Abstract Accurate modeling of variably saturated flow (VSF) in fractured porous media with the discrete fracture-matrix (DFM) model is a computationally challenging problem. The applicability of DFM model to VSF in real field studies at large space and time scales is often limited, not only because it requires detailed fracture characterization, but also as it involves excessive computational efforts. We develop an efficient numerical scheme to solve the Richards equation in discretely fractured porous media. This scheme combines the mixed hybrid finite element method for space discretization with the method of lines for time integration. The fractures are modeled as lower-dimensional interfaces (1D), within the 2D porous matrix. We develop a new mass-lumping (ML) technique for the fractures to eliminate unphysical oscillations and convergence issues in the solution, which significantly improves efficiency, enabling larger field applications. The proposed new scheme is validated against a commercial simulator for problems involving water table recharge at the laboratory scale. The computational efficiency of the developed scheme is examined on a challenging problem for water infiltration in fractured dry soil, and compared with standard numerical techniques. We show that the ML technique is crucial to improve robustness and efficiency, which outperforms the commonly used methods that we tested. The applicability of our method is then demonstrated in a study concerning the effect of climate change on groundwater resources in a karst aquifer/spring system in El Assal, Lebanon. Simulations, including recharge predictions under climate change scenarios, are carried out for about 80 years, up to 2099. This study demonstrates the applicability of our proposed scheme to deal with real field cases involving large time and space scales with high variable recharge. Our results indicate that the water-table level is sensitive to the presence of fractures, where neglecting fractures leads to an overestimation of the available groundwater amount. The proposed numerical approach is generic for DFM model and can be extended to different 2D and 3D finite-element frameworks.

中文翻译：

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裂隙多孔介质中可变饱和流动的先进离散裂隙模型

摘要 使用离散裂缝矩阵 (DFM) 模型对裂缝性多孔介质中的可变饱和流 (VSF) 进行精确建模是一个具有计算挑战性的问题。DFM 模型在大空间和时间尺度的实际现场研究中对 VSF 的适用性通常是有限的，不仅因为它需要详细的裂缝表征，还因为它涉及过多的计算工作。我们开发了一种有效的数值方案来求解离散裂缝多孔介质中的理查兹方程。该方案将空间离散化的混合混合有限元方法与时间积分的线法相结合。裂缝被建模为二维多孔基质内的低维界面 (1D)。我们为裂缝开发了一种新的质量集总 (ML) 技术，以消除解决方案中的非物理振荡和收敛问题，从而显着提高效率，实现更大的现场应用。针对涉及实验室规模地下水位补给问题的商业模拟器，对提议的新方案进行了验证。已开发方案的计算效率在一个具有挑战性的裂缝干燥土壤渗水问题上进行了检查，并与标准数值技术进行了比较。我们表明 ML 技术对于提高鲁棒性和效率至关重要，其性能优于我们测试的常用方法。然后，我们的方法的适用性在一项关于气候变化对 El Assal 岩溶含水层/泉水系统地下水资源影响的研究中得到证明，黎巴嫩。模拟，包括气候变化情景下的补给预测，进行了大约 80 年，直到 2099 年。这项研究证明了我们提出的方案在处理涉及大时空尺度和高可变补给的真实现场案例中的适用性。我们的结果表明，地下水位对裂缝的存在很敏感，忽略裂缝会导致对可用地下水量的高估。所提出的数值方法对于 DFM 模型是通用的，并且可以扩展到不同的 2D 和 3D 有限元框架。这项研究证明了我们提出的方案在处理涉及大时间和空间尺度以及高可变补给的实际现场情况方面的适用性。我们的结果表明，地下水位对裂缝的存在很敏感，忽略裂缝会导致对可用地下水量的高估。所提出的数值方法对于 DFM 模型是通用的，并且可以扩展到不同的 2D 和 3D 有限元框架。这项研究证明了我们提出的方案在处理涉及大时间和空间尺度以及高可变补给的实际现场情况方面的适用性。我们的结果表明，地下水位对裂缝的存在很敏感，忽略裂缝会导致对可用地下水量的高估。所提出的数值方法对于 DFM 模型是通用的，并且可以扩展到不同的 2D 和 3D 有限元框架。