  We propose two models of the Boltzmann equation (BGK and Fokker-Planck
models) for rarefied flows of diatomic gases in vibrational non-equilibrium.
These models take into account the discrete repartition of vibration energy
modes, which is required for high temperature flows, like for atmospheric
re-entry problems. We prove that these models satisfy conservation and entropy
properties (H-theorem), and we derive their corresponding compressible
Navier-Stokes asymptotics.
