A third-order compact gas-kinetic scheme is proposed for three-dimensional compressible flow computations. The new scheme is based on three key ingredients: the time-accurate gas evolution model for interface flux, the Hermite weighted essentially nonoscillatory reconstruction, and the two-stage temporal discretization. In contrast to the Riemann-solver-based methods, due to the use of time-accurate flux function the proposed scheme can achieve a third-order temporal accuracy with two stages instead of three stages in the standard Runge–Kutta method. As an extension of the existing high-order reconstructions, a Hermite weighted essentially nonoscillatory reconstruction is specifically designed for the current scheme with the implementation of the constrained least-square technique, which subsequently improves the accuracy and robustness of the compact scheme. There is no trouble cell identification in the current scheme. A third-order accuracy can be achieved even with curved boundary. Numerical examples for both smooth and discontinuous flows show the robustness and high accuracy of the compact third-order scheme, which has a comparable performance as the fifth-order noncompact gas-kinetic scheme. A large Courant–Friedrichs–Lewy number around 0.5 can be used in the computations.

提出了用于三维可压缩流动计算的三阶紧凑气体动力学方案。新方案基于三个关键要素：界面通量的时间精确气体演化模型、Hermite 加权基本非振荡重建和两阶段时间离散化。与基于黎曼求解器的方法相比，由于使用了时间精确的通量函数，所提出的方案可以通过两级而不是标准 Runge-Kutta 方法中的三级来实现三阶时间精度。作为现有高阶重建的扩展，Hermite 加权基本非振荡重建是专门为当前方案设计的，并实施了约束最小二乘技术，这随后提高了紧凑方案的准确性和鲁棒性。当前方案中没有故障小区识别。即使是曲线边界，也可以达到三阶精度。光滑和不连续流动的数值例子表明紧凑三阶方案的鲁棒性和高精度，其性能与五阶非紧凑气体动力学方案相当。计算中可以使用大约 0.5 的大 Courant-Friedrichs-Lewy 数。它具有与五阶非紧致气体动力学方案相当的性能。计算中可以使用大约 0.5 的大 Courant-Friedrichs-Lewy 数。它具有与五阶非紧致气体动力学方案相当的性能。计算中可以使用大约 0.5 的大 Courant-Friedrichs-Lewy 数。