Generalized van der Waals equation of state for in-line use in hydrodynamic codes

Basic physical and mathematical properties of one of the simplest generalizations of the van der Waals equation of state (EOS), where the power exponent n in the attractive term is treated as a free parameter, are investigated. The main focus is on the parameter range around the gas-liquid phase transition, and on the possibility of in-line use of the equilibrium EOS branch (based on the Maxwell construction in the phase coexistence region) in one-dimensional (1D) hydrodynamic simulations. Conditions are elucidated for emergence of such flow structures as a 'rarefaction shock' and a 'binodal shelf' in rarefaction waves by unloading of compressed matter into vacuum. The quality of numerical modeling of such structures is illustrated with the 1D Lagrangian code DEIRA.