Journal
INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS
Volume 34, Issue 1, Pages 1-13Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10618562.2019.1687888
Keywords
WENO scheme; smoothness indicators; convergence accuracy; hyperbolic conservation laws
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Funding
- National Natural Science Foundation of China [51579206]
- Key R&D Projects in Shaanxi Province, China [2018SF-352]
- Water Conservancy Science and Technology Project of Shaanxi Province, China [2017slkj-17]
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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.
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