This work demonstrates that in advection–diffusion Lattice Boltzmann schemes, the local mass-conserving boundary rules, such as bounce-back and local specular reflection, may modify the transport coefficients predicted by the Chapman–Enskog expansion when they enforce to zero not only the normal, but also the tangential boundary flux. In order to accommodate it to the bulk solution, the system develops a Knudsen-layer correction to the non-equilibrium part of the population solution. Two principal secondary effects—(i) decrease in the diffusion coefficient, and (ii) retardation of the average advection velocity, obtained in a closed analytical form, are proportional, respectively, to freely assigned diagonal weights for equilibrium mass and velocity terms. In addition, due to their transverse velocity gradients, the boundary layers affect the longitudinal diffusion coefficient similarly to Taylor dispersion, as they grow as the square of the Péclet number. These numerical artifacts can be eliminated or reduced by a proper space distribution of the free-tunable collision eigenvalue in two-relaxation-time schemes.
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Irina Ginzburg 1; Laetitia Roux 1; Goncalo Silva 1
@article{CRMECA_2015__343_10-11_518_0,
author = {Irina Ginzburg and Laetitia Roux and Goncalo Silva},
title = {Local boundary reflections in lattice {Boltzmann} schemes: {Spurious} boundary layers and their impact on the velocity, diffusion and dispersion},
journal = {Comptes Rendus. M\'ecanique},
pages = {518--532},
publisher = {Elsevier},
volume = {343},
number = {10-11},
year = {2015},
doi = {10.1016/j.crme.2015.03.004},
language = {en},
}
TY - JOUR AU - Irina Ginzburg AU - Laetitia Roux AU - Goncalo Silva TI - Local boundary reflections in lattice Boltzmann schemes: Spurious boundary layers and their impact on the velocity, diffusion and dispersion JO - Comptes Rendus. Mécanique PY - 2015 SP - 518 EP - 532 VL - 343 IS - 10-11 PB - Elsevier DO - 10.1016/j.crme.2015.03.004 LA - en ID - CRMECA_2015__343_10-11_518_0 ER -
%0 Journal Article %A Irina Ginzburg %A Laetitia Roux %A Goncalo Silva %T Local boundary reflections in lattice Boltzmann schemes: Spurious boundary layers and their impact on the velocity, diffusion and dispersion %J Comptes Rendus. Mécanique %D 2015 %P 518-532 %V 343 %N 10-11 %I Elsevier %R 10.1016/j.crme.2015.03.004 %G en %F CRMECA_2015__343_10-11_518_0
Irina Ginzburg; Laetitia Roux; Goncalo Silva. Local boundary reflections in lattice Boltzmann schemes: Spurious boundary layers and their impact on the velocity, diffusion and dispersion. Comptes Rendus. Mécanique, Lattice Boltzmann methods for solving problems in mechanics / Méthodes de Boltzmann sur réseau pour la résolution de problèmes de mécanique, Volume 343 (2015) no. 10-11, pp. 518-532. doi : 10.1016/j.crme.2015.03.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.03.004/
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