Lattice Boltzmann method for one and two-dimensional Burgers equation

In this paper, a new method, higher-order moment lattice Boltzmann method for one and two-dimensional Burgers’ equation is proposed. The lattice Boltzmann models presented here are based on a series of lattice Boltzmann equations in different time scales. In order to achieve higher order accuracy, we use seven and four moments of the equilibrium distribution function in one and two-dimensional models respectively. We find two kinds of strategy to seek equilibrium distribution functions for the two-dimensional model with second order accuracy. These two are equivalent when a scale factor k=23. Lastly, we provide a fine numerical result of a one-dimensional Burgers’ equation. Numerical examples show the method can be used to simulate one and two-dimensional Burgers’ equation.