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We propose two models of the Boltzmann equation (BGK and Fokker-Planckmodels) for rarefied flows of diatomic gases in vibrational non-equilibrium.These models take into account the discrete repartition of vibration energymodes, which is required for high temperature flows, like for atmosphericre-entry problems. We prove that these models satisfy conservation and entropyproperties (H-theorem), and we derive their corresponding compressibleNavier-Stokes asymptotics.

BGK and Fokker-Planck models of the Boltzmann equation for gases with discrete levels of vibrational energy