We worked a lot for this paper, where we implemented the freezing = drying theory of frozen soil. The theoretical work behind it open the way to generalizations that we will pursue in the next months. Here it is the abstract:
Phenomena involving frozen soil or rock are important in many natural systems and, as a consequence, there is a great interest in the modeling of their behavior. Few models exist that describe this process for both saturated and unsaturated soil and in conditions of freezing and thawing, as the energy equation shows strongly non-linear characteristics and is often difficult to handle with normal methods of iterative integration. Therefore in this paper we propose a method for solving the energy equation in freezing soil. The solver is linked with the solution of Richards equation, and is able to approximate water movement in unsaturated soils and near the liquid-solid phase transition. A globally-convergent Newton method has been implemented to achieve robust convergence of this scheme. The method is tested by comparison with an analytical solution to the Stefan problem and by comparison with experimental data derived from the literature.
The paper and the previous discussion paper can be freely downloaded at The Cryosphere site
For who is interested, a nice companion of the paper is the reading of Matteo Dall'Amico thesis, where there is some other remarkable material, and an introduction to equilibrium Thermodynamics that can make happy those who never really understood the notation used by thermodynamicists. Matteo and I made an effort to derive the basic thermodynamics from some postulates (derived from Callen's book), and use the normal algebra (the one we learn at the beginning of our undergraduate studies): I think we were quite successful, and for us Thermodynamics is not anymore the "a dismal swamp of obscurity", as C. Truesdal said. Also the books by Garbrect-and -Bohren, and Muller-and-Weiss were very useful to achieve our results.
Please take the time to read the reviews which added very informed and beautiful literature, and knowledge to the first paper.
Bohren C. F., and Albrecth B. A., Atmospheric Thermodynamics, Oxford University Press, 1998
Callen, H. B., Thermodynamics and an Introduction to Thermostatistics, J. Wiley and Sons, 1985
Muller, I., and Weiss, Entropy and Energy: A Universal Competition, Springer, 2005
Truesdall, C., The tragicomical history of thermodynamics 1822-1854, Springer Verlag, 1980 (the sentence is at page 6)
For who interested in thermodynamics, I found also another couple of good books:
Ganguly A., Thermodynamics in Earth and Planetary Sciences, Springer, 2010
Zdunkowski W., and Bott, A., Thermodynamics of the Atmosphere: A Course in Theoretical Meteorology, Cambridge University Press, 2004