Abstract

Common smoothness indicators used in Weighted Essentially Non-Oscillatory (WENO) reconstructions (Jiang and Shu in J Comput Phys 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 and Carpenter in J Comput Phys 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.