Computational Implementation of a Mixed-Dimensional Model of Heat Transfer in the Soil–Pipe System in Cryolithic Zone

• Published in: Computational mathematics and mathematical physics Vol. 61; no. 12; pp. 2054 - 2067
• Main Authors: Vasil’ev, V. I., Vasil’eva, M. V., Nikiforov, D. Ya, Sidnyaev, N. I., Stepanov, S. P., Tseeva, A. N.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-12-2021; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Enthalpy; Freezing; Heat transfer; Mathematical models; Mathematical Physics; Mathematics; Mathematics and Statistics; Numerical methods; Permafrost; Pipes; cryolithic zone; finite element method; Stefan problem; heat and mass transfer; computational algorithm
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542521120162

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.