A Two-Dimensional Lattice Boltzmann Scheme for Analyzing Equilibrium States in a Two-Fluid-Phase Porous Medium System

Lattice Boltzmann methods (LBMs) are routinely used to simulate fluid flow in porous medium systems. Recently LBMs have been used to study both the dynamics and equilibrium states in two-fluid-phase systems. We illustrate that true equilibrium involves changes in fluid pressures, interfacial areas, and interfacial curvatures. We further show that the approach to an equilibrium state involves a relatively slow process in which fluid interfaces relax to their equilibrium state and that the time scale of this process makes accurate and complete resolution of equilibrium states computationally expensive. Motivated by this bifurcated physical process, we illustrate a temporally adaptive domain decomposition algorithm based upon level-set methods that enables the accurate simulation of equilibrium states with a considerable savings in computational costs compared to standard approaches.