Theory and Application of the Numerical Simulation in the Frozen Soil Problems

The freezing-thawing processes in soils are important components of terrestrial hydrology, which significantly influence energy and water exchanges between land surface and sub-surface. Long-term changes in frost and thaw depths are also an important indicator of climate change. A water-heat coupled movements model is established with frozen soil in this paper, which treats the freezing/thawing front as a moving interface governed by some Stefan problems with two free boundaries. The numerical simulation is conducted by using the modified finite difference method. The model is validated to compare its predictions with GEWEX Asian Monsoon Experiment(GAME)-Tibet observations at D66 site in Tibetan Plateau. The results show that the simulated soil temperature, soil water content and frost/thaw depth are in excellent agreement with the measured values. Finally, optimal error estimation for L^∞ norm is derived on the model problem by using coordinate transformation method. The numerical simulation system is established on the basis of rigorous mathematics and mechanics, which successfully solved the important and difficult problems of environmental science.