Lattice Boltzmann model for time sub-diffusion equation in Caputo sense

Abstract

Anomalous diffusions, including subdiffusion and superdiffusion, are usually encountered in many diverse applications in science and engineering. Although many numerical methods have been proposed to study anomalous diffusion problems that are modeled by fractional advection-diffusion equations, in this paper, a fresh lattice Boltzmann (LB) model for time sub-diffusion equation in Caputo sense is proposed. Through the Chapman-Enskog analysis, the time-fractional diffusion equation can be recovered from the developed LB model. In addition, we also test the present LB model through some problems, and find that the numerical results agree well with the analytical solutions to these problems.