Lattice Boltzmann convection-diffusion model with non-constant advection velocity

The main objective of this contribution is to investigate multiple relaxation time lattice Boltzmann schemes for convection-diffusion equations. In particular, we discuss the issue obtaining second order exact when advection velocity non-constant. Our study based on previous results by authors that allow identify extra term, coming from non-constancy velocity, prevent exactness such schemes. We show how these terms can be cancelled, either a suitable choice momentum equilibrium or adding forcing term applied non-conserved momentum. It leads same expression collision. Numerical experiments are performed using Poiseuille, Couette and Taylor-Green flows. They proposed collision increases numerical convergence rate up two.