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On the wave interactions for the drift-flux equations with the Chaplygin gas

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Abstract

The Riemann problem for the isentropic drift-flux equations of gas-liquid two-phase flows under the equation of state for Chaplygin gas is investigated in detail, whose Riemann solution consists of either a delta shock wave or the combination of three contact discontinuities depending on the choice of Riemann initial data. In the delta shock wave solution, the Dirac delta function is developed simultaneously in the two densities of gas and liquid. Moreover, the weights of Dirac delta functions for the two densities and the propagation speed of delta shock wave are calculated explicitly by using the generalized Rankine-Hugoniot conditions. Furthermore, the wave interaction problems are considered in some specially designated circumstances. Some interesting nonlinear phenomena can be observed and analyzed carefully during the process of wave interactions. For instance, the interaction between a delta shock wave and a contact discontinuity produces two contact discontinuities and one delta contact discontinuity as well as the interaction between contact discontinuities belonging to different families leads to a delta shock wave.

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Acknowledgements

The authors would like to thank the anonymous referee for his/her very helpful comments and suggestions which improve the original manuscript greatly. This work is partially supported by Natural Science Foundation of Shandong Province (ZR2019MA058).

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Authors and Affiliations

  1. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, Shandong Province, People’s Republic of China

    Shuangrong Li & Chun Shen

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Shuangrong Li

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  1. Shuangrong Li
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  2. Chun Shen
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Correspondence to Chun Shen.

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Communicated by David Lannes.

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This work is partially supported by Shandong Provincial Natural Science Foundation (ZR2019MA058)

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Li, S., Shen, C. On the wave interactions for the drift-flux equations with the Chaplygin gas. Monatsh Math 197, 635–654 (2022). https://doi.org/10.1007/s00605-022-01688-z

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