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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 timescale 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.