Novel local smoothness indicators for improving the third‐order WENO scheme |
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| Authors: | Shengping Liu Yiqing Shen Bei Chen Fangjun Zeng |
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| Institution: | 1. State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China;2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China |
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| 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. |
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| Keywords: | local smoothness indicator numerical dissipation third‐order WENO scheme |
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