Lattice Boltzmann Modeling of Advection-Diffusion-Reaction Equations: Pattern Formation Under Uniform Differential Advection (Communications in Computational Physics, 2020)
A lattice Boltzmann model for the study of advection-diffusion-reaction(ADR) problems is proposed. Via multiscale expansion analysis, we derive from theLB model the resulting macroscopic equations. It is shown that a linear equilibriumdistribution is sufficient to produce ADR equations within error terms of the order ofthe Mach number squared. Furthermore, we study spatially varying structures arisingfrom the interaction of advective transport with a cubic autocatalytic reaction-diffusionprocess under an imposed uniform flow. While advecting all the present species leadsto trivial translation of the Turing patterns, differential advection leads to flow inducedinstability characterized with traveling stripes with a velocity dependent wave vectorparallel to the flow direction. Predictions from a linear stability analysis of the modelequations are found to be in line with these observations.