Burnett equations for the ellipsoidal statistical BGK model

In order to discuss the agreement of the ellipsoidal statistical BGK (ES-BGK) model with the Boltzmann equation, Burnett equations are computed by means of the second-order Chapman-Enskog expansion of the ES-BGK model. It is found that the Burnett equations for the ES-BGK model with the correct Prandtl number are identical to the Burnett equations for the Boltzmann equation for Maxwell molecules (fifthorder power potentials). However, for other types of particle interaction, the Boltzmann Burnett equations cannot be reproduced from the ES-BGK model. Furthermore, the linear stability of the ES-BGK Burnett equations is discussed. It is shown that the ES-BGK Burnett equations are linearly stable for Prandtl numbers of 1