Mathematical Modeling of Underground Construction Temperature Influence on Permafrost Soils

Mathematical modeling of heat distribution with phase transitions is usually described by the Stefan problem. For north regions that situated on permafrost soils very common problem is to build constructions taking into account thawing process on soil. In this work we solve heat equation with phase transition numerically using finite elements method. Approximation was verified on one-dimensional problem by comparing with the analytical solution. Solver can be used on unstructured meshes with subdomains on two-dimensional problems. As a practical application, computational algorithm was used to forecast influence of construction heating to permafrost front of melting.