Lattice Bhatnagar–Gross–Krook model for the Lorenz attractor

Abstract

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 t 0 . 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.

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