Journal
ADVANCES IN WATER RESOURCES
Volume 70, Issue -, Pages 172-184Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.advwatres.2014.05.005
Keywords
Analytical solutions; Thawing front; Phase change; Thermohydraulic models; Stefan problem; Freezing and thawing
Categories
Funding
- Natural Sciences and Engineering Research Council of Canada
- Canadian Water Resources Association Dillon Scholarship
- O'Brien Fellowship
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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. (C) 2014 Elsevier Ltd. All rights reserved.
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