In this work, a free energy based lattice-Boltzmann method (LBM) [1] for simulating phase-change
process driven by temperature difference without lattice-unity conversion is proposed. For this pur-
pose, two lattice-Boltzmann equations (LBE) are used: one for modeling the full Navier-Stokes (NS)
equations and another for modeling the energy equation written in terms of the temperature and spe-
cific heat at constant volume. To fully recover the non-ideal effects inherent to multi-phase systems,
the Korteweg stress tensor was introduced into the hydrodynamic LBE as a forcing term through
the grad-P approach. In the thermal LBE, the compressibility effects are derived from the equation
of state (EoS) following its thermodynamic description, while viscous heating effects are assumed to
be negligible. By disregarding the lattice-unity conversion the EoS parameters were fitted to match
real fluids, thus approaching realistic conditions, in addition, by directly discretizing the domain, the
method was stabilized by a mesh refinement procedure. To precisely validate the proposed model,
theoretical problems with known solutions were studied, especially the one-dimensional Neumann
problem, with the proposed approach presenting a good agreement between the solutions, as shown
in Fig. 1.

Neumman problem.,lattice-Boltzmann method,free energy,phase-change,temperature difference