A Pseudopotential Lattice Boltzmann Analysis for Multicomponent Flow

Abstract

This paper presents a pseudopotential lattice Boltzmann analysis to show the deficiency of previous pseudopotential models, i.e., inconsistency between equilibrium velocity and mixture velocity. To rectify this problem, there are two strategies: decoupling relaxation time and kinematic viscosity or introducing a system mixture relaxation time. Then, we constructed two modified models: a two-relaxation-time (TRT) scheme and a triple-relaxation-time (TriRT) scheme to decouple the relaxation time and kinematic viscosity. Meanwhile, inspired by the idea of a system mixture relaxation time, we developed three mixture models under different collision schemes, viz. mix-SRT, mix-TRT, and mix-TriRT models. Afterwards, we derived the advection-diffusion equation for the multicomponent system and derived the mutual diffusivity in a binary mixture. Finally, we conducted several numerical simulations to validate the analysis on these models. The numerical results show that these models can obtain smaller spurious currents than previous models and have a wider range for the accessible viscosity ratio with fourth-order isotropy. Compared to previous models, present models avoid complex matrix operations and only fourth-order isotropy is required. The increased simplicity and higher computational efficiency of these models make them easy to apply to engineering and industrial applications.