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

Authors:
Lina Ye;Guangwu Yan;Tingting Li
Affiliations:
College of Mathematics, Jilin University, Changchun, P.R. China 130012;College of Mathematics, Jilin University, Changchun, P.R. China 130012;College of Mathematics, Jilin University, Changchun, P.R. China 130012
Venue:
Journal of Scientific Computing
Year:
2011

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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.