Direct simulation Monte Carlo based on the vibrationally state-resolved rotational relaxation model

This study implements a vibrationally state-resolved rotational relaxation model within the direct simulation Monte Carlo (DSMC) framework. The model, which employs an exponential correlation function to characterize rotational energy transition probabilities, is integrated via two approaches: (i) the temperature-dependent rotational collision number Zrot(T) is constructed based on a set of pre-calculated vibrationally state-specific rotational relaxation times; (ii) instead of computing Zrot, the probabilities of the rotational–translational energy exchange are calculated directly in accordance with the vibrationally state-resolved rotational relaxation model based on the statistical inelastic cross section theory. Both approaches yield density and temperature profiles in good agreement with experimental normal shock data over Mach number 1.53–12.7, with the approach (i) offering a significant reduction in computational cost compared to the approach (ii). Compared to the classical Parker and Boyd models, both approaches provide improved predictions of rotational relaxation rates at elevated temperatures. Another contribution of this work is the identification of the precise non-equilibrium regimes where the use of the vibrationally state-resolved model becomes essential. The two-dimensional flat-plate simulations reveal that under conditions of strong vibrational non-equilibrium, neglecting vibrational excitation results in systematically underpredicted rotational–translational relaxation rates, leading to substantial differences in the flow field. In such regimes, the vibrationally state-resolved formulation is required to accurately capture the internal energy relaxation dynamics. These findings provide a practical framework for selecting the appropriate level of modeling detail in DSMC simulations of high-enthalpy flows, enabling a balanced trade-off between predictive accuracy and computational efficiency for engineering applications.