Novel local smoothness indicators for improving the third‐order WENO scheme

다국어 초록 (Multilingual Abstract)

The local smoothness indicators play an important role in the performance of a weighted essentially nonoscillatory (WENO) scheme. Due to having only 2 points available on each substencil, the local smoothness indicators calculated by conventional methods make the third‐order WENO scheme too dissipative. In this paper, we propose a different method to calculate the indicators by using all the 3 points on the global stencil of the third‐order WENO scheme. The numerical results demonstrate that the WENO scheme with the new indicators has less dissipation and better resolution than the conventional third‐order WENO scheme of Jiang and Shu for both smooth and discontinuous solutions.







Due to having only 2 points available on each substencil, the local smoothness indicators calculated by conventional methods make the third‐order WENO schemes (including its improved schemes) too dissipative. In this paper, we propose a novel way to calculate the local indicators by using all 3 points on the global stencil. In monotone smooth regions, the 2 new indicators are the same. Because of this important advantage, the new WENO scheme can greatly decrease the numerical dissipation.