The discrete unified gas kinetic scheme (DUGKS) combines the advantages of both the unified gas kinetic scheme (UGKS) and the lattice Boltzmann method. It can adopt the flexible meshes, meanwhile, the flux calculation is simple. However, the original DUGKS is proposed for the compressible flows. When we try to solve a problem governed by the incompressible Navier-Stokes (N-S) equations, the original DUGKS may bring some undesirable errors because of the compressible effect. To eliminate the compressible effect, the DUGKS for incompressible N-S equations is developed in this work. In addition, the Chapman-Enskog analysis ensures that the present DUGKS can solve the incompressible N-S equations exactly, meanwhile, a new non-extrapolation scheme is adopted to treat the Dirichlet boundary conditions. To test the present DUGKS for incompressible N-S equations, four problems are adopted. The first one is a periodic problem driven by an external force, which is used to test the influences of Courant–Friedrichs–Lewy condition number and the $Mach$ number (Ma). Besides, some comparisons between the present DUGKS and some available results are also conducted. The second problem is Womersley flow, it is also used to test the influence of Ma, and the results show that the compressible effect is reduced obviously. Then, the two-dimensional lid-driven cavity flow is considered. In these simulations, the Reynolds number is varied from 400 to 1000000 to illustrate the accuracy, stability and efficiency of the present DUGKS. Finally, the numerical solutions of the three-dimensional lid-driven cavity flow suggest that the present DUGKS is suitable for the three-dimensional problems.

离散统一气体动力学方案 (DUGKS) 结合了统一气体动力学方案 (UGKS) 和格子 Boltzmann 方法的优点。可采用柔性网格，同时通量计算简单。然而，最初的 DUGKS 是针对可压缩流提出的。当我们试图解决由不可压缩的 Navier-Stokes (NS) 方程控制的问题时，由于可压缩效应，原始 DUGKS 可能会带来一些不希望有的错误。为了消除可压缩效应，在这项工作中开发了不可压缩 NS 方程的 DUGKS。此外，Chapman-Enskog 分析确保现有的 DUGKS 能够准确求解不可压缩的 NS 方程，同时采用新的非外推方案处理 Dirichlet 边界条件。为了测试当前 DUGKS 的不可压缩 NS 方程，采用了四个问题。第一个是外力驱动的周期性问题，用于检验 Courant-Friedrichs-Lewy 条件数和$米\mathrm{一种}CH$数（马）。此外，还对当前 DUGKS 和一些可用结果进行了一些比较。第二个问题是Womersley 流，也用来测试Ma的影响，结果表明可压缩效应明显降低。然后，考虑二维盖子驱动的腔流。在这些模拟中，雷诺数从 400 到 1000000 不等，以说明当前 DUGKS 的准确性、稳定性和效率。最后，三维盖驱动腔流的数值解表明，目前的 DUGKS 适用于三维问题。