In this paper, we design a new type of high order weighted compact scheme based on ZJS method (Zhang et al., 2008) [35] and ZQ method (Zhu and Qiu, 2016) [16]. These nonlinear weighted compact schemes are designed based on the cell-centered compact scheme of Lele (Lele, 1992) [22]. Instead of using WENO interpolation with equal-sized sub-stencil in ZJS formulae in Zhang et al. (2008) [35] for the fluxes on the cell centers, a new type of WENO interpolation with unequal sized sub-stencil is proposed following the similar idea of WENO reconstruction by Zhu and Qiu (2016) [16]. Through systematic numerical tests and comparisons with the weighted compact schemes and traditional WENO scheme, we observe that the new type weighted compact scheme has better resolution, smaller dissipation, while the ability to capture strong shock waves is maintained.

在本文中，我们设计了一种基于 ZJS 方法（Zhang et al., 2008）[35] 和 ZQ 方法（Zhu and Qiu，2016）[16] 的新型高阶加权紧凑方案。这些非线性加权紧凑方案是基于 Lele (Lele, 1992) [22] 的以单元为中心的紧凑方案设计的。而不是在 Zhang 等人的 ZJS 公式中使用具有相同大小子模板的 WENO 插值。(2008) [35] 对于细胞中心的通量，根据 Zhu 和 Qiu (2016) [16] 提出的类似 WENO 重建的想法，提出了一种具有不等大小子模板的新型 WENO 插值。通过系统的数值试验和与加权紧凑方案和传统WENO方案的比较，我们观察到新型加权紧凑方案具有更好的分辨率、更小的耗散，同时保持了捕获强冲击波的能力。