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.

中文翻译：

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非线性对流扩散方程的离散统一气体动力学方案

在本文中，我们为一般的非线性对流扩散方程（NCDE）开发了离散统一气体动力学方案（DUGKS），并表明通过Chapman-Enskog分析可以从本模型中正确恢复NCDE。然后，我们通过一些经典的对流扩散方程对当前的DUGKS进行了测试，发现数值结果与解析解非常吻合，并且DUGKS模型具有二阶收敛速度。最后，作为有限体积方法，DUGGS也可以采用非均匀网格。此外，我们在DUGKS，有限体积格子Boltzmann模型（FV-LBM），单松弛时间格子Boltzmann模型（SLBM）和多松弛时间格子Boltzmann模型（MRT-LBM）之间进行了比较。 ）。结果表明，目前的DUGKS比FV-LBM更准确，比SLBM更稳定，并且几乎与MRT-LBM相同。此外，使用非均匀网格可以使DUGKS模型更灵活。