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Transport diffuse interface model for simulation of solid-fluid interaction

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Abstract

For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a “0=0” equation when the volume fraction of a certain phase takes the value of zero or unity. This is because the conservative variables in phase-density equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves, such as shear waves in fluids, are introduced by the artificial treatment. In this paper, a transport diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, a new formulation for phase densities is derived, which is unrelated to volume fractions. Consequently, the new model is able to handle zero/unity volume fractions, and nonphysical waves caused by artificial volume fractions are prevented. One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.

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Acknowledgements

The authors are grateful to Prof. Jiequan LI from the Institute of Applied Physics and Computational Mathematics for his valuable suggestions.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Li Li, Qian Chen & Baolin Tian

Authors
  1. Li Li
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  2. Qian Chen
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  3. Baolin Tian
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Corresponding author

Correspondence to Baolin Tian.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11702029, 11771054, U1730118, 91852207, and 11801036) and the China Postdoctoral Science Foundation (No. 2016M600967)

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Li, L., Chen, Q. & Tian, B. Transport diffuse interface model for simulation of solid-fluid interaction. Appl. Math. Mech.-Engl. Ed. 40, 321–330 (2019). https://doi.org/10.1007/s10483-019-2443-9

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  • DOI: https://doi.org/10.1007/s10483-019-2443-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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