WIAS Preprint No. 1620, (2011)

Exact solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows with and without phase transition


  • Dreyer, Wolfgang
  • Hantke, Maren
  • Warnecke, Gerald

2010 Mathematics Subject Classification

  • 80A22 76T15 35L65

2008 Physics and Astronomy Classification Scheme

  • 05.70.Fh, 05.70.Ce


  • Conservation laws, phase transitions, non-classical shocks, two phase flow model, exact Riemann solver, sharp interface model, thermodynamics


We consider the isothermal Euler equations with phase transition between a liquid and a vapor phase. The mass transfer is modeled by a kinetic relation. We prove existence and uniqueness results. Further, we construct the exact solution for Riemann problems. We derive analogous results for the cases of initially one phase with resulting condensation by compression or evaporation by expansion. Further we present numerical results for these cases. We compare the results to similar problems without phase transition.

Appeared in

  • Quart. Appl. Math., 71 (2013) pp. 509--540.

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