Lattice Boltzmann flux scheme for the convection–diffusion equation and its applications

In this work a lattice Boltzmann flux scheme for the convection–diffusion equation (CDE) is proposed. In this scheme, the fluxes across the cell interface are calculated by using the local solution of the multiple-relaxation-time lattice Boltzmann equation for CDE. The present method is suitable for simulating both isotopic and anisotropic diffusion processes. Meanwhile, through applying the midpoint time integration technique, the present method relaxes the time step constraint in the original lattice Boltzmann flux scheme. Four convection–diffusion problems are simulated to validate the present scheme. The obtained results agree well with the analytical or previous published solutions.