Discrete unified gas kinetic scheme for nonlinear convection-diffusion equations.

Abstract

In this paper, we develop a discrete unified gas kinetic scheme (DUGKS) for a 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 we find that the numerical results are in good agreement with analytical solutions and that the DUGKS model has a second-order convergence rate. Finally, as a finite-volume method, the DUGKS can also adopt the nonuniform mesh. Besides, we perform some comparisons among the DUGKS, the finite-volume lattice Boltzmann model (FV-LBM), the single-relaxation-time lattice Boltzmann model (SLBM), and the multiple-relaxation-time lattice Boltzmann model (MRT-LBM). The results show that the present DUGKS is more accurate than the FV-LBM, more stable than the SLBM, and almost has the same accuracy as the MRT-LBM. Moreover, the use of nonuniform mesh may make the DUGKS model more flexible.