A lattice Boltzmann equation method for real fluids with the equation of state known in tabular form only in regions of liquid and vapor phases

We propose several simple interpolations of the isotherms for real fluids in the region below the binodal curve, where data concerning the equation of state is absent, especially in the thermodynamically prohibited region. All interpolations satisfy the boundary conditions at the points on the binodal curve. The Maxwell rule is also fulfilled. As an example, we construct several isotherms for real water. The data for the isotherms of water, in the liquid and vapor states, is given in tabular form. All smooth interpolations of the isotherms show similar hydrodynamic behavior of two-phase systems in LBE simulations. The reduced specific volumes of the liquid and vapor phases and the reduced pressure on the binodal curve obtained in the LBE simulations for the different interpolations agree well with the experimental data for real EOS of water. The surface tension depends on the form of the interpolation of the isotherm under the binodal curve. Hence, the value of surface tension can be varied in some range by changing the interpolation curve. Actually, our variant of the LBE method allows one to obtain the values of the liquid and vapor densities at the interface corresponding to the saturation curve of real fluids with high accuracy. At low temperatures, the large values of the liquid-to-vapor density ratio can be obtained, in accordance with the EOS of real fluids.