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

Journal of Applied Mathematics, 2012, vol. 2012, 1-13

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:925920

DOI: 10.1155/2012/925920

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