A multilevel finite difference scheme for one-dimensional Burgers equation derived from the lattice Boltzmann method (Q443133)

Summary: 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 \(L_2, L_\infty\) and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.