A multi-relaxation lattice kinetic method for passive scalar diffusion

A kinetic Lattice-Boltzmann scheme for advection-diffusion is presented. The scheme is based on a matrix formulation of the lattice Boltzmann method which permits to handle non-isotropic diffusion-advection problems. In addition, by adjusting the kinetic eigenvectors defining the collision matrix to the local value of the flow velocity, the scheme is also shown to preserve isotropy under genuinely two-dimensional flow.