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

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.