Direct Numerical Simulation of Single and Two-Phase Flows at Pore-Scale

The paper is devoted to numerical techniques for an analysis of single and multiphase fluid flows in the pore space of core samples with direct resolution of the pore space structure. The core of the approach is quasi-hydrodynamic (QHD) regularization of classical Navier-Stokes (1-phase flow) and Navier-Stokes-Cahn-Hilliard (2-phase flow) equations. In essence QHD regularization consists in specific addition of physically based dissipative terms to initial equations. These terms act as stabilizers and allow to use logically simple explicit finite difference schemes with central difference approximations. Moreover, for moderately-rarefied gas flows these terms provide good agreement of obtained numerical results with the experimental data for microflows. A number of simulations demonstrating consistency of the model and algorithms as well as realistic flow simulations within realistic mu-CT models are presented.