A new closure for Grad’s 13 moment equations is presented that adds terms of Super-Burnett order to the balances of pressure deviator and heat flux vector. The additional terms are derived from equations for higher moments by means of the distribution function for 13 moments. The resulting system of equations contains the Burnett and Super-Burnett equations when expanded in a series in the Knudsen number. However, other than the Burnett and Super-Burnett equations, the new set of equations is linearly stable for all wavelengths and frequencies. Dispersion relation and damping for the new equations agree better with experimental data than those for the Navier–Stokes–Fourier equations, or the original 13 moments system. The new equations also allow the description of Knudsen boundary layers.

Recently a new system of field equations for the accurate description of flows in rarefied gases, called regularized 13-moment equations, was obtained by means of a hybrid gas kinetic approach. The first part of this paper discusses the relationship of the new system to classical high-order theories like the Burnett and super-Burnett equations as well as to modified models like the augmented and regularized Burnett equations. In the second part, shock structure calculations with the new theory are presented and compared to direct-simulation Monte Carlo (DSMC) solutions and to solutions of the Burnett models. Owing to additional higher-order dissipation in the system, the profiles are smooth for any Mach number, in contrast to the results of Grad's 13-moment case. The results show reliable quantitative agreement with DSMC simulations for Mach numbers up to $M_{0}\approx 3.0$. The agreement is better for Maxwell molecules than for hard spheres. The results of the augmented Burnett equations are comparable, but these equations are shown to be spatially unstable. Additionally, a validiation procedure for the new equations is presented by investigating the positivity of Grad's distribution function.

A generalization of the classical Hertz-Knudsen and Schrage laws for the evaporation mass and energy fluxes at a liquid-vapor interface is derived from kinetic theory and a simple model for a velocity dependent condensation coefficient. These expressions, as well as the classical laws and simple phenomenological expressions, are then considered for the simulation of recent experiments [G. Fang and C. A. Ward, Phys. Rev. E 59, 419 (1999)]. It is shown that mean condensation and evaporation coefficients in the mass flow influence the results only if they are small compared to unity and that the expression for evaporation mass flow determines the temperature of the liquid. Moreover, it is shown that the expression for evaporation energy flow plays the leading role in determining the interface temperature jump, which can be obtained in good agreement with the experiment from the generalized kinetic theory model and phenomenological approaches, but not from the classical kinetic-theory-based Hertz-Knudsen and Schrage laws. Analytical estimates show that the interface temperature jump depends strongly on the temperature gradient of the vapor just in front of the interface, which explains why much larger temperature jumps are observed in spherical geometry and the experiments as compared to planar settings.