A lattice Boltzmann model for the fractional advection-diffusion equation coupled with incompressible Navier-Stokes equation

The fractional advection diffusion problem coupled with incompressible Navier Stokes equations is important in science and engineering. In this paper, a fresh lattice Boltzmann model with double-distribution functions for this problem is presented. One distribution function is used for pressure and velocity. The other is applied for concentration. Through Chapman-Enskog expansion, the macroscopic continuum equations can be recovered from the LB model. Numerical simulations are carried out to verify the numerical accuracy and efficiency. (C) 2019 Elsevier Ltd. All rights reserved.