Abstract In this article, a new 6th-order weighted essentially non-oscillatory (WENO) scheme is developed. As with previous 6th-order central-upwind WENO schemes, the present scheme is a convex combination of four candidate linear reconstructions. The difference is that the most upwind and downwind stencils use four cell values, while the inner two stencils nominally use three cell values but the original quadratic reconstructions are modified to be 4th-order approximations by adding cubic correction terms involving the five cell values of the classical 5th-order WENO scheme. Sixth-order accuracy of the new scheme in smooth regions including critical points is achieved by using a reference smoothness indicator. Several numerical examples show that the new scheme has higher resolution compared with the recently developed 6th-order WENO schemes.

中文翻译：

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一种新的 6 阶 WENO 方案，带有修改的模板

摘要 在本文中，开发了一种新的 6 阶加权基本非振荡 (WENO) 方案。与之前的 6 阶中央上风 WENO 方案一样，本方案是四个候选线性重构的凸组合。不同之处在于，最上风和最下风的模板使用四个单元值，而内部的两个模板名义上使用三个单元值，但通过添加涉及五个单元值的三次校正项，将原始二次重建修改为四阶近似值。经典的五阶 WENO 方案。新方案在包括临界点的平滑区域中的六阶精度是通过使用参考平滑度指标实现的。几个数值例子表明，与最近开发的 6 阶 WENO 方案相比，新方案具有更高的分辨率。