Geodesic
Numerical solution of the inverse Stefan problem in the analysis of artificial freezing of rock mass
Matematičeskoe modelirovanie, Tome 33 (2021) no. 2, pp. 93-108

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The article considers the adjustment of parameters for the heat transfer model in a rock mass in the conditions of its artificial freezing. Adjustment of the model parameters according to the temperature measurements of the rock mass in the control-thermal wells is made by solving the coefficient inverse Stefan problem. The statement of the inverse Stefan problem is presented, and a numerical algorithm for its solution is proposed and implemented. The numerical algorithm is based on iterative minimization of the smoothing functional of the mismatch between the measured and calculated temperatures in control-thermal wells. The properties of the smoothing functional in the phase space of the rock thermophysical properties and peculiarities of selection of smoothing functional parameters are studied.
Keywords: artificial ground freezing, frozen wall, inverse Stefan problem, mathematical model, model parameterization, Tikhonov regularization. 
@article{MM_2021_33_2_a6,
     author = {M. A. Semin and A. V. Zaitsev and L. Y. Levin},
     title = {Numerical solution of the inverse {Stefan} problem in the analysis of artificial freezing of rock mass},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {93--108},
     publisher = {mathdoc},
     volume = {33},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_2_a6/}
}
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M. A. Semin; A. V. Zaitsev; L. Y. Levin. Numerical solution of the inverse Stefan problem in the analysis of artificial freezing of rock mass. Matematičeskoe modelirovanie, Tome 33 (2021) no. 2, pp. 93-108. http://geodesic.mathdoc.fr/item/MM_2021_33_2_a6/