Since the classical weighted essentially non-oscillatory (WENO) scheme is proposed, various improved versions have been developed, and a typical one is the WENO-Z scheme. Although better resolution is achieved, it is shown in this article that, the result of WENO-Z scheme suffers evident distortion in the long-time simulation of the linear advection equation. In order to fix the problem of WENO-Z, a symmetry-preserving mapping method is proposed in this article. In the original mapping method, the weight of each sub-stencil is used to map, which is demonstrated to cause asymmetric improvement about a discontinuity. This asymmetric improvement will lead to a distorted solution, more severe with longer output time. In the symmetry-preserving mapping method, a new variable related to the smoothness indicator is selected to map, which has the same ideal value for each sub-stencil. Using the new mapping method can not only fix the distortion problem of WENO-Z, but also improve the numerical resolution. Several benchmark problems are conducted to show the improved performance of the resultant scheme.

中文翻译：

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带有对称对称映射的改进的WENO-Z方案

由于提出了经典的加权基本非振荡（WENO）方案，因此已经开发了各种改进的版本，典型的是WENO-Z方案。尽管获得了更好的分辨率，但本文表明，在线性对流方程的长期仿真中，WENO-Z方案的结果遭受了明显的失真。为了解决WENO-Z问题，本文提出了一种保持对称性的映射方法。在原始的映射方法中，每个子模板的权重用于映射，这被证明会导致不连续性的不对称改善。这种不对称的改进将导致解决方案失真，随着输出时间的延长，解决方案将变得更加严重。在保持对称性的映射方法中，选择与平滑度指示器相关的新变量进行映射，每个子模板具有相同的理想值。使用新的映射方法不仅可以解决WENO-Z的失真问题，而且可以提高数值分辨率。进行了几个基准测试问题，以显示所得方案的改进性能。