Abstract Groundwater, being a vital component of the natural water resource system, needs continuous monitoring and dynamic management strategies. That said, we require computationally inexpensive groundwater flow models for repetitive solutions with desirable accuracy under budgetary limitation(s). Natural aquifer systems inherit strong heterogeneity at local scales. In this work, we have proposed ordinary kriging-based sequential algorithm for generating replicates of randomly distributed heterogeneous hydraulic conductivity field (Monte Carlo method-based algorithm) conditioned by field values from sampled locations in an irregular-unstructured grid system. Finite Volume method-based groundwater models often encounter difficulties with the representation of point source/sink terms operating within the domain. In this paper, we have proposed an irregular-unstructured grid Finite Volume discretization technique for overcoming the singularity of point source/sink term to yield a consistent output with different grid dimensions. Furthermore, full-system groundwater models often come with a substantial computational burden. Hence, reduction in model order cuts down the computational expenses (in terms of CPU time and usage) to a significant level. We have also put forth a model order reduction methodology for three different illustrative pumping tests. The proposed framework for the model order reduction projects the governing groundwater flow equation onto a set of identified patterns or orthonormal basis functions, applying the Galerkin Projection method to compute a vector of time-dependent coefficients. We have performed pattern identification by Singular Value Decomposition (SVD) of snapshots of full-system model simulation data at selected time instants within the pumping test time domain. The numerical results of the proposed reduced-order models show a good approximation of the full-system models at a comparatively lesser computational time. The accuracy and efficiency of the models attempt to ensure their potential applicability for identifying groundwater dynamics.

中文翻译：

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基于适当正交分解（POD）的地下水流通过具有点源奇异性的非均质多孔介质的降阶建模

摘要 地下水是天然水资源系统的重要组成部分，需要持续监测和动态管理策略。也就是说，我们需要计算成本低廉的地下水流模型，用于在预算限制下具有理想精度的重复解决方案。天然含水层系统在局部尺度上继承了强烈的异质性。在这项工作中，我们提出了基于普通克里金法的顺序算法，用于生成随机分布的异质水力传导率场（基于蒙特卡罗方法的算法）的复制，该场以来自不规则非结构化网格系统中采样位置的场值为条件。基于有限体积方法的地下水模型在域内操作的点源/汇项的表示方面经常遇到困难。在本文中，我们提出了一种不规则非结构化网格有限体积离散化技术，用于克服点源/汇项的奇异性，以产生具有不同网格尺寸的一致输出。此外，全系统​​地下水模型通常伴随着大量的计算负担。因此，模型顺序的减少将计算费用（在 CPU 时间和使用方面）降低到一个显着的水平。我们还为三种不同的说明性泵送测试提出了模型阶数减少方法。模型降阶的建议框架将控制地下水流方程投影到一组识别的模式或正交基函数上，应用伽辽金投影方法来计算时间相关系数的向量。我们通过抽水测试时域内选定时间点的全系统模型模拟数据快照的奇异值分解 (SVD) 进行了模式识别。所提出的降阶模型的数值结果显示了在相对较短的计算时间内对全系统模型的良好近似。模型的准确性和效率试图确保它们在识别地下水动态方面的潜在适用性。