  We propose an extension of the Ellipsoidal-Statistical BGK model to account
for discrete levels of vibrational energy in a rarefied polyatomic gas. This
model satisfies an H-theorem and contains parameters that allow to fit almost
arbitrary values for the Prandtl number and the relaxation times of rotational
and vibrational energies. With the reduced distribution technique , this model
can be reduced to a three distribution system that could be used to simulate
polyatomic gases with rotational and vibrational energy for a computational
cost close to that of a simple monoatomic gas.
