NUMERICAL SIMULATION OF THE TIME FRACTIONAL THERMOPOROELASTICITY PROBLEM USING ONLINE GENERALIZED MULTISCALE FINITE ELEMENT METHOD

Abstract

This paper considers the time of fractional derivatives thermoporoelasticity in a fracture and heterogeneous media. The mathematical model is formulated as a related system of equations that regulate the pressure of the fluid, temperature and mechanical displacement. We use the finite element method (FEM) with a fine mesh for spatial sampling integrated with a discrete fracture model (DFM) to capture the complexity of fractures in the heterogeneous media. Temporary sampling is achieved using an implicit scheme of final differences. To increase the effectiveness of computing technology, we use the Generalized Multiscale Finite Element Method (GMSFEM) for coarse grid approximation, effectively reducing the dimension of the problem while maintaining accuracy. A multiscale approach uses precalculated offline functions and dynamically updated online functions to process local residues, ensuring a rapid decrease in errors. Numerical experiments demonstrate the ability of the method to accurately imitate the temporal processes in a fractured porous media, reaching significant computing savings without lowering the accuracy of the solution.