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首页> 外文期刊>International Journal for Numerical Methods in Fluids >An improved third-order finite difference weighted essentially nonoscillatory scheme for hyperbolic conservation laws
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An improved third-order finite difference weighted essentially nonoscillatory scheme for hyperbolic conservation laws

机译：改进的三阶有限差异加权基本上非触控法的非张开方案

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摘要

In this article, we present an improved third-order finite difference weighted essentially nonoscillatory (WENO) scheme to promote the order of convergence at critical points for the hyperbolic conservation laws. The improved WENO scheme is an extension of WENO-ZQ scheme. However, the global smoothness indicator has a little different from WENO-ZQ scheme. In this follow-up article, a convex combination of a second-degree polynomial with two linear polynomials in a traditional WENO fashion is used to compute the numerical flux at cell boundary. Although the same three-point information is adopted by the improved third-order WENO scheme, the truncation errors are smaller than some other third-order WENO schemes in L-infinity and L-2 norms. Especially, the convergence order is not declined at critical points, where the first and second derivatives vanish but not the third derivative. At last, the behavior of improved 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 other third-order WENO schemes.
机译：在本文中，我们提出了一种改进的三阶有限差异权，基本上非振动（Weno）方案，以促进双曲胁迫法的关键点处的收敛顺序。改进的Weno方案是Weno-ZQ方案的延伸。然而，全球平滑度指示器与Weno-ZQ方案有点不同。在该后续物品中，使用传统Weno时尚中的两个线性多项式的二级多项式的凸起组合用于计算细胞边界的数值通量。尽管通过改进的三阶WENO方案采用了相同的三点信息，但是截断误差小于L-Infinity和L-2规范中的其他三阶Weno方案。特别是，收敛顺序在关键点处没有下降，其中第一和第二衍生物消失但不是第三衍生物。最后，证明了改进方案的行为在各种单一和二维标准数值例子上。数值结果表明，与其他三阶WENO方案相比，所提出的方案提供了更好的性能。

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