerical methods for the reinterpreted discrete fracture model on non-conforming meshes and their applications in contaminant transportation in fractured porous media
Advances in Water Resources ( IF 4.7 ) Pub Date : 2021-05-20 , DOI: 10.1016/j.advwatres.2021.103951
Hui Guo , Wenjing Feng , Ziyao Xu , Yang Yang

The discrete fracture model (DFM) has been widely used to simulate fluid flow in fractured porous media. Traditional DFM is considered to be limited on conforming meshes, hence significant difficulty may arise in generating high-quality unstructured meshes due to the complexity of the fracture networks. Recently, Xu and Yang reinterpreted DFM and demonstrated that it can actually be extended to non-conforming meshes without any essential changes. However, the continuous Galerkin (CG) method was applied and the local mass conservation was missing. This paper is a follow-up work, and we apply the interior penalty discontinuous Galerkin (IPDG) method and enriched Galerkin (EG) method for the pressure equation. With the numerical fluxes, the local mass is conservative. As an application, we combine the reinterpreted DFM (RDFM) with the incompressible miscible displacements in porous media. The bound-preserving techniques are applied to the coupled system. We can theoretically guarantee that the concentration is between 0 and 1. Finally, several numerical experiments are given to demonstrate the good performance of the RDFM based on the above two methods on non-conforming meshes and the effectiveness of the bound-preserving technique.



中文翻译:

非一致网格上离散断裂模型重新解释的保守数值方法及其在断裂多孔介质污染物输送中的应用

离散裂缝模型(DFM)已被广泛用于模拟裂缝多孔介质中的流体流动。传统的 DFM 被认为仅限于一致的网格,因此由于裂缝网络的复杂性,在生成高质量的非结构化网格方面可能会遇到很大的困难。最近,Xu 和 Yang 重新解释了 DFM,并证明它实际上可以扩展到不符合要求的网格而无需任何本质的改变。但是,应用了连续伽辽金 (CG) 方法并且缺少局部质量守恒。本文是后续工作,我们对压力方程应用内罚不连续伽辽金(IPDG)方法和富集伽辽金(EG)方法。对于数值通量,局部质量是保守的。作为应用程序,我们将重新解释的 DFM (RDFM) 与多孔介质中的不可压缩混相位移相结合。保界技术应用于耦合系统。我们理论上可以保证浓度在0到1之间。最后,通过几个数值实验证明了基于上述两种方法的RDFM在非一致性网格上的良好性能和保界技术的有效性。

更新日期:2021-05-30
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