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A higher-order moment method of the lattice Boltzmann model for the conservation law equation
Authors:Yinfeng Dong   Jianying Zhang  Guangwu Yan  
Affiliation:aCollege of Mathematics, Jilin University, Changchun 130012, PR China
Abstract:
In this paper, we proposed a higher-order moment method in the lattice Boltzmann model for the conservation law equation. In contrast to the lattice Bhatnagar–Gross–Krook (BGK) model, the higher-order moment method has a wide flexibility to select equilibrium distribution function. This method is based on so-called 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 third-order dispersion term and the fourth-order dissipation term. As results, the conservation law 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 conservation law equation.
Keywords:Lattice Boltzmann model   Higher-order moment method   Conservation law equation
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