Lattice-Boltzmann coupled models for advection-diffusion flow on a wide range of Peclet numbers

Traditional Lattice-Boltzmann modelling of advection-diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Peclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice-Boltzmann Navier-Stokes solver is coupled to a Lattice-Boltzmann advection-diffusion model. In a novel model, the Lattice-Boltzmann Navier-Stokes solver is coupled to an explicit finite-difference algorithm for advection-diffusion. The finite-difference algorithm also includes a novel approach to mitigate the numerical diffusivity connected with the upwind differentiation scheme. The models are validated using two non-trivial benchmarks, which includes discontinuous initial conditions and the case Pe(g) -> infinity for the first time, where Pe(g) is the grid Peclet number. The evaluation of Pe(g) alongside Pe is discussed. Accuracy, stability and the order of convergence are assessed for a wide range of Peclet numbers. Recommendations are then given as to which model to select depending on the value Pe(g)-in particular, it is shown that the coupled finite-difference/Lattice-Boltzmann provide stable solutions in the case Pe -> infinity, Pe(g) -> infinity.