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A Lattice Boltzmann Model for the Reaction-Diffusion Equations with Higher-Order Accuracy

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Abstract

In this paper, a lattice Boltzmann model based on the higher-order moment method for the reaction-diffusion equations is proposed. In order to obtain higher-order accuracy of truncation error and to overcome the drawbacks of “error rebound” in the previous models, a new assumption of additional distribution is presented. As results, the reaction-diffusion equations are recovered with the fourth-order accuracy of truncation error. Based on this model, the Fitzhugh-Nagumo equations are simulated. The comparisons between the LBM results and the Alternative Direction Implicit (ADI) results are given in detail. The numerical examples show that the higher-order moment method can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the reaction-diffusion equations.

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Authors and Affiliations

  1. College of Engineering, Peking University, Beijing, 100871, P.R. China

    Jianying Zhang

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

    Guangwu Yan

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  1. Jianying Zhang
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  2. Guangwu Yan
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Correspondence to Guangwu Yan.

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Zhang, J., Yan, G. A Lattice Boltzmann Model for the Reaction-Diffusion Equations with Higher-Order Accuracy. J Sci Comput 52, 1–16 (2012). https://doi.org/10.1007/s10915-011-9530-2

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