Numerical Solution of the Inverse Stefan Problem in the Analysis of the Artificial Freezing of a Rock Mass

The problem of parametrization of a heat transfer model in a rock mass in the conditions of its artificial freezing is considered. To clarify the parameters of the model according to the data of measurements of the temperature of the rock mass in the control-thermal wells, it is proposed to solve St...

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Vydáno v:Mathematical models and computer simulations Ročník 13; číslo 5; s. 877 - 886
Hlavní autoři: Semin, M. A., Zaitsev, A. V., Levin, L. Yu
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.09.2021
Springer Nature B.V
Témata:
Algorithms
Freezing
Inverse problems
Iterative methods
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Parameterization
Parameters
Rock masses
Simulation and Modeling
Smoothing
Thermophysical properties
inverse Stefan problem
artificial ground freezing
mathematical model
Tikhonov regularization
frozen wall
model parameterization
ISSN:2070-0482, 2070-0490
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Shrnutí:The problem of parametrization of a heat transfer model in a rock mass in the conditions of its artificial freezing is considered. To clarify the parameters of the model according to the data of measurements of the temperature of the rock mass in the control-thermal wells, it is proposed to solve Stefan’s coefficient inverse problem. In this study, the formulation of the inverse problem is considered and a numerical algorithm for its solution is proposed and implemented. The numerical algorithm is based on the iterative minimization of the smoothing functional of the mismatch between the measured and calculated temperatures in the control-thermal wells. The properties of the smoothing functional in the phase space of the thermophysical properties of the rock mass and the features of the choice of the parameters of the smoothing functional are investigated.
Bibliografie:ObjectType-Article-1
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ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048221050197