Implementation of fundamental equations of state in a lattice Boltzmann model

In the pseudopotential lattice Boltzmann (LB) model, the physical behaviors of fluids are modeled through interparticle forces, which are closely tied to the equation of state (EOS). Existing simulations mainly rely on cubic EOS, which significantly lags behind modern multiparameter EOS in terms of the prediction of thermodynamic properties. However, there have been no reports on the application of such a high-precision EOS in LB simulations. In this study, a method for implementing fundamental equations of state in Helmholtz energy form (HEOS) in the LB framework is proposed. A novel unit conversion approach is developed, which enables the appropriate conversion of all information between lattice and physical units, overcoming the limitations of existing methods that fail to correctly convert energy information. This approach allows the direct conversion of the pressure between the lattice and physical units without the need to specify the lattice unit values for each parameter in the equation of state. The HEOS of water is used as an example to validate the feasibility of the proposed method and unit conversion approach. The average error of liquid–vapor coexistence densities obtained from the LB simulations using the HEOS is 0.46%, significantly lower than 22.5% by using the typical cubic Peng–Robinson (PR) EOS. Although the computational resource consumption tripled that of the PR EOS, the incorporation of HEOS demonstrated much stronger capabilities in simulations with phase-change phenomena, accurately predicting the specific latent heat of water in film evaporation from 100 to 341.6 °C where the one with PR EOS failed.