GAUSS QUADRATURES-THE KEYSTONE OF LATTICE BOLTZMANN MODELS

Benjamin Piaud (1) , Stéphane Blanco (2) , Richard A Fournier (2) , Victor Eugen Ambruş , Victor Sofonea (3)

1 Méso-Star
2 LAPLACE-GREPHE - Groupe de Recherche Energétique, Plasmas et Hors Equilibre
3 Romanian Academy

In this paper we compare two families of Lattice-Boltzmann models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N; Qx, Qy, Qz) family, derived by using the Cartesian coordinate system and the Gauss-Hermite quadra-ture. The second one is the SLB(N; K, L, M) family, derived by using the spherical coordinate system and the Gauss-Laguerre, as well as the Gauss-Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number up to 0.25.

Mots clés: Lattice Boltzmann; Gauss quadrature; microfluidics; Couette flow

Domaines: Mécanique statistique [cond-mat.stat-mech]

Benjamin Piaud, Stéphane Blanco, Richard A Fournier, Victor Eugen Ambruş, Victor Sofonea. GAUSS QUADRATURES-THE KEYSTONE OF LATTICE BOLTZMANN MODELS. International Journal of Modern Physics C, 2014, 25 (01), pp.1340016. ⟨10.1142/S0129183113400160⟩. ⟨hal-02025696⟩