A new approach of the Ellipsoidal Statistical Model

Stéphane Brull (1) , Jacques Schneider (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ANLA - Laboratoire d'Analyse Non Linéaire Appliquée

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].

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Stéphane Brull, Jacques Schneider. A new approach of the Ellipsoidal Statistical Model. Continuum Mechanics and Thermodynamics, 2008. ⟨hal-01934311⟩