On equations of state in a lattice Boltzmann method

We investigate the use of various equations of state (EOS) in the single-component multiphase lattice Boltzmann model. Several EOS are explored: van der Waals, Carnahan–Starling and Kaplun–Meshalkin EOS [A.B. Kaplun, A.B. Meshalkin, Thermodynamic validation of the form of unified equation of state for liquid and gas, High Temperature 41 (3) (2003) 319–326]. The last one was modified in order to obtain the correct critical point. The Carnahan–Starling and modified Kaplun–Meshalkin EOS are in better agreement with the experimental data on coexistence curves than the van der Waals EOS.It is shown that the approximation of the gradient of special potential is crucial to obtain the correct coexistence curve, especially its low-density part. The correct method of incorporating the body forces into the lattice Boltzmann model is also very important. We propose a new scheme which allows us to obtain large density ratio (up to 109 in the stationary case) and to reproduce the coexistence curve with high accuracy. The spurious currents at vapor–liquid interface are also greatly reduced.