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 dispeion in a three dimensional Poiseuille flow. Good agreement between simulation and teh tehory is found, with relative errors smaller than $2\\%$. The P\'eclet number limits on the moment propagation method are studied, and maximum parameter values are obtained. We show that a modifcation of the moment-propagation method allows advection-diffusion simulations with higher P\'eclet numbers, in particular in the low Reynolds number limit