Common smoothness indicators used in Weighted Essentially Non\--Os\-cil\-la\-to\-ry (WENO) reconstructions [Jiang, G.S., Shu, C.W.: Efficient implementation of {Weighted} {ENO} schemes, J.\ Comput.\ Phys. \textbf{126}, 202--228 (1996)] have quadratic cost with respect to the order. A set of novel smoothness indicators with linear cost of computation with respect to the order is presented. These smoothness indicators can be used in the context of schemes of the type introduced by Yamaleev and Carpenter [Yamaleev, N.K., Carpenter, M.H.: A systematic methodology to for constructing high-order energy stable WENO schemes. J. Comput. Phys. \textbf{228}(11), 4248-4272 (2009)]. The accuracy properties of the resulting non-linear weights are the same as those arising from using the traditional Jiang-Shu smoothness indicators in Yamaleev-Carpenter-type reconstructions. The increase of the efficiency and ease of implementation are shown.

翻译：加权本质无振荡（WENO）重构[Jiang, G.S., Shu, C.W.: Efficient implementation of {Weighted} {ENO} schemes, J.\ Comput.\ Phys. \textbf{126}, 202--228 (1996)]中常用的光滑性指标在阶数方向上具有二次计算成本。本文提出了一组新型光滑性指标，其计算成本在阶数方向上呈线性。这些光滑性指标可应用于Yamaleev和Carpenter [Yamaleev, N.K., Carpenter, M.H.: A systematic methodology to for constructing high-order energy stable WENO schemes. J. Comput. Phys. \textbf{228}(11), 4248-4272 (2009)]提出的同类格式框架中。由此生成的非线性权重与在Yamaleev-Carpenter型重构中使用传统Jiang-Shu光滑性指标具有相同的精度特性。文中展示了效率的提升与实现的简化。