Modified lattice Boltzmann scheme for nonlinear convection diffusion equations

To further improve the simulation performance of nonlinear convection diffusion equations (NCDE), in this paper, a modified lattice Boltzmann (LB) scheme is put forward by introducing a new parameter that offers more opportunities in studying NCDE while increases the computation cost hardly, the derivation of LB scheme is investigated in detail, and the numerical experiments are carried out in different NCDE, including Nonlinear Heat Conduction Equation, Burgers–Fisher Equation and Nonlinear Schrödinger Equation. The simulation results obtained not only agree well with the analytical solutions, but also demonstrate that the proposed scheme under the best choice of the parameters can preserve the better stability and higher accuracy in comparison with previous schemes.

► In this study we model nonlinear convection diffusion equations by lattice Boltzmann method.
► By introducing a new parameter to the old one, this scheme offers more selection opportunities.
► The proposed scheme has better stability and higher accuracy compared with the previous ones.