Multiscale model reduction for the poroelasticity problems using embedded fracture model

Abstract

In this paper, we present the application of an generalized multiscale finite element method in numerical simulation of poroelasticity problems in fractured media. Mathematical model contains a coupled system of equations for displacement and pressure, where for fractures we use an embedded fracture model. The most important feature of mathematical models of poroelasticity is that the equations of the system are coupled. Fine grid approximation is constructed based on the finite element method for the displacements and finite volume approximation for the pressure in fractured media. To construct structured coarse grid approximation a generalized multiscale finite element method is used, where we solve local spectral problem for construction of the multiscale basis functions for displacement and pressures. Numerical results are presented for the two and three-dimensional model problem with different number of the multiscale basis functions. We compute relative L2 error between the multiscale solution with the fine-scale solutions by choosing different numbers of multiscale basis functions.