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The adiabatic exponential limits of Riemann solutions in the isentropic three-component model

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  • Jiang, Yiheng
  • Shen, Chun

Abstract

The explicit construction of Riemann solutions is achieved for an ideally isentropic three-component model owning a unitary velocity and a collective pressure in one space dimension under the hypotheses without mass and heat transfer and also without viscosity. In addition, the asymptotic results of Riemann solutions are explored at length by sending the adiabatic exponent drop to one. On the one side, it reveals the concentration phenomenon, where the Riemann solution with a 1-shock, 2,3-contact and 4-shock waves converges to a delta shock solution. On the other side, it also exhibits the cavitation phenomenon, where all internal states in the 1-rarefaction and 4-rarefaction waves become vacuum ones by sending this limit. Finally, some representative numerical simulations are offered to observe the formation of delta shock wave and vacuum state in a more intuitive way as the adiabatic exponent tends to one, which is consistent with the theoretical analysis.

Suggested Citation

  • Jiang, Yiheng & Shen, Chun, 2026. "The adiabatic exponential limits of Riemann solutions in the isentropic three-component model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PB), pages 48-70.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pb:p:48-70
    DOI: 10.1016/j.matcom.2025.10.002
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    References listed on IDEAS

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    1. Kuila, Sahadeb & Raja Sekhar, T. & Zeidan, D., 2015. "A Robust and accurate Riemann solver for a compressible two-phase flow model," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 681-695.
    2. Wei, Zhijian & Guo, Lihui, 2025. "The singular wave in a pressureless hydrodynamic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 234(C), pages 15-30.
    3. Daude, F. & Galon, P. & Potapov, S. & Beccantini, A. & Mianné, G., 2023. "A hyperbolic conservative one-velocity one-pressure barotropic three-component model for fast-transient fluid-structure interaction problems," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    4. Minhajul, & Zeidan, D. & Raja Sekhar, T., 2018. "On the wave interactions in the drift-flux equations of two-phase flows," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 117-131.
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