Improvement of third-order finite difference WENO scheme at critical points. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Li, Xiaogang; Li, Guodong; Ge, Yongbin
• Is Part Of: International journal of computational fluid dynamics. Volume 34:Issue 1(2020)
• Page Start: 1
• Page End: 13
• Publication Date: 2020-01-02
• Subjects: WENO scheme -- smoothness indicators -- convergence accuracy -- hyperbolic conservation laws; Fluid dynamics -- Data processing -- Periodicals; 532.05
• DOI: 10.1080/10618562.2019.1687888
• Languages: English
• ISSNs: 1061-8562

Abstract

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.