SCALINGS IN DIFFUSION-DRIVEN REACTION A-]C - NUMERICAL SIMULATIONS BYLATTICE BGK MODELS(B)

We are interested in applying lattice BGK models to the diffusion-driv en reactive system A + B --> C, which was investigated by Galfi and Ra cz with an asymptotic analysis and by Chopard and Droz with a cellular automaton model. The lattice BGK model is free from noise and flexibl e for various applications. We derive the general reaction-diffusion e quations for the lattice BGK models under the assumption of local diff usive equilibrium. Two fourth-order terms are derived and verified by numerical simulations. The motivation of this study is to compare the lattice BGK results with existing results before we apply the models t o more complicated systems. The scalings concern two exponents alpha a nd beta appearing in the production rate of C component R(x, t) simila r to t(-beta)G(xt(-alpha)). We find the same values for alpha = 1/6 an d beta = 2/3 as Galfi and Racz found at the long time limit. A Gaussia n-like function for G is numerically obtained, which confirms a simila r result of Galfi and Racz. On the one hand, when compared with the as ymptotic analysis, lattice BGK models are easy to apply to cases where no analytic or asymptotic results exist; on the other hand, when comp ared with cellular automaton models, lattice BGK models are faster, si mpler, and more accurate. The discrepancy of the results between the c ellular automaton model and the lattice BGK models for the exponents c omes from the role of the intrinsic fluctuation. Once the time and spa ce correlation of stochastic stirring is given, we can incorporate a r andom fluctuating term in lattice BGK models. The Schlogl model is als o tested, showing the ability of lattice BGK models for generating Tur ing patterns, which may stimulate further interesting investigations.