A moving boundary problem derived from heat and water transfer processes in frozen and thawed soils and its numerical simulation

摘要

The seasonal change in depths of the frozen and thawed soils within their active layer is reduced to a moving boundary problem,which describes the dynamics of the total ice content using an independent mass balance equation and treats the soil frost/thaw depths as moving(sharp)interfaces governed by some Stefan-type moving boundary conditions,and hence simultaneously describes the liquid water and solid ice states as well as the positions of the frost/thaw depths in soil.An adaptive mesh method for the moving boundary problem is adopted to solve the relevant equations and to determine frost/thaw depths,water content and temperature distribution.A series of sensitivity experiments by the numerical model under the periodic sinusoidal upper boundary condition for temperature are conducted to validate the model,and to investigate the effiects of the model soil thickness,ground surface temperature,annual amplitude of ground surface temperature and thermal conductivity on frost/thaw depths and soil temperature.The simulated frost/thaw depths by the model with a periodical change of the upper boundary condition have the same period as that of the upper boundary condition,which shows that it can simulate the frost/thaw depths reasonably for a periodical forcing.