Lattice-Boltzmann model for van der Waals fluids with liquid-vapor phase transition

A B S T R A C T A lattice Boltzmann model (LBM) for two-phase flows with liquid-vapor phase transition based on a dy-namic van der Waals theory [Phys. Rev. Lett. 94, 054501 (2005)] is proposed. The proposed model con-sists of two lattice Boltzmann equations (LBE): one for the Navier-Stokes-Korteweg (NSK) equations and the other for the temperature equation. In the thermal LBE, the equilibrium distribution function is re-designed by introducing a reference temperature, which is used to reduce the numerical errors of velocity divergence in the thermal LBE. A free-energy-based LBE is developed for the hydrodynamic equations and a novel force term is used to correctly recover the NSK equations. Several numerical simulations, includ-ing the liquid-vapor coexistence curve, phase separation, stationary droplet, droplet on partially wetting surface, droplet evaporation and bubble nucleate and departure, are conducted to validate the capability and performance of the present model. The numerical results of the proposed model are found to be in excellent agreement with the results of theoretical and/or the hybrid method. It is also shown that nu-merical stability and accuracy of the present models can be greatly improved by adjusting the reference temperature. The present models provide an effective predictive tool for two-phase flows involving phase change. (c) 2021 Elsevier Ltd. All rights reserved.