When simulating groundwater flow in unconfined and convertible aquifers using a groundwater model with the block-centered finite-difference approach, such as MODFLOW, it frequently encounters drying and rewetting of cells. Although many drying and rewetting simulation methods have been proposed in the past, balancing simulation accuracy and convergence capability all at once is difficult. MODFLOW-2005, which has second-order accuracy, employs a trial-and-error method, but it suffers from computational instability when large quantities of grid cells are dried. MODFLOW-NWT adopts the upstream-weighting approach and Newton iteration method to ensure the stability of the drying and rewetting simulations. However, the upstream-weighting approach has only first-order accuracy, and the Newton iteration method is complex to implement because it necessitates the establishment of an additional Jacobian matrix. The methods employed by MODFLOW-NWT are also available in MODFLOW 6, therefore it inherits both the strengths and weaknesses of MODFLOW-NWT. In this study, a new method, Picard iteration-based always active cell (PAAC), is proposed. Similar to MODFLOW-NWT, the PAAC method also uses dry cells as active cells. The PAAC method, however, does not use the upstream-weighting approach and has second-order accuracy. Moreover, it ensures good convergence stability even under the Picard iteration method. In addition to discussing the algorithm, five cases were used to comprehensively compare the simulation effects of the PAAC method with MODFLOW-2005 and MODFLOW-NWT, including an analytical solution, repeated drying-rewetting of multi-layer grids, pumping well problem, perched aquifer problem and a nearly dry single-layer grid, which verified the practicability of the PACC method.

中文翻译：

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使用基于皮卡德迭代的新方法模拟地下水数值模型中的干燥-再润湿过程

当使用以块为中心的有限差分方法（例如MODFLOW）的地下水模型模拟无承压和可转换含水层中的地下水流时，经常会遇到单元的干燥和再润湿问题。尽管过去已经提出了许多干燥和再润湿模拟方法，但很难同时平衡模拟精度和收敛能力。 MODFLOW-2005具有二阶精度，采用试错法，但当大量网格单元被干燥时，它会遇到计算不稳定的问题。 MODFLOW-NWT采用上游加权方法和牛顿迭代法来保证干燥和再润湿模拟的稳定性。然而，上游加权方法仅具有一阶精度，并且牛顿迭代法需要建立额外的雅可比矩阵，因此实现起来很复杂。 MODFLOW-NWT 采用的方法在 MODFLOW 6 中也可用，因此它继承了 MODFLOW-NWT 的优点和缺点。在这项研究中，提出了一种新方法——基于皮卡德迭代的始终活动单元（PAAC）。与MODFLOW-NWT类似，PAAC方法也使用干电池作为活性电池。然而，PAAC方法不使用上游加权方法并且具有二阶精度。而且即使在Picard迭代法下也能保证良好的收敛稳定性。除了讨论算法外，还通过五个案例综合比较了PAAC方法与MODFLOW-2005和MODFLOW-NWT的模拟效果，包括解析解、多层网格的重复干燥-再润湿、抽水井问题、栖息问题含水层问题和接近干燥的单层网格，验证了PACC方法的实用性。