Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2012 (2012), Article ID 925920, 13 pages.
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 satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have been compared with the exact solutions reported in previous studies. The , and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.
J. Appl. Math., Volume 2012 (2012), Article ID 925920, 13 pages.
First available in Project Euclid: 14 December 2012
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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