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A numerical study for WENO scheme-based on different lattice Boltzmann flux solver for compressible flows

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Abstract

In this paper, the finite difference weighted essentially non-oscillatory (WENO) scheme is incorporated into the recently developed four kinds of lattice Boltzmann flux solver (LBFS) to simulate compressible flows, including inviscid LBFS I, viscous LBFS II, hybrid LBFS III and hybrid LBFS IV. Hybrid LBFS can automatically realize the switch between inviscid LBFS I and viscous LBFS II through introducing a switch function. The resultant hybrid WENO–LBFS scheme absorbs the advantages of WENO scheme and hybrid LBFS. We investigate the performance of WENO scheme based on four kinds of LBFS systematically. Numerical results indicate that the devopled hybrid WENO–LBFS scheme has high accuracy, high resolution and no oscillations. It can not only accurately calculate smooth solutions, but also can effectively capture contact discontinuities and strong shock waves.

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Acknowledgements

This study was supported by the National Natural Science Foundation of China (Grants 11372168, 11772179).

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Authors and Affiliations

  1. College of Engineering, Shantou University, Shantou, 515063, China

    You Li, Xiao-Dong Niu,  Adnan Khan & Xiang Li

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    Hai-Zhuan Yuan

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  1. You Li
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  2. Xiao-Dong Niu
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  5. Xiang Li
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Correspondence to Xiao-Dong Niu.

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Li, Y., Niu, XD., Yuan, HZ. et al. A numerical study for WENO scheme-based on different lattice Boltzmann flux solver for compressible flows. Acta Mech. Sin. 34, 995–1014 (2018). https://doi.org/10.1007/s10409-018-0785-9

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  • DOI: https://doi.org/10.1007/s10409-018-0785-9

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