Lattice Boltzmann simulation of pattern formation under cross-diffusion

In this paper, a lattice Boltzmann model for cross-reaction-diffusion system is proposed. In order to recover the cross-diffusion equations by lattice Boltzmann method, we transform the equations into a complex reaction-diffusion equation. This complex reaction-diffusion equation is recovered with higher-order accuracy of the truncation error. Based on this model, two typical reaction-diffusion systems with cross-diffusion, predator-prey system and inhomogeneous Brusselator model are simulated. The numerical results show that this model can be used to simulate the cross-reaction-diffusion systems.