Mathematics & Physics 2016, 9(2), 158–165 УДК 517.9 A Numerical Model of the Seasonal Thawing of Permafrost in the Swamp-lake Landscapes Victor M.Belolipetskii∗ Institute of Computational Modelling SB RAS Akademgorodok, 50/44, Krasnoyarsk, 660036 Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Svetlana N.Genova† Institute of Computational Modelling SB RAS Akademgorodok, 50/44, Krasnoyarsk, 660036 Russia Received 25.11.2015, received in revised form 30.01.2016, accepted 20.02.2016 The theoretical description of the temperature field in the soils during freezing or thawing is carried out using solutions of Stefan’s problem. <...> A mathematical model based on the equations of thermal conductivity for frozen and thawed layers. <...> We distinguished the following layers in the vertical structure of the zone of permafrost: thawed soil, frozen soil, water, ice, snow. <...> We offer a simplified numerical algorithm for solving of one-dimensional (in the vertical direction) heat conduction problems with moving boundaries of phase transition with the formation of new and cancellation of existing layers. <...> A simplified numerical algorithm for solving one-dimensional (in the vertical direction) heat conduction problems with moving boundaries of phase transition with the formation of new and cancellation of existing layers is offering. <...> Keywords: permafrost, Stefan’s problem, thawed and frozen soil, small dimensional numerical model. <...> Introduction In connection with the change in global temperature is of interest assess the response of permafrost to climate change. <...> We consider the areas in which there is a lake or swamp. <...> Since the vertical temperature gradients are usually larger than the horizontal one, so all physical process assumes one-dimensional in the vertical direction in the description of the heat transfer. <...> The theoretical description of the temperature field in the water and soils during their freezing and thawing is carried out using solutions of Stefan problem [1]. <...> A mathematical model based on the equations of thermal conductivity for frozen and thawed areas. <...> At the borders of phase transition (freezing-thawing) the conditions of equality of temperatures to the phase ∗belolip@icm.krasn.ru †sv@icm.krasn.ru ⃝ Siberian Federal University. <...> All rights reserved c – 158 – Victor M.Belolipetskii, Svetlana N.Genova A Numerical Model of the Seasonal Thawing of Permafrost . . . transition temperature and the Stefan condition <...>