A new scheme for source term in LBGK model for convection–diffusion equation

A new scheme for source term in the lattice BGK (LBGK) model for convection–diffusion equation is proposed. Unlike the models proposed previously, the present scheme only requires the source term in order of the Knudsen number by adding a differential operator of the source term to the evolution equation. The scheme can be applied to reaction–diffusion systems directly. Numerical results are found to be in excellent agreement with the analytical solutions. It is also found that the numerical accuracy of the present scheme is generally much better than that of the existing models.