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Numerical Method Based on the Lattice Boltzmann Model for the Kuramoto-Sivashinsky Equation

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Abstract

In this paper, we proposed a lattice Boltzmann model based on the higher-order moment method for the Kuramoto-Sivashinsky equation. A series of partial differential equations obtained by using multi-scale technique and Chapman-Enskog expansion. According to Hirt’s heuristic stability theory, the stability of the scheme can be controlled by modulating some special moments to design the fifth-order dispersion term and the sixth-order dissipation term. As results, the Kuramoto-Sivashinsky equation is recovered with higher-order truncation error. The numerical examples show the higher-order moment method can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the Kuramoto-Sivashinsky equation.

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Authors and Affiliations

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

    Lina Ye, Guangwu Yan & Tingting Li

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  1. Lina Ye
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  2. Guangwu Yan
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  3. Tingting Li
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Corresponding author

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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Ye, L., Yan, G. & Li, T. Numerical Method Based on the Lattice Boltzmann Model for the Kuramoto-Sivashinsky Equation. J Sci Comput 49, 195–210 (2011). https://doi.org/10.1007/s10915-010-9455-1

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  • DOI: https://doi.org/10.1007/s10915-010-9455-1

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