  In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for
general nonlinear convection-diffusion equation (NCDE), and show that the NCDE
can be recovered correctly from the present model through the Chapman-Enskog
analysis. We then test the present DUGKS through some classic
convection-diffusion equations, and find that the numerical results are in good
agreement with analytical solutions and the DUGKS model has a second-order
convergence rate. Finally, as a finite-volume method, DUGKS can also adopt the
non-uniform mesh. Besides, we performed some comparisons among the DUGKS,
finite-volume lattice Boltzmann model (FV-LBM), single-relaxation-time lattice
Boltzmann model (SLBM) and multiple-relaxation-time lattice Boltzmann model
(MRT-LBM). The results show that the DUGKS model is more accurate than FV-LBM,
more stable than SLBM, and almost has the same accuracy as the MRT-LBM.
Besides, the using of non-uniform mesh may make DUGKS model more flexible.
