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The simulation and visualization of geodynamical processes poses a major challenge for due to spatial and time scales spanning many orders of magnitude and highly nonlinear phenomena. Modeling and solving such processes are necessary in order to accurately predict changes in natural systems. Two-phase models of fluid flow in deformable porous media are widely used to explain the various processes that occur in the Earths interior and subsurface. However, thermal processes, especially volume changes caused by thermal expansion, are typically ignored. In this study, numerical simulation methods were used to describe a mathematical model of heat transfer processes in a porous media. The purpose of these studies is to determine the influence of nondimensional parameters (Rayleigh numbers) on the convection regimes (free and porous convections). To study these problems, numerical modeling of a nonlinear thermo-hydro-mechanical processes in porous materials filled with a fluid under gravity. The finite difference staggered grid discretization and a graphics processing unit based pseudo-transient solver are utilized in the numerical simulation. We perform systematic numerical simulations and dimensional analysis to classify the regimes of convection.
Antonenko et al. (Sat,) studied this question.