Study of single-component two-phase free energy lattice Boltzmann models using various equations of state

Abstract

In single-component two-phase flow simulations by the lattice Boltzmann method (LBM), one key topic of interest is the equation of state (EOS), which has been studied more in the pseudo-potential approach but much less in the free energy approach. Here, we conducted fair assessment of several popular non-ideal gas EOS in free energy LBM. The inability to independently tune the surface tension and interface thickness was identified for existing free energy formulation using most EOS. A simple modification was proposed and incorporated into three free energy LBM models, including the pressure tensor model, Lee–Fischer's model, and Guo's well-balanced model. Good compatibility with all of them was demonstrated by numerical simulations. In addition, a piecewise-linear (PWL) EOS proposed in pseudo-potential LBM was found to be also feasible in free energy LBM. Extensive numerical experiments on diverse problems (some containing contact lines) revealed that the influence of EOS was rather limited when key parameters are nearly the same (easily achievable with the proposed modification). The capability of the Lee–Fischer and well-balanced models to reduce the spurious currents down to machine accuracy (for static drop tests) was found to be independent of the EOS (including the customized PWL EOS). Overall, the pressure tensor LBM is associated with larger spurious currents and deviations in the density and chemical potential, thus less accurate than the other two. However, it is less sensitive to the relaxation parameter and grid number, thus more robust.