INVESTIGATION OF DIFFERENCE METHODS FOR SOLVING STEFAN'S PROBLEM OF FREEZING WET SOIL

Abstract

In this paper, we study a special class of mathematical models that describes physical processes with phase transitions. One of the characteristic features of such models is the previously unknown and changing position of the interphase boundary over time. The difference methods for solving the two-phase Stefan problem in the one-dimensional case with a boundary condition of the second kind are investigated. Two numerical methods for solving the problem of freezing wet soil are compared --- the method of catching a front into a spatial grid node and the coordinate transformation method. A study has been conducted in the field of finding the functional dependence of the level of displacement of the interphase boundary on time. Numerical modeling of all considered methods for solving the problem of thermal conductivity with phase transitions is carried out. The results obtained showed the advantage of the coordinate transformation method in comparison with the method of catching the front into a spatial grid node. This advantage lies in the possibility of choosing an arbitrary time step.