Approximation of liquid-vapor phase transition for compressible fluids with tabulated EOS

This Note investigates the approximation of phase change in compressible fluids with complex equation of state (EOS). Assuming a local and instantaneous equilibrium with respect to phasic pressures, temperatures and chemical potentials when both phases are present leads to the classical definition of an equilibrium EOS for the two-phase medium. Unfortunately, there is no explicit expression of the equilibrium EOS in most cases. We propose simple means to approximate the equilibrium EOS when both phases are governed by very general EOS, including tabulated ones. We present a relaxation type numerical algorithm based on this approximation for simulating two-phase flows with phase change.