A recently developed model of vibrational relaxation is applied to the study of strongly non-equilibrium flows of nitrogen and air. The model is implemented in the DLR-TAU solver and assessed in a wide range of conditions. Also implemented is a modification of the Treanor-Marrone model for non-equilibrium dissociation, along with Arrhenius law-style fits for the equilibrium rates obtained from quasi-classical trajectory simulations. Results of computations show that the new models give better agreement with experimental data than the widely used combination of the Landau-Teller and Park models.