# Models of thermoelasticity for porous materials with fractures taken into account

• Alekseev Valentin N., alekseev.valen@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
• Vasilyeva Maria V., vasilyevadotmdotv@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
• Prokopiev Grigorii A., reilroot@gmail.com M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
• Tyrylgin Aleksey A., kocglk@mail.ru M. K. Ammosov North-Eastern Federal University, Institute of Mathematics and Informatics, 42 Kulakovsky Street, Yakutsk 677000, Russia
Keywords: thermoelasticity, fracture, porous medium, fuel element, double diffusion model, interface condition, discontinuous Galerkin method, numerical simulation

### 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.

### References

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How to Cite
Alekseev, V., Vasilyeva, M., Prokopiev, G. and Tyrylgin, A. (2017) “Models of thermoelasticity for porous materials with fractures taken into account”, Mathematical notes of NEFU, 24(3), pp. 19-37. doi: https://doi.org/10.25587/SVFU.2018.3.10887.
Issue
Section
Mathematical Modeling