A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and...

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Bibliographic Details
Main Authors: Qiaojie Li, Zhoushun Zheng, Shuang Wang, Jiankang Liu
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/925920
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Summary:An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmann method. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. The L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.
ISSN:1110-757X
1687-0042