Lattice-Boltzmann algorithm for simulating thermal two-phase flow

An algorithm is described for incorporating thermal effects into lattice-Boltzmann simulations of two-phase flow. This algorithm is a combination of a two-distribution model for simulating single-phase thermal flow recently proposed by the authors and the thermodynamically-based model for isothermal two-phase flow of Swift et al. [Phys. Rev. E 54, 5041 (1996)]. The algorithm also corrects a problem with the original single-phase thermal flow model, which described the thermal energy flux as proportional to a gradient of the internal energy instead of being proportional to the gradient of the temperature. For ideal-gas systems, these two descriptions are equivalent but for nonideal systems there is a systematic discrepancy between the original thermal model and classical hydrodynamics. The algorithm is tested on several simple problems. These include formation of a free-standing isothermal thin liquid film, evaporation of a thin liquid film from a heated plate, evaporation of an isolated droplet, and condensation of liquid in a channel. Where possible, the simulations are compared against known analytic results.