Lattice Boltzmann method for general convection-diffusion equations: MRT model and boundary schemes

Abstract

This paper is concerned with the lattice Boltzmann method for general convection-diffusion equations. For such equations, we develop a multiple-relaxation-time lattice Boltzmann model and show its consistency under the diffusive scaling. The second-order accuracy of the half-way anti-bounce-back scheme accompanying the present MRT model is justified based on an elegant relation of the collision matrix. Using the half-way anti-bounce-back scheme as a central step, we further construct some parameterized single-node second-order schemes for curved boundaries. The accuracy of the proposed model and boundary schemes are numerically validated with several nonlinear convection-diffusion equations.