Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: One-dimensional soil thaw with conduction and advection |
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| Affiliation: | 1. U.S. Geological Survey, Earth System Processes Division, Hydrogeophysics Branch, 11 Sherman Place, Unit 5015, Storrs, CT 06269, USA;2. U.S. Geological Survey, Leetown Science Center, Aquatic Ecology Branch, 11649 Leetown Road, Kearneysville, WV 25430, USA;3. Department of Civil and Resource Engineering, Centre for Water Resources Studies, Dalhousie University, 1360 Barrington Street, Halifax, NS B3H 4R2, Canada;4. Department of Earth Sciences, Heroy Geology Building, Syracuse University, NY, USA;5. College of Science and Engineering, National Centre for Groundwater Research and Training, Flinders University, Sturt Road, Bedford Park, South Australia 5042, Australia;6. Massachusetts Division of Fisheries and Wildlife, 195 Bournedale Road, Buzzards Bay, MA 02532, USA;1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China;2. School of Mechanics and Civil Engineering, China University of Mining and Technology, Jiangsu 221116, China;3. State Key Laboratory of Coal Resource and Safe Mining, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China |
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| Abstract: | Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing. |
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| Keywords: | Analytical solutions Thawing front Phase change Thermohydraulic models Stefan problem Freezing and thawing |
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