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A Robust High Order Alternative WENO Scheme for the Five-Equation Model

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Abstract

High order methods play important roles in the modelling of compressible multi-component flows. However, they may generate negative sound speed, which leads to an instability of the numerical schemes. In this paper, we propose bound- and positivity-preserving limiters for high order finite difference schemes, based on which the equilibriums of the velocity and pressure are preserved throughout the whole computation of contact moving interface problems with the ideal and stiffened equations of state. For illustration purpose, high order alternative WENO scheme is taken for example. Numerical examples verify the theory and demonstrate the robustness of the proposed bound- and positivity-preserving limiters.

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Data availability

The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

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Funding

The research of Yaguang Gu and Zhen Gao is partially supported by the NNSFC (11871443) and Shandong Provincial Qingchuang Science and Technology Project (2019KJI002). The research of Guanghui Hu is partially supported by NNSFC (11922120) and Multi-Year Research Grant (2019-00154-FST) of University of Macau. The research of Peng Li is partially supported by the NNSFC (11801383) and Hebei Provincial NSF (A2020210047). The research of Lifeng Wang is partially supported by the NNSFC (11975053).

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong, China

    Yaguang Gu & Zhen Gao

  2. College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao, Shandong, China

    Yaguang Gu

  3. Department of Mathematics, University of Macau, Macao S.A.R., China

    Guanghui Hu

  4. Zhuhai UM Science & Technology Research Institute, Zhuhai, Guangdong, China

    Guanghui Hu

  5. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, Hebei, China

    Peng Li

  6. Institute of Applied Physics and Computational Mathematics, Beijing, China

    Lifeng Wang

  7. Center for Applied Physics and Technology, HEDPS, and College of Engineering, Peking University, Beijing, China

    Lifeng Wang

Authors
  1. Yaguang Gu
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  2. Zhen Gao
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  3. Guanghui Hu
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  4. Peng Li
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Corresponding author

Correspondence to Zhen Gao.

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We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. There is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

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The custom codes generated during the current study are available from the corresponding author on reasonable request.

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Gu, Y., Gao, Z., Hu, G. et al. A Robust High Order Alternative WENO Scheme for the Five-Equation Model. J Sci Comput 88, 12 (2021). https://doi.org/10.1007/s10915-021-01529-5

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  • DOI: https://doi.org/10.1007/s10915-021-01529-5

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