A Lattice Boltzmann Method for the Chemical Clock in the Belousov-Zhabotinskii Reaction

A lattice Boltzmann method for the Belousov-Zhabotinskii reaction is proposed to simulate the chemical clock. Applying the Chapman-Enskog expansion and multiscale technique, we obtain a series of lattice Boltzmann equations in different timescales, the conservation law in time scale t₀ and coefficients of macroscopic equations to find the equilibrium distribution functions. A simple numerical scheme is designed to simulate the diffusion-reaction systems. The numerical example shows that the proposed method can be used to simulate chemical systems with the chemical clock.