WENO schemes are a popular class of shock-capturing schemes which adopt an adaptive-stencil approach to interpolation. WENO schemes rely on smoothness indicators to assess the relative smoothness of the solution within the sub-stencils. Computing these smoothness indicators is the most expensive operation in the WENO reconstruction procedure. In this paper, an efficient algorithm is proposed to compute these quantities without sacrificing the positivity property of the smoothness indicators. The proposed algorithm involves linear combinations of the undivided differences which can be computed efficiently in a recursive manner. This allows the computation of the smoothness indicators to be performed using significantly fewer floating-point operations compared to conventional implementations. Moreover, the proposed algorithm is simple to implement and involves fewer constants.

WENO 方案是一类流行的冲击捕获方案，它采用自适应模板方法进行插值。WENO 方案依靠平滑度指标来评估子模板内解决方案的相对平滑度。计算这些平滑度指标是 WENO 重建过程中最昂贵的操作。在本文中，提出了一种有效的算法来计算这些数量，而不会牺牲平滑度指标的积极性。所提出的算法涉及可以以递归方式有效计算的未分割差的线性组合。与传统实现相比，这允许使用显着更少的浮点运算来执行平滑度指标的计算。而且，