SummaryThis paper presents a new WENO‐Z scheme (WENO‐MZ) that incorporates a mapping function to enhance the weights of the less smooth sub‐stencils. The mapping function uses an innovative approach to modify the weight ratio of the less smooth sub‐stencil to the smooth stencil. In addition, we present the WENO‐MD scheme, which is a further development of the WENO‐MZ scheme that incorporates a modifier function. The WENO‐MD scheme shows improvements over the WENO‐MZ scheme by achieving an improved optimal order at critical points in higher orders and by increasing the proportion of less smooth sub‐stencils. Theoretical and numerical experiments have shown that the newly developed methods have improved shock capture capabilities and resolution compared to WENO‐JS, WENO‐Z, WENO‐M, WENO‐D, and WENO‐AIM, and also lead to significant computational time savings compared to WENO‐M and WENO‐AIM.

中文翻译：

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用于求解可压缩流的高分辨率映射型 WENO-Z 方案

摘要本文提出了一种新的 WENO-Z 方案（WENO-MZ），该方案结合了映射函数来增强不太平滑的子模板的权重。映射函数使用创新方法来修改不太平滑的子模板与平滑模板的权重比。此外，我们还提出了 WENO-MD 方案，它是 WENO-MZ 方案的进一步发展，结合了修饰符函数。WENO-MD 方案通过在高阶关键点实现改进的最优阶以及增加不太平滑的子模板的比例，显示出对 WENO-MZ 方案的改进。理论和数值实验表明，与 WENO-JS、WENO-Z、WENO-M、WENO-D 和 WENO-AIM 相比，新开发的方法提高了冲击捕获能力和分辨率，并且与WENO-M 和 WENO-AIM。