Thermal Enskog-Vlasov Lattice Boltzmann model with phase separation

An Enskog-Vlasov finite-difference Lattice Boltzmann (EV-FDLB) for liquid–vapor systems with variable temperature is introduced. The model involves both the simplified Enskog collision operator and the self-consistent force field which accounts for the long-range interaction between the fluid particles. Full-range Gauss–Hermite quadratures were used for momentum space discretization. The numerical solutions of the Enskog-Vlasov equation obtained employing the EV-FDLB model and the Direct Simulation Monte Carlo-like particle method are compared. Furthermore, we present two implementations of the self-consistent force field evaluation in the EV-FDLB model, one involving the full integral and one using an approximation of the integral, denoted EV1 and EV2, respectively. Reasonable agreement is found between the three approaches when simulating the liquid–vapor phase separation and the liquid slab evaporation. The EV2 method maintains interface profile errors within 5% while reducing computational cost by approximately 60%–70% with respect to EV1.