Abstract.
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 (fifth-order 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 \(1 \le \Pr \le 5/4\) and for \(\Pr \rightarrow \infty\), while they are linearly unstable for \(2/3 \le \Pr < 1\) and \(5/4 < \Pr < \infty\).
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Communicated by G. Kremer
Received: 29 April 2003, Accepted: 20 June 2003
PACS:
510.10.-y, 47.45.-n
Correspondence to: Y. Zheng
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Zheng, Y., Struchtrup, H. Burnett equations for the ellipsoidal statistical BGK model. Continuum Mech. Thermodyn. 16, 97–108 (2004). https://doi.org/10.1007/s00161-003-0143-3
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DOI: https://doi.org/10.1007/s00161-003-0143-3