Lattice Boltzmann method for coupled Burgers equations

Abstract

In this paper, we propose a lattice Boltzmann model for coupled Burgers equations (CBEs). With a proper time-space scale and the Chapman-Enskog expansion, the governing equations are recovered successfully from the lattice Boltzmann equations, and the resulting local equilibrium distribution functions are also obtained. The partial derivative $\partial(uv)/\partial x$ in the model is treated as a source term and discretized with a 2nd-order central difference scheme. Numerical experiments show that the numerical results by the Lattice Boltzmann Method (LBM) either agree well with the corresponding exact solutions or are quite comparable with those available numerical results in the literature.

Keywords

• Lattice Boltzmann model
• equilibrium distribution
• coupled Burgers equations
• Chapman-Enskog expansion