Abstract: In this paper, we propose a new Bhatnagar-Gross-Krook (BGK) model for
simulation of the Lorenz attractor. The new model is based on a nonlinear
diffusion-reaction system. We formulate a lattice BGK 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 as well as 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.
Keywords: lattice BGK model, multiscale technique, Lorenz attractor.