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Lattice Boltzmann Model Based on the Rebuilding-Divergency Method for the Laplace Equation and the Poisson Equation

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Abstract

In this paper, a new lattice Boltzmann model based on the rebuilding-divergency method for the Poisson equation is proposed. In order to translate the Poisson equation into a conservation law equation, the source term and diffusion term are changed into divergence forms. By using the Chapman-Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales and several higher-order moments of equilibrium distribution functions are obtained. Thus, by rebuilding the divergence of the source and diffusion terms, the Laplace equation and the Poisson equation with the second accuracy of the truncation errors are recovered. In the numerical examples, we compare the numerical results of this scheme with those obtained by other classical method for the Green-Taylor vortex flow, numerical results agree well with the classical ones.

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Authors and Affiliations

  1. College of Mathematics, Jilin University, Changchun, 130012, P.R. China

    Huimin Wang, Guangwu Yan & Bo Yan

  2. College of Applied Mathematics, Jilin University of Finance and Economics, Changchun, 130117, P.R. China

    Huimin Wang

Authors
  1. Huimin Wang
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  2. Guangwu Yan
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  3. Bo Yan
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Correspondence to Guangwu Yan.

Additional information

This work is Project 20092005 supported by Graduate Innovation Fund of Jilin University and the Chuangxin Foundation of Jilin University (No. 2004CX041).

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Wang, H., Yan, G. & Yan, B. Lattice Boltzmann Model Based on the Rebuilding-Divergency Method for the Laplace Equation and the Poisson Equation. J Sci Comput 46, 470–484 (2011). https://doi.org/10.1007/s10915-010-9414-x

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