In this article, we present two improved third‐order weighted essentially nonoscillatory (WENO) schemes for recovering their design‐order near first‐order critical points. The schemes are constructed in the framework of third‐order WENO‐Z scheme. Two new global smoothness indicators, τ_L3 and τ_L4, are devised by a nonlinear combination of local smoothness indicators (IS_k) and reference values (IS_G) based on Lagrangian interpolation polynomial. The performances of the proposed schemes are evaluated on several numerical tests governed by one‐dimensional linear advection equation or one‐ and two‐dimensional Euler equations. Numerical results indicate that the presented schemes provide less dissipation and higher resolution than the original WENO3‐JS and subsequent WENO3‐N scheme.

中文翻译：

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具有新的平滑度指标的改进的三阶加权基本非振荡方案

在本文中，我们提出了两种改进的三阶加权基本非振荡（WENO）方案，用于恢复其在一阶临界点附近的设计阶。这些方案是在三阶WENO-Z方案的框架中构建的。两个新的全局平滑度的指标，τ_大号3和τ_大号4中，通过局部平滑度指标（非线性组合设计IS _ķ）和参考值（IS _ģ）基于拉格朗日插值多项式。所提出的方案的性能在由一维线性对流方程或一维和二维欧拉方程控制的数个数值测试中进行了评估。数值结果表明，与原始的WENO3-JS和后续的WENO3-N方案相比，所提出的方案具有更低的功耗和更高的分辨率。