Simulation of Drying‐Rewetting Processes in Numerical Groundwater Models Using a New Picard Iteration‐Based Method
Abstract 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 prop...
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| Format: | Article |
| Language: | English |
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Wiley
2024-04-01
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| Series: | Water Resources Research |
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| Online Access: | https://doi.org/10.1029/2022WR034334 |
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| author | Chuiyu Lu Wen Lu Qingyan Sun Xin He Lingjia Yan Tao Qin Chu Wu Shangqi Han Zhenjiang Wu Weichen Wu |
| author_facet | Chuiyu Lu Wen Lu Qingyan Sun Xin He Lingjia Yan Tao Qin Chu Wu Shangqi Han Zhenjiang Wu Weichen Wu |
| author_sort | Chuiyu Lu |
| collection | DOAJ |
| description | Abstract 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. |
| format | Article |
| id | doaj-art-344eda53675e45ba8871da6cdaa47d3f |
| institution | OA Journals |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2024-04-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-344eda53675e45ba8871da6cdaa47d3f2025-08-20T02:09:24ZengWileyWater Resources Research0043-13971944-79732024-04-01604n/an/a10.1029/2022WR034334Simulation of Drying‐Rewetting Processes in Numerical Groundwater Models Using a New Picard Iteration‐Based MethodChuiyu Lu0Wen Lu1Qingyan Sun2Xin He3Lingjia Yan4Tao Qin5Chu Wu6Shangqi Han7Zhenjiang Wu8Weichen Wu9State Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaState Key Laboratory of Simulation and Regulation of Water Cycles in River Basins China Institute of Water Resources and Hydropower Research (IWHR) Beijing ChinaAbstract 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.https://doi.org/10.1029/2022WR034334groundwater numerical simulationdrying‐rewetting processes of groundwater model cellsPicard iteration methodNewton iteration methodCOMUS modelMODFLOW‐NWT |
| spellingShingle | Chuiyu Lu Wen Lu Qingyan Sun Xin He Lingjia Yan Tao Qin Chu Wu Shangqi Han Zhenjiang Wu Weichen Wu Simulation of Drying‐Rewetting Processes in Numerical Groundwater Models Using a New Picard Iteration‐Based Method Water Resources Research groundwater numerical simulation drying‐rewetting processes of groundwater model cells Picard iteration method Newton iteration method COMUS model MODFLOW‐NWT |
| title | Simulation of Drying‐Rewetting Processes in Numerical Groundwater Models Using a New Picard Iteration‐Based Method |
| title_full | Simulation of Drying‐Rewetting Processes in Numerical Groundwater Models Using a New Picard Iteration‐Based Method |
| title_fullStr | Simulation of Drying‐Rewetting Processes in Numerical Groundwater Models Using a New Picard Iteration‐Based Method |
| title_full_unstemmed | Simulation of Drying‐Rewetting Processes in Numerical Groundwater Models Using a New Picard Iteration‐Based Method |
| title_short | Simulation of Drying‐Rewetting Processes in Numerical Groundwater Models Using a New Picard Iteration‐Based Method |
| title_sort | simulation of drying rewetting processes in numerical groundwater models using a new picard iteration based method |
| topic | groundwater numerical simulation drying‐rewetting processes of groundwater model cells Picard iteration method Newton iteration method COMUS model MODFLOW‐NWT |
| url | https://doi.org/10.1029/2022WR034334 |
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