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Mathematical notes of NEFU, 2017, Volume 24, Issue 3, Pages 19–37 (Mi svfu188)  

Mathematical modeling

Models of thermoelasticity for porous materials with fractures taken into account

V. N. Alekseev, M. V. Vasil'eva, G. A. Prokop'ev, A. A. Tyrylgin

M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 48 Kulakovsky Street, Yakutsk 677891, Russia

Abstract: We propose a mathematical model and a computational algorithm for solving thermoelasticity problems in fractured porous media. To simulate heat transfer in porous media, a mathematical model is constructed using double diffusion models. The heat transfer in the cracks is taken into account by setting the interface condition which allows modeling the temperature jump at the crack boundary. To calculate the stress-strain state, a linear elasticity model is used with an additional condition on the crack. For the numerical solution of the problem an approximation is constructed using the Galerkin discontinuous method which allows taking into account the interface condition in the variational formulation. We present the results of the numerical realization of the model problem using the proposed model of thermoelasticity.

Keywords: thermoelasticity, fracture, porous medium, fuel element, double diffusion model, interface condition, discontinuous Galerkin method, numerical simulation.

Funding Agency Grant Number
Russian Science Foundation 17-71-20055
Ministry of Education and Science of the Russian Federation MK-9613.2016
MK-9613.2016.1
14.Y26.31.0013
V. N. Alekseev was supported by the Presidential Grant MKЦ9613.2016.1. M. V. Vasilyeva was supported by the Russian Science Foundation (Grant 17Ц71Ц20055) and by the Presidential Grant MKЦ9613.2016. G. A. Prokopiev and A. A. Tyrylgin were supported by the Government of Russian Federation Megagrant No. 14.Y26.31.0013.


DOI: https://doi.org/10.25587/SVFU.2018.3.10887

Full text: PDF file (5821 kB)
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UDC: 519.63
Received: 22.08.2017

Citation: V. N. Alekseev, M. V. Vasil'eva, G. A. Prokop'ev, A. A. Tyrylgin, “Models of thermoelasticity for porous materials with fractures taken into account”, Mathematical notes of NEFU, 24:3 (2017), 19–37

Citation in format AMSBIB
\Bibitem{AleVasPro17}
\by V.~N.~Alekseev, M.~V.~Vasil'eva, G.~A.~Prokop'ev, A.~A.~Tyrylgin
\paper Models of thermoelasticity for porous materials with fractures taken into account
\jour Mathematical notes of NEFU
\yr 2017
\vol 24
\issue 3
\pages 19--37
\mathnet{http://mi.mathnet.ru/svfu188}
\crossref{https://doi.org/10.25587/SVFU.2018.3.10887}
\elib{https://elibrary.ru/item.asp?id=32651433}


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