Vibrational-vibrational energy transfer between the modes of diatomic molecules for simulating nonequilibrium gas flows

Implementation of the Candler model of vibrational-vibrational energy transfer between diatomic molecules in an inelastic collision is discussed. An example of oxygen O$_2$ and nitrogen N$_2$ interaction is used to analyze the method of simple iterations, the Newton method, the method of bisection, and the approximate formula for calculating the equilibrium vibrational temperature, which is necessary in the Candler model. The method recommended for simulations is the Newton method or bisection. The model of vibrational-vibrational energy transfer is tested by examples of zero-dimensional vibrational relaxation, the flow around a cylinder, and the flow in a wedge-shaped nozzle. It is demonstrated that vibrational-vibrational energy transfer affects the distribution of vibrational temperatures.