Lattice Boltzmann Method for Advection and Anisotropic Dispersion Equation

Abstract

A lattice Boltzmann method is developed for the solution of the advection and anisotropic dispersion equation. In the approach, a novel local equilibrium distribution function is formulated to preserve the advantage of using a single relaxation time for the recovery of the isotropic or anisotropic dispersion tensor in the equation. The method fully retains the innate kinetic features and the simple procedure of the standard lattice Boltzmann method, with an additional benefit of being suitable for rectangular lattices at little extra computational cost. The model has been verified and the results have shown that it can produce accurate solutions with great potential to general advection and dispersion problems, leading to broad applications within a variety of interdisciplinary areas.