Abstract
In this paper, we compare two families of Lattice Boltzmann (LB) 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 quadrature. 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 (kn) up to 0.25.
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