Models of thermoelasticity for porous materials with fractures taken into account

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.