A higher-order moment method of the lattice Boltzmann model for the Korteweg‐de Vries equation

A higher-order moment method of the lattice Boltzmann model for the Korteweg‐de Vries equation

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Article ID: iaor201527006
Volume: 79
Issue: 5
Start Page Number: 1554
End Page Number: 1565
Publication Date: Jan 2009
Journal: Mathematics and Computers in Simulation
Authors: ,
Keywords: error analysis, stability, partial differential equations (PDE)
Abstract:

In this paper, a lattice Boltzmann model for the Korteweg–de Vries (KdV) equation with higher‐order accuracy of truncation error is presented by using the higher‐order moment method. In contrast to the previous lattice Boltzmann model, our method has a wide flexibility to select equilibrium distribution function. The higher‐order moment method bases on so‐called a series of lattice Boltzmann equation obtained by using multi‐scale technique and Chapman–Enskog expansion. We can also control the stability of the scheme by modulating some special moments to design the dispersion term and the dissipation term. The numerical example shows the higher‐order moment method can be used to raise the accuracy of truncation error of the lattice Boltzmann scheme.

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