In this work, a high-order upwind compact finite-difference lattice Boltzmann method (UCDLBM) is developed to efficiently solve viscous incompressible flow problems. A fifth-order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice Boltzmann equation, and the third-order total-variation-diminishing Runge–Kutta scheme is utilized for the discretization of the temporal term. Compared to the existing central compact finite-difference lattice Boltzmann method (CFDLBM), the present UCDLBM can prevent non-physical oscillations without filtering due to the natural dissipative property of upwind schemes. Three benchmark problems involving the Taylor–Green vortex problem, the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method. Numerical results computed are in good agreement with the analytical solution or other available numerical results. And, the present UCDLBM is less time-consuming than the CFDLBM without degenerating the order of accuracy of the numerical solutions.

在这项工作中，开发了一种高阶迎风紧致有限差分格子玻尔兹曼方法（UCDLBM），以有效解决粘性不可压缩流动问题。采用五阶迎风紧致差分格式来离散化玻尔兹曼方程的空间导数，并使用三阶总变差减小的朗格-库塔方案来对时间项进行离散化。与现有的中央紧凑型有限差分格子玻尔兹曼方法（CFDLBM）相比，本发明的UCDLBM由于迎风方案的自然耗散特性，可以防止非物理振荡而不进行滤波。涉及泰勒-格林涡旋问题的三个基准问题，通过数值求解双周期剪切层流动问题和盖驱动方腔流动问题，证明了本方法的准确性和有效性。计算得出的数值结果与解析解或其他可用数值结果非常吻合。并且，本发明的UCDLBM比CFDLBM耗时少，而不会降低数值解的精度顺序。