Abstract:

A lattice Boltzmann model for the Poisson equation was proposed. By means of the ChapmanEnskog expansion and the multiscale time expansion, a series of partial differential equations in different time scales was obtained. Moreover, the equilibrium distribution functions and the modified partial differential equation of the Poisson equation with the thirdorder truncation error were obtained. In numerical examples, the Kolmogorov flow and GreenTaylor vortex flow were simulated, and the comparison between numerical results of the lattice Boltzmann models and exact solutions were given. The numerical results are acceptable.

Key words: lattice Boltzmann model, Poisson equation, Kolmogorov flow