A novel scheme, based on third-order Weighted Essentially Non-Oscillatory (WENO) reconstructions, is presented. It attains unconditionally optimal accuracy when the data is smooth enough, even in presence of critical points, and second-order accuracy if a discontinuity crosses the data. The key to attribute these properties to this scheme is the inclusion of an additional node in the data stencil, which is only used in the computation of the weights measuring the smoothness. The accuracy properties of this scheme are proven in detail and several numerical experiments are presented, which show that this scheme is more efficient in terms of the error reduction versus CPU time than its traditional third-order counterparts as well as several higher-order WENO schemes that are found in the literature.

翻译：本文提出了一种基于三阶加权本质无振荡（WENO）重构的新型格式。当数据足够光滑时，该格式能达到无条件最优精度（即使在存在临界点的情况下）；而当数据中存在间断时，则达到二阶精度。赋予该格式这些特性的关键在于，在数据模板中引入了一个额外节点，该节点仅用于计算衡量光滑性的权重。本文详细证明了该格式的精度特性，并通过多个数值实验表明，相较于传统的三阶格式及文献中若干高阶WENO格式，该格式在降低误差与提高CPU时间效率方面更具优势。