Computational implementation of a mixed-dimensional model of heat transfer in the soil–pipe system in cryolithic zone

A mathematical model of heat transfer between the permafrost foundation of a building with a system of freezing pipes and atmospheric air is constructed and numerically implemented. As a mathematical model of heat transfer in the building foundation, the Stefan problem in the enthalpy statement with smoothed coefficients and a smeared temperature source is used. The heat transfer in the system of pipes is described by a one-dimensional convection–conduction equation. Numerical results obtained on model problems showed that the proposed numerical method significantly reduces the computational complexity of the problem.