The high-order gas-kinetic scheme (HGKS) features good robustness, high efficiency and satisfactory accuracy,the performaence of which can be further improved combined with WENO-AO (WENO with adaptive order) scheme for reconstruction. To reduce computational costs in the reconstruction procedure, this paper proposes to combine HGKS with a hybrid WENO-AO scheme. The hybrid WENO-AO scheme reconstructs target variables using upwind linear approximation directly if all extreme points of the reconstruction polynomials for these variables are outside the large stencil. Otherwise, the WENO-AO scheme is used. Unlike combining the hybrid WENO scheme with traditional Riemann solvers, the troubled cell indicator of the hybrid WENO-AO method is fully utilized in the spatial reconstruction process of HGKS. During normal and tangential reconstruction, the gas-kinetic scheme flux not only needs to reconstruct the conservative variables on the left and right interfaces but also to reconstruct the derivative terms of the conservative variables. By reducing the number of times that the WENO-AO scheme is used, the calculation cost is reduced. The high-order gas-kinetic scheme with the hybrid WENO-AO method retains original robustness and accuracy of the WENO5-AO GKS, while exhibits higher computational efficiency.

翻译：高阶气体动理学格式（HGKS）具有鲁棒性强、效率高、精度好的特点，若与自适应阶WENO（WENO-AO）重构格式结合，其性能可进一步优化。为降低重构过程的计算成本，本文提出将HGKS与混合WENO-AO格式相结合的方法。该混合WENO-AO格式首先判断目标变量重构多项式的所有极值点是否均位于大模板外部，若满足条件则直接采用迎风线性近似重构目标变量；反之则激活WENO-AO格式。与将混合WENO格式与传统黎曼求解器相结合的方式不同，混合WENO-AO方法中的扰动单元指示器在HGKS空间重构过程中得到充分利用。在法向和切向重构中，气体动理学格式通量不仅需要重构界面左右两侧的守恒变量，还需重构守恒变量的导数项。通过减少WENO-AO格式的使用次数，有效降低了计算成本。采用混合WENO-AO方法的高阶气体动理学格式保留了WENO5-AO GKS原有的鲁棒性和精度，同时展现出更高的计算效率。