“…Therefore, compared with the conventional thermochemical non-equilibrium models, the collisional-radiative model can more reasonably predict the energy relaxation processes, chemical non-equilibrium and excited energy levels non-equilibrium phenomena. At present, the collisional-radiative model is usually implemented in zero-dimensional (0-D) (Teulet, Sarrette & Gomes 2001;Bultel et al 2006;Capitelli et al 2007;Annaloro & Bultel 2014) and one-dimensional (1-D) models (Panesi et al 2009;Campoli et al 2020;Du et al 2022), but has not been used in multi-dimensional flow calculations so far due to its intensive computational cost, and some simplification methods, such as the multi-group maximum entropy method, were proposed for simplifying the CR model for future coupling to multi-dimensional computational fluid dynamics (CFD) simulation (Liu et al 2015;Munafo, Liu & Panesi 2015;Munafo, Mansour & Panesi 2017;Sahai et al 2017Sahai et al , 2019Sahai et al , 2020Sharma, Liu & Panesi 2020). The 0-D calculations of the air collisional-radiative model for typical re-entry conditions indicated that the distributions of chemical species exhibit large differences from the results obtained by the global air chemical models (Bultel et al 2006;Annaloro & Bultel 2014).…”