Three-time-level methods for the numerical solution of soil freezing problems

Finite element and finite difference methods for heat and mass transfer problems are usually based on two-time-level schemes for treating the time derivative. In freezing and thawing problems the equations are non-linear. The non-linearity arises because of the dependence of the material properties on both temperature and moisture fields. With two-time-level schemes it is usually necessary to iterate the solution in order to obtain accurate results. For non-linear problems of this type iteration can be avoided by using a three-time-level scheme with material properties evaluated at the intermediate time level. The most well known three-time-level scheme is, however, subject to oscillation which seriously limits its usefulness. This paper discusses a new three-time-level scheme and compares it with several other time marching schemes from the standpoint of accuracy and susceptibility to oscillation.