A lattice BGK model for advection and anisotropic dispersion equation

This paper presents a lattice Boltzmann model (LBM) for 2-D advection and anisotropic dispersion equation (AADE) based on the Bhatnagar, Gross and Krook (BGK) model. In the proposed model, the particle speed space is discretized using a rectangular lattice that has four speeds in nine directions, and the single relaxation time is assumed to be directionally dependent. To ensure that the collision is mass-invariant when the relaxation time is directionally dependent, the concentration is calculated from a weighted summation of the particle distribution functions. The proposed model was verified against benchmark problems and the finite difference solution of solute transport with spatially variable dispersion coefficients and non-uniform velocity field. The significant results are that it conserves mass perfectly and offers accurate and efficient solutions for both dispersion-dominated and advection-dominated problems.