Lattice Boltzmann method for the fractional sub-diffusion equation

Summary A lattice Boltzmann model for the fractional sub‐diffusion equation is presented. By using the Chapman–Enskog expansion and the multiscale time expansion, several higher‐order moments of equilibrium distribution functions and a series of partial differential equations in different time scales are obtained. Furthermore, the modified partial differential equation of the fractional sub‐diffusion equation with the second‐order truncation error is obtained. In the numerical simulations, comparisons between numerical results of the lattice Boltzmann models and exact solutions are given. The numerical results agree well with the classical ones. Copyright © 2015 John Wiley & Sons, Ltd. Lattice Boltzmann method can be used to implement the numerical simulation of the fractional sub‐diffusion equation. The results by the lattice Boltzmann model are compared with the results of classical method. This figure is a snapshot of the three‐dimensional example by Lattice Boltzmann method.