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.
J. Comput. Phys.