The Moment Propagation Method for Advection–Diffusion in the Lattice Boltzmann Method: Validation and Péclet Number Limits

We numerically validate the moment propagation method for advection–diffusion in a lattice Boltzmann simulation against the analytic Taylor–Aris prediction for dispersion in a three-dimensional Poiseuille flow. Good agreement between simulation and theory is found, with relative errors smaller than 2%. The Péclet number limits on the moment propagation method are studied, and maximum parameter values are obtained. We show that a modification of the moment propagation method allows advection–diffusion simulations with higher Péclet numbers, in particular in the low Reynolds number limit.