ABSTRACT In the paper, an improved third-order finite difference weighted essentially non-oscillatory scheme is presented for achieving the optimal order near critical points. A new global smoothness indicator is obtained with the way of Taylor expansion for the local smoothness indicator. In the framework of the conventional WENO-Z scheme, we present an improved third-order finite difference WENO scheme. The proposed scheme is verified to achieve third-order accuracy by several benchmarks and the behaviour of the present scheme is proved on a variety of one- and two- dimensional standard numerical examples. Numerical results demonstrate that the proposed scheme gives better performance in comparison with the other third-order WENO schemes.

中文翻译：

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关键点三阶有限差分WENO方案的改进

摘要 本文提出了一种改进的三阶有限差分加权基本非振荡方案，以实现临界点附近的最优阶数。局部平滑度指标采用泰勒展开的方式得到一个新的全局平滑度指标。在传统的 WENO-Z 方案的框架内，我们提出了一种改进的三阶有限差分 WENO 方案。所提出的方案通过几个基准验证实现了三阶精度，并且本方案的行为在各种一维和二维标准数值例子中得到了证明。数值结果表明，与其他三阶 WENO 方案相比，所提出的方案具有更好的性能。