Generalized Multiscale Finite Element Method for thermoporoelasticity problems in heterogeneous and fractured media

In this paper, we consider the thermoporoelasticity problem in heterogeneous and fractured media. The mathematical model is described by a coupled system of equations for pressure, temperature, and displacements. We apply a multiscale approach to reduce the size of the discrete system. We use a continuous finite element method and a Discrete Fracture Model (DFM) for fine grid approximation. For coarse grid approximation, we apply the Generalized Multiscale Finite Element Method (GMsFEM). The main idea of this method is to calculate multiscale basis functions by solving local spectral problems. We present numerical results for two-and three-dimensional model problems in heterogeneous and heterogeneous fractured media. We calculate relative errors between the reference fine grid solution and the multiscale solution for different numbers of multiscale basis functions. The results show that the proposed method can provide good accuracy with a few degrees of freedom.(C) 2021 Elsevier B.V. All rights reserved.