In this paper we recover a latent advantage of WENO-Z schemes. Taking the fifth-order WENO-Z scheme for instance, we realize that the scheme can be regarded as a nonlinear combination of a five-cell stencil and three three-cell stencils. The five-cell stencil is allotted a global higher-order indicator of smoothness than three-cell stencils. Then the five-cell stencil dominates the nonlinear combination and ensures the optimal accuracy in the smooth regions even at extremal points. In non-smooth regions, the three-cell stencils dominate the combination and compress the nonphysical oscillations. As the adaptive order WENO schemes which release the requirement of linear optimal weights, we will show that there is no requirement of linear optimal weights for the WENO-Z schemes as well, and even it is unnecessary to require the sum of linear optimal weights to be one.

在本文中，我们恢复了WENO-Z方案的潜在优势。以五阶WENO-Z方案为例，我们意识到该方案可以看作是五单元模板和三个三单元模板的非线性组合。与三单元模板相比，五单元模板被分配为光滑度的全局高阶指标。然后，五单元模板占主导地位的非线性组合，并确保即使在极值点的平滑区域中的最佳精度。在非平滑区域，三单元模板占主导地位，并压缩非物理振荡。作为释放线性最优权重要求的自适应阶次WENO方案，我们将证明WENO-Z方案也没有线性最优权重的要求，