Abstract 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.

中文翻译：

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用富伽辽金法研究低维裂缝多孔介质中的流动

摘要 本文介绍了使用混合维方法对裂缝性多孔介质中的流体流动进行建模的丰富 Galerkin 离散化。所提出的方法已针对已发布的基准进行了测试。由于裂缝和多孔介质的不连续性会显着影响单相和多相流体流动，因此利用非均质和各向异性基质渗透率设置来评估在处理基质域内以及基质和裂缝域之间的不连续性方面的丰富 Galerkin 性能。我们的结果表明，富集伽辽金法与非连续伽辽金法具有相同的优势；例如，它保存局部和全局流体质量，捕获压力不连续性，并提供最佳误差收敛率。然而，与经典形式的不连续 Galerkin 方法相比，丰富的 Galerkin 方法需要更少的自由度。无论是传导性还是非传导性裂缝或基质渗透率的非均质性，这两种方法产生的压力解是相似的。该分析表明，丰富的 Galerkin 方案降低了计算成本，同时提供了与不连续 Galerkin 相同的精度，因此它可以应用于大规模流动问题。此外，三维几何的时间相关问题的结果揭示了将不连续性正确捕获为障碍或高传导性裂缝的价值。无论是传导性还是非传导性裂缝或基质渗透率的不均匀性，这两种方法产生的压力解都是相似的。该分析表明，丰富的 Galerkin 方案降低了计算成本，同时提供了与不连续 Galerkin 相同的精度，因此它可以应用于大规模流动问题。此外，三维几何的时间相关问题的结果揭示了将不连续性正确捕获为障碍或高传导性裂缝的价值。无论是传导性还是非传导性裂缝或基质渗透率的非均质性，这两种方法产生的压力解是相似的。该分析表明，丰富的 Galerkin 方案降低了计算成本，同时提供了与不连续 Galerkin 相同的精度，因此它可以应用于大规模流动问题。此外，三维几何的时间相关问题的结果揭示了将不连续性正确捕获为障碍或高传导性裂缝的价值。