GAUSS QUADRATURES – THE KEYSTONE OF LATTICE BOLTZMANN MODELS

Benjamin Piaud (), Stéphane Blanco (), Richard Fournier (), Victor Eugen Ambruş () and Victor Sofonea ()
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Benjamin Piaud: HPC – SA, 3 Chemin du Pigeonnier de la Cepière, F – 31100 Toulouse, France
Stéphane Blanco: Université de Toulouse, UPS, INPT; GREPHE/Laboratorie Plasma et Conversion d' Energie, UMR 5213, 118 Route de Narbonne, F – 31062 Toulouse Cedex 9, France
Richard Fournier: Université de Toulouse, UPS, INPT; GREPHE/Laboratorie Plasma et Conversion d' Energie, UMR 5213, 118 Route de Narbonne, F – 31062 Toulouse Cedex 9, France
Victor Eugen Ambruş: Center for Fundamental and Advanced Technical Research, Romanian Academy, Bd. Mihai Viteazul 24, RO – 300223 Timişoara, Romania
Victor Sofonea: Center for Fundamental and Advanced Technical Research, Romanian Academy, Bd. Mihai Viteazul 24, RO – 300223 Timişoara, Romania

International Journal of Modern Physics C (IJMPC), 2014, vol. 25, issue 01, 1-8

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 theHLB(N;Qx,Qy,Qz)family, derived by using the Cartesian coordinate system and the Gauss–Hermite quadrature. The second one is theSLB(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 orderNof 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.

Keywords: Lattice Boltzmann; Gauss quadrature; microfluidics; Couette flow; 47.11.–j; 47.61.–k; 51.10.+y (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0129183113400160

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