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

الملخص EN

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 L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show that the scheme is accurate and effective.