A coupled model of fluid flow and heat transfer is developed to characterize steady groundwater flow within a mountain massif. A coupled model is necessary because high-relief terrain can enhance groundwater flow to depths where elevated temperatures are encountered. A wide range in water table form and elevation expected in high-relief terrain is accommodated using a free-surface method. This approach allows us to examine the influence of thermal conditions on the patterns and rates of groundwater flow and the position of the water table. Vertical fluid flow is assumed to occur within the unsaturated zone to provide a simple basis for modeling advective heat transfer above the water table. This approach ensures that temperatures at the water table, and throughout the domain, are consistent with temperature conditions specified at the bedrock surface. Conventional free-surface methods provide poor estimates of the water table configuration in high-relief terrain. A modified free-surface approach is introduced to accommodate recharge at upper elevations on the seepage face, in addition to recharge at the free surface.
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