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High Order Finite Difference Alternative WENO Scheme for Multi-component Flows

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Abstract

A fifth order finite difference alternative weighted essentially non-oscillatory scheme is studied for a five-equation model, which plays an important role in the modelling of compressible multi-component flows. In our algorithm, the primitive variables are used in the weighted essentially non-oscillatory interpolation, from which it can be proved that the equilibriums of the velocity and pressure are preserved respectively throughout the whole computation of contact moving interface problems, under the ideal and stiffened gases equations of state. In addition, it is found that with the interpolation being performed on the characteristic variables which are the projections of the primitive variables, non-physical oscillations appearing around the contact waves can be significantly restrained. Numerical examples verify the theory and illustrate the robustness of the proposed scheme.

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Acknowledgements

The research of Yaguang Gu and Zhen Gao was partially supported by the NNSFC (11871443) and Shandong Provincial Qingchuang Science and Technology Project (2019KJI002). The research of Guanghui Hu was partially supported by NNSFC (11922120) and Multi-Year Research Grant (2019-00154-FST) of University of Macau. The research of Peng Li was partially supported by the NNSFC (11801383) and Hebei Provincial NSF (A2020210047). The research of Lifeng Wang was partially supported by the NNSFC (11975053). The author Yaguang Gu would also like to thank Dr. Dongmi Luo for helpful discussions.

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

    Peng Li

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

    Lifeng Wang

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

    Lifeng Wang

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  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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  5. Lifeng Wang
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Correspondence to Zhen Gao.

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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. High Order Finite Difference Alternative WENO Scheme for Multi-component Flows. J Sci Comput 89, 52 (2021). https://doi.org/10.1007/s10915-021-01659-w

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  • DOI: https://doi.org/10.1007/s10915-021-01659-w

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