Multiscale modeling of coupled thermo-hydro-mechanical analysis of heterogeneous porous media

This paper presents a numerical multiscale formulation for analysis of the transient heat and fluid flow in deformable heterogeneous porous media. Due to the heterogeneity of the media, the direct numerical simulation of the micro-structures leads to high computational costs. Hence, the multi-scale method can provide an efficient computational procedure. To this end, the first-order computational homogenization is adopted for two-scale simulation of THM problems. The governing equations of the problem contain a stress equilibrium equation, a mass continuity equation and an advection–diffusion equation in a fully coupled manner. Accordingly, the proper virtual power relations are defined as a bridging stage between the scales. The boundary conditions of the microscopic domain are specified in terms of the macroscopic information to fulfill the averaging constraints. In order to consider the transient effects, the micro-inertial terms are included in the micro-scale simulation, and then the microscopic boundary conditions are enhanced to assess the efficiency and accuracy. The macroscopic properties including the homogenized tangent operators and equivalent quantities are determined from the microscopic solution through the appropriate mathematical procedures. Moreover, an upwind finite element squared method is employed for highly advective heat transfer to achieve the accurate spatial results. Finally, several comprehensive examples are simulated to study the effectiveness and validity of the proposed computational model, particularly the boundary conditions; moreover, different case studies are discussed such as the highly advective flow, pure conduction heat transfer and a combined conduction–convection heat transfer. •A two-scale method is developed for transient heat and fluid flow in porous media.•Advection-diffusion equation is adopted to account for heat transfer phenomenon.•Micro-inertial terms are included in the micro-scale analysis.•The microscopic boundary conditions are enhanced to assess the accuracy.•An upwind FE2 is employed for highly advective heat transfer.