Flow in porous media with low dimensional fractures by employing enriched Galerkin method
Flow in porous media with low dimensional fractures by employing enriched Galerkin method
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DOI：
10.1016/j.advwatres.2020.103620
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发表时间：
2020-08
影响因子：
4.7
通讯作者：
T. Kadeethum;H. Nick;Sanghyu Lee;F. Ballarin
中科院分区：
文献类型：
--
作者：
T. Kadeethum;H. Nick;Sanghyu Lee;F. Ballarin
本文提出了一种基于混合维方法的富伽辽金离散方法，用于模拟裂隙多孔介质中的流体流动。所提出的方法已经过测试，对出版的基准。由于裂缝和多孔介质的不连续性可以显着地影响单相和多相流体流动，非均质和各向异性的矩阵渗透率设置被用来评估丰富的Galerkin性能在处理矩阵域内的不连续性和矩阵和裂缝域之间。我们的结果表明，丰富的Galerkin方法具有相同的优点，间断Galerkin方法，例如，它保存了本地和全球的流体质量，捕捉压力的不连续性，并提供了最佳的误差收敛速度。然而，丰富的Galerkin方法需要更少的自由度比在其经典形式的间断Galerkin方法。无论裂缝是导电还是非导电，也不管基质渗透率的非均质性如何，两种方法产生的压力解都是相似的。分析表明，丰富的Galerkin格式降低了计算成本，同时提供了相同的精度，间断Galerkin，使它可以应用于大规模的流动问题。此外，一个三维几何形状的时间相关的问题的结果揭示了正确捕获的障碍或高导电性骨折的不连续性的价值。
This paper presents the enriched Galerkin discretization for modeling fluid flow in fractured porous media using the mixed-dimensional approach. The proposed method has been tested against published benchmarks. Since fracture and porous media discontinuities can significantly influence single- and multi-phase fluid flow, the heterogeneous and anisotropic matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as the discontinuous Galerkin method; for example, it conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method in its classical form. The pressure solutions produced by both methods are similar regardless of the conductive or non-conductive fractures or heterogeneity in matrix permeability. This analysis shows that the enriched Galerkin scheme reduces the computational costs while offering the same accuracy as the discontinuous Galerkin so that it can be applied for large-scale flow problems. Furthermore, the results of a time-dependent problem for a three-dimensional geometry reveal the value of correctly capturing the discontinuities as barriers or highly-conductive fractures.