Abstract
In this work, we consider the heat transfer problem during artificial ground freezing. We present the mathematical model and the fine grid approximation for heterogeneous porous media, where freezing pipes are considered as line source terms. Mathematical model is described by a two-phase Stefan problem. Fine grid approximation is performed using a finite element method. The main goal of the work is the construction of the coarse grid approximation using the Generalized Multiscale Finite Element Method (GMsFEM). In GMsFEM, we solve local spectral problem in order to determine main heat flow characteristics in the heterogeneous porous media and construct special additional multiscale basis functions in order to perform an accurate approximation of the line source terms (freezing pipes). We present numerical results for two heat transfer model problems in the two and three-dimensional formulations and investigate accuracy of the proposed multiscale methods for different numbers of the multiscale basis functions.
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