Abstract
In this paper we aim to introduce a systematic way to derive relaxation terms for the Boltzmann equation based on the minimization problem for the entropy under moments constraints (Levermore in J. Stat. Phys. 83:1021–1065, 1996; Schneider in M2AN 38:541–561, 2004). In particular the moment constraints and corresponding coefficients are linked with the eigenfunctions and eigenvalues of the linearized collision operator through the Chapman–Enskog expansion. Then we deduce from this expansion a single relaxation term of BGK type. Here we stop the moments constraints at order two in the velocity v and recover the ellipsoidal statistical model (Holway in Rarefied Gas Dynamics, vol I, pp 193–215, 1966).
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Communicated by H. Spohn
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Brull, S., Schneider, J. A new approach for the ellipsoidal statistical model. Continuum Mech. Thermodyn. 20, 63–74 (2008). https://doi.org/10.1007/s00161-008-0068-y
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DOI: https://doi.org/10.1007/s00161-008-0068-y