Mathematical Modeling of Temperature Regime of Soils of Foundation on Permafrost

In the article we consider a mathematical model describing the heat transfer processes in the frozen and thawed soils. We provide a mathematical formulation of the problem with the appropriate initial and boundary conditions. Numerical implementation is based on the finite-element method, which allows us to take into account the complication caused by difficulties with geometry, since piles are small comparing with whole domain. In this paper we include the comparison of two-dimensional and threedimensional models of heat transfer calculation in a soil, taking into account the installation of piles and the seasonal fluctuations of ambient temperature. We present the results of numerical simulation of soil temperature on the example of engineering solutions containing several piles installed in the soil with a layered structure. We discuss the elements of the developed applied software for the predicting the temperature regime of soils on permafrost. Numerical simulations of the problem in three-dimensional case on the computational cluster of NEFU “Arian Kuzmin” are provided.

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