Journal of Applied Mathematics

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

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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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 925920, 13 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495149

Digital Object Identifier
doi:10.1155/2012/925920

Mathematical Reviews number (MathSciNet)
MR2927262

Zentralblatt MATH identifier
1244.76066

Citation

Li, Qiaojie; Zheng, Zhoushun; Wang, Shuang; Liu, Jiankang. A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method. J. Appl. Math. 2012 (2012), Article ID 925920, 13 pages. doi:10.1155/2012/925920. https://projecteuclid.org/euclid.jam/1355495149


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