Abstract
In this article, a new reference smoothness indicator for the third-order WENO scheme is proposed. The main construction idea is to analyze the first derivative of the reconstruction polynomial of the candidate sub-stencil and the first derivative of the reconstruction polynomial of the global stencil. Then calculate the normalized square sum of the L2-norm approximation of the linear convex combination of the first derivative of the reconstruction polynomial of all candidate sub-stencils and the first derivative of the reconstruction polynomial of the global stencil. The new reference smoothness indicator obtained based on the above strategy is denoted as τRe. The newly developed solution is called the WENO-Re solution. A series of one-dimensional and two-dimensional numerical examples show that the new scheme has higher resolution and smaller dissipation compared to several recently improved third-order WENO schemes.
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