Comparison of laplace transform and finite difference solutions for an evolving permafrost region

Laplace transform solutions are derived for an evolving permafrost region in saturated ground when the freezing interface moves with constant speed. The solution is inverse in the sense that the melting temperature at the interface and the groud surface temperature are prescribed functions of time. The solution procedure incorporates an initial temperature distribution in a domain extended above the ground surface. This allows, by asymptotic analysis, the construction of initially continuous melting and surface temperatures with bounded first and second derivatives. Solutions for two classes of initial conditions are determined by numerical inversion of the transforms. These solutions are used to test the corresponding solutions obtained by a direct finite difference algorithm developed earlier.¹ Good agreements for both interface path and temperature profiles are obtained in both classes.