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Riemann solvers for phase transition in a compressible sharp-interface method

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  • Jöns, Steven
  • Munz, Claus-Dieter

Abstract

In this paper, we consider Riemann solvers with phase transition effects based on the Euler–Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition process via the theory of classical irreversible thermodynamics. Closure is obtained by appropriate Onsager coefficients for evaporation and condensation. We use the proposed Riemann solvers in a sharp-interface level-set ghost fluid method to couple the individual phases with each other. The proposed sharp-interface method is validated against molecular dynamics data of evaporating Lennard–Jones truncated and shifted fluid. We further study the effects of phase transition on a shock-drop interaction with the novel approximate Riemann solvers.

Suggested Citation

  • Jöns, Steven & Munz, Claus-Dieter, 2023. "Riemann solvers for phase transition in a compressible sharp-interface method," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s009630032200697x
    DOI: 10.1016/j.amc.2022.127624
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    References listed on IDEAS

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    1. Caputa, J.P. & Struchtrup, Henning, 2011. "Interface model for non-equilibrium evaporation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(1), pages 31-42.
    2. Johannessen, Eivind & Bedeaux, Dick, 2006. "Integral relations for the heat and mass transfer resistivities of the liquid–vapor interface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 258-274.
    3. 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.
    4. Bedeaux, D. & Kjelstrup, S., 1999. "Transfer coefficients for evaporation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(3), pages 413-426.
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