Lattice Bhatnagar–Gross–Krook model for the Lorenz attractor

In this paper, we propose a new lattice Bhatnagar–Gross–Krook model for simulation of the Lorenz attractor. The new model is based on a nonlinear diffusion-reaction system. We formulate a lattice Bhatnagar–Gross–Krook model for the nonlinear diffusion-reaction system by using a method of higher moments of the lattice Boltzmann equation. As a special case where the diffusion effect disappears, we get the Lorenz equation. In the model, we obtain a series of lattice Boltzmann equations at different time scales, and the conservation law at time scale t0. The equilibrium distribution functions are simpler than those for the standard lattice Boltzmann model. The numerical examples show that the method can be used to simulate the Lorenz equation.