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Numerical Studies Based on Higher-Order Accuracy Lattice Boltzmann Model for the Complex Ginzburg-Landau Equation

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Abstract

In this paper, a higher-order accuracy lattice Boltzmann model for the complex Ginzburg-Landau equation 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 to improve the accuracy of the model for the complex partial differential equation with nonlinear source term. As results, the complex Ginzburg-Landau equation is recovered with the fourth-order accuracy of truncation error. Based on this model, the problems of a single spiral wave in two-dimensional (2D) space and a single scroll in three-dimensional (3D) space are implemented to test the lattice Boltzmann scheme. The comparisons between the LBM results and the Alternative Direction Implicit results are given in detail. The numerical examples show that assumptions of source term can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the complex Ginzburg-Landau equation.

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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. Numerical Studies Based on Higher-Order Accuracy Lattice Boltzmann Model for the Complex Ginzburg-Landau Equation. J Sci Comput 52, 656–674 (2012). https://doi.org/10.1007/s10915-011-9565-4

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