The variable soft sphere (VSS) molecular model is introduced for both the viscosity and diffusion cross sections (coefficients) to be consistent with those of the inverse-power-law (IPL) or Lennard-Jones (LJ) potential. The VSS model has almost the same analytical and computational simplicity (computation time) as the variable hard sphere (VHS) model in the Monte Carlo simulation of rarefied gas flows. The null-collision Monte Carlo method is used to make comparative calculations for the molecular diffusion in a heat-bath gas and the normal shock wave structure in a simple gas. For the most severe test of the VSS model for the IPL potential, the softest practical model corresponding to the Maxwell molecule is chosen. The agreement in the molecular diffusion and shock wave structure between the VSS model and the IPL or LJ potential is remarkably good.

A reliable set of cross-section parameters of the variable soft sphere (VSS) molecular model is determined for the Monte Carlo simulation of air species from the transport collision integrals or potential parameters provided by Cubley and Mason [Phys. Fluids 18, 1109 (1975)] over the high-temperature range 300–15 000 K. The VSS cross-section parameters for the inverse-power-law potential are also determined from the viscosity coefficients recommended by Maitland and Smith [J. Chem. Eng. Data 17, 150 (1972)] for common species in the low (20–300 K) and high (300–2000 K) temperature ranges.

The null-collision concept is introduced into the direct-simulation Monte Carlo method in the rarefied gas dynamics. The null-collision technique overcomes the principle fault in the time-counter technique and the difficulties in the collision-frequency technique. The computation time required for the null-collision technique is comparable to that for the time-counter technique. Therefore, it is concluded that the null-collision technique is superior to any other existing techniques in the direct-simulation Monte Carlo method.

Monte Carlo direct (test-particle) simulation of rotational and vibrational relaxation and dissociation of diatomic molecules using classical trajectory calculations AIP Conf.Monte Carlo direct simulation of rotational relaxation of nitrogen through high total temperature shock waves using classical trajectory calculations

Calculation of the total scattering cross section for the collision of hard spheres: The atom-diatom case J. Chem. Phys. 93, 2469(1990; 10.1063/1.459027Effect of rotational temperature on the glory undulations in the atom-diatom total collision cross section A set of model cross sections for atom-diatom collisions is presented for use in the Monte Carlo simulation of rarefied real gases and in the master relaxation equation. The elastic and rotationally inelastic cross sections are taken as the variable-soft-sphere and statistical-inelastic-cross-section models, respectively. The vibrationally inelastic and dissociation cross sections are derived by combining the improvement-to-forced-oscillator-impulsive-transfer-semiclassical vibrational transition probability and the weak-vibrational-bias dissociation probability, respectively, with the line-of-centers cross section. The recombination is modeled by the two-step binary collision process with two cross sections for the formation and stabilization of an orbiting pair. Assessment of reality and feasibility of the model cross sections is made by comparing the master-relaxation-equation and Monte Carlo results with available experimental data of the vibrational relaxation time, dissociation rate constant and induction time, and recombination rate constant of oxygen diluted in argon.