Journal of Applied Mathematics
Volume 2012 (2012), Article ID 925920, 13 pages
http://dx.doi.org/10.1155/2012/925920
Research Article

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

Qiaojie Li, Zhoushun Zheng, Shuang Wang, and Jiankang Liu

School of Mathematics and Statistics, Central South University, Changsha 410083, China

Received 13 February 2012; Revised 28 March 2012; Accepted 28 March 2012

Academic Editor: Junjie Wei

Copyright © 2012 Qiaojie Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 𝐿 2 ,  𝐿 ∞ and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.