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A New Hybrid WENO Scheme with the High-Frequency Region for Hyperbolic Conservation Laws

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Abstract

In this paper, a new kind of hybrid method based on the weighted essentially non-oscillatory (WENO) type reconstruction is proposed to solve hyperbolic conservation laws. Comparing the WENO schemes with/without hybridization, the hybrid one can resolve more details in the region containing multi-scale structures and achieve higher resolution in the smooth region; meanwhile, the essentially oscillation-free solution could also be obtained. By adapting the original smoothness indicator in the WENO reconstruction, the stencil is distinguished into three types: smooth, non-smooth, and high-frequency region. In the smooth region, the linear reconstruction is used and the non-smooth region with the WENO reconstruction. In the high-frequency region, the mixed scheme of the linear and WENO schemes is adopted with the smoothness amplification factor, which could capture high-frequency wave efficiently. Spectral analysis and numerous examples are presented to demonstrate the robustness and performance of the hybrid scheme for hyperbolic conservation laws.

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  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, Anhui, China

    Yifei Wan & Yinhua Xia

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  1. Yifei Wan
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  2. Yinhua Xia
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Correspondence to Yinhua Xia.

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Yinhua Xia: Research supported by the National Numerical Windtunnel Project NNW2019ZT4-B08 and the NSFC grant No. 11871449.

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Wan, Y., Xia, Y. A New Hybrid WENO Scheme with the High-Frequency Region for Hyperbolic Conservation Laws. Commun. Appl. Math. Comput. 5, 199–234 (2023). https://doi.org/10.1007/s42967-021-00153-2

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  • DOI: https://doi.org/10.1007/s42967-021-00153-2

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