Comparison of analytical solution of the semi-infinite problem of soil freezing with numerical solutions in various simulation software

Abstract

The objective of this research is to determine the most suitable software packages for simulation of thermal effect of various constructions on seasonally frozen or permafrost ground. The abrupt change in soil physical properties at freeze/thaw boundaries is a considerable challenge because it introduces a strong nonlinearity into the heat transfer model. Mathematically speaking, there appears a Stefan condition at the moving boundary of the phase transition. A problem of soil column freezing is considered. The simulation results, obtained by different software, are compared with the analytical solution of the corresponding semi-infinite Stefan problem. The frost penetration depth and the depth profiles of temperature and its absolute error, after 300 days, are presented.