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A Conservative Sharp-Interface Numerical Method for Two-dimensional Compressible Two-phase Flows

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Abstract

In this work, a conservative sharp-interface numerical method is developed to simulate compressible two-medium flows with a free interface. In the method, the cut-cell method is introduced to achieve a sharp interface. To avoid the complicated geometric cell merging approach in the cut-cell method, the small cut cells are updated using a flux/conserved variable merging/mixing method that considers the type of small cut cells (general, singular, and vanished). In addition, the residual conserved quantity is redistributed to ensure conservation during the re-initialization process of the level set function. Moreover, to handle thin or small-scale structures where the numerical oscillation may appear, the mixing cut-cell and ghost fluid method is adopted to update these cut cells with a conserved variables mixing approach. Various numerical tests are performed to verify the conservation and robustness of the proposed method.

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The data of this study is available from the first author upon reasonable request.

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Acknowledgements

Xiao Bai is partially supported by the Natural Science Foundation of Universities in Anhui Province (Grant No. KJ2021A0515), the Pre-research Project of National Natural Science Foundation of China (Grant No. KZ42019112) and the Scientific Research Starting Foundation for Anhui Polytechnic University (Grant No. S022018028). Maojun Li is partially supported by the National Natural Science Foundation of China (Grant Nos. 11871139, 12271082, 62231016).

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  1. School of Mathematics-Physics and Finance, Anhui Polytechnic University, Wuhu, 241000, Anhui, People’s Republic of China

    Xiao Bai

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Maojun Li

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  1. Xiao Bai
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Bai, X., Li, M. A Conservative Sharp-Interface Numerical Method for Two-dimensional Compressible Two-phase Flows. J Sci Comput 97, 30 (2023). https://doi.org/10.1007/s10915-023-02338-8

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