This article is cited in 1 paper

Mathematical modeling

Simulation of the process of infiltration into fractured porous soil in permafrost

S. P. Stepanov^ab, A. V. Grigor'ev^b, N. M. Afanas'eva<sup>b

a</sup> International Research Laboratory "Multiscale model reduction", North-Eastern Federal University named after M. K. Ammosov, Ammosov North-Eastern Federal University, 42 Kulakovsky Street, Yakutsk 677980, Russia
^b Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia

Abstract: The article provides mathematical modeling of the complex multiphysical problem relevant for the territories of the Far North and the Arctic. The relevance of this task is characterized by importance of the seepage process in the formation and thawing of the permafrost layer. Modern applications for the most part require consideration of complex geometries, as well as a large number of different processes and their mutual relationship. The multiphysical model consists of the Richards equation to describe the seepage process, the double porosity model to describe natural soil fracturing, the Stefan task to describe the temperature regime of the soil in permafrost zone conditions. The computational algorithm is based on finite-element space approximation on triangulated Delone meshes and using of a time splitting scheme using linearization from a previous time layer.

Keywords: the Richards equation, the Stefan problem, double porosity, fractured porous media.

UDC: 519.63

Received: 19.11.2019
Revised: 13.02.2019
Accepted: 30.04.2020

DOI: 10.25587/SVFU.2020.15.67.007

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