A novel procedure is given for choosing smoothest stencil to construct less oscillatory ENO schemes. The procedure is further used to define the smoothness parameter in the non-linear weights of new WENO schemes. The main significant features of these new ENO and WENO schemes are that they are less oscillatory and achieve their relevant order of accuracy in the presence of critical points in the exact solution. It is shown theoretically as well as computationally in $L^1$ and $L^{\infty }$ norm. Moreover, computational results are given to show less oscillatory behaviour of the new WENO scheme compared to WENO5-JS and WENO5-Z schemes.

中文翻译：

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使用基于弧长的平滑度测量的ENO和WENO方案

给出了一种新颖的方法，用于选择最平滑的模板以构造振荡频率较小的ENO方案。该过程还用于在新WENO方案的非线性权重中定义平滑度参数。这些新的ENO和WENO方案的主要显着特征是，在精确解决方案中存在临界点时，它们的振荡较少，并达到了相应的精度顺序。它在理论上和计算上都显示在${\mathrm{大号}}^{\mathrm{1个}}$ 和 ${\mathrm{大号}}^{\infty }$规范。此外，计算结果表明，与WENO5-JS和WENO5-Z方案相比，新WENO方案的振荡行为更少。