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We describe in detail a recently proposed lattice-Boltzmann model X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993) for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey nonideal gas equations of state and can undergo a liquid-gas-type phase transition. The model is shown to be momentum conserving. From the microscopic mechanical stability condition, the densities in bulk liquid and gas phases are obtained as functions of a temperaturelike parameter. Comparisons with the thermodynamic theory of phase transitions show that the lattice-Boltzmann-equation model can be made to correspond exactly to an isothermal process. The density profile in the liquid-gas interface is also obtained as a function of the temperaturelike parameter and is shown to be isotropic. The surface tension, which can be changed independently, is calculated. The analytical conclusions are verified by numerical simulations.
Shan et al. (Fri,) studied this question.