Abstract: In this paper, a 5-bit single relaxation lattice Boltzmann model with additional terms is proposed for solving the generalized Ginzburg-Landau equation. Firstly, by using Chapman-Enskog expansion and Taylor expansion, we obtain a series of partial differential equations in different time scales and several high-order moments of equilibrium distribution functions. Then we establish a lattice Boltzmann model with truncation error by applying a series of moments of equilibrium distribution functions and derive the numerical dissipation term. Moreover, we obtain the stability condition of the model by ultilizing the Hirt heuristic method. Finally, we provide some numerical examples of the generalized Ginzburg-Landau equation. Numerical results indicate that the method can be used to simulate the generalized Ginzburg-Landau equation.

Key words: generalized Ginzburg-Landau equation, lattice Boltzmann model, multi-scale Chapman-Enskog expansion, equilibrium distribution function