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Volume 2, Issue 5
Analytical Solution for the Lattice Boltzmann Model Beyond Naviers-Stokes

Jianping Meng & Yonghao Zhang

DOI: 10.4208/aamm.10-10S09

Adv. Appl. Math. Mech., 2 (2010), pp. 670-676.

Published online: 2010-02

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  • Abstract

To understand lattice Boltzmann model capability for capturing non-equilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer.

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@Article{AAMM-2-670, author = {Meng , Jianping and Zhang , Yonghao}, title = {Analytical Solution for the Lattice Boltzmann Model Beyond Naviers-Stokes}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2010}, volume = {2}, number = {5}, pages = {670--676}, abstract = {

To understand lattice Boltzmann model capability for capturing non-equilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-10S09}, url = {http://global-sci.org/intro/article_detail/aamm/8353.html} }
TY - JOUR T1 - Analytical Solution for the Lattice Boltzmann Model Beyond Naviers-Stokes AU - Meng , Jianping AU - Zhang , Yonghao JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 670 EP - 676 PY - 2010 DA - 2010/02 SN - 2 DO - http://doi.org/10.4208/aamm.10-10S09 UR - https://global-sci.org/intro/article_detail/aamm/8353.html KW - AB -

To understand lattice Boltzmann model capability for capturing non-equilibrium effects, the model with first-order expansion of the equilibrium distribution function is analytically investigated. In particular, the velocity profile of Couette flows is exactly obtained for the D2Q9 model, which shows retaining the first order expansion can capture rarefaction effects in the incompressible limit. Meanwhile, it clearly demonstrates that the D2Q9 model is not able to reflect flow characteristics in the Knudsen layer.

Jianping Meng & Yonghao Zhang. (1970). Analytical Solution for the Lattice Boltzmann Model Beyond Naviers-Stokes. Advances in Applied Mathematics and Mechanics. 2 (5). 670-676. doi:10.4208/aamm.10-10S09
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