A new approach of the Ellipsoidal Statistical Model
Résumé
In this paper we aim to introduce a systematic way to derive relaxation terms for the Boltzmann equation based under minimization problem of the entropy under moments constraints [7], [11]. 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 the order 2 in the velocity v and recover the Ellipsoidal Statistical model [8].
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