Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

Authors: Maren Hantke, Wolfgang Dreyer and Gerald Warnecke
Journal: Quart. Appl. Math. 71 (2013), 509-540
MSC (2010): Primary 80A22, 76T15, 35L65
DOI: https://doi.org/10.1090/S0033-569X-2013-01290-X
Published electronically: May 17, 2013
MathSciNet review: 3112826
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Abstract | References | Similar Articles | Additional Information

Abstract: 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.

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Additional Information

Maren Hantke
Affiliation: Institute for Analysis and Numerics, Otto-von-Guericke-University Magdeburg, PSF 4120, D-39016 Magdeburg, Germany
Email: maren.hantke@ovgu.de

Wolfgang Dreyer
Affiliation: Weierstraß-Institut für angewandte Analysis and Stochastik (WIAS), Mohrenstraße 39, D-10117 Berlin, Germany
Email: dreyer@wias-berlin.de

Gerald Warnecke
Affiliation: Institute for Analysis and Numerics, Otto-von-Guericke-University Magdeburg, PSF 4120, D-39016 Magdeburg, Germany
Email: gerald.warnecke@ovgu.de

DOI: https://doi.org/10.1090/S0033-569X-2013-01290-X
Keywords: Conservation laws, phase transitions, nonclassical shocks, two-phase flow model, exact Riemann solver, sharp interface model, thermodynamics
Received by editor(s): August 19, 2011
Published electronically: May 17, 2013
Additional Notes: This work was supported by the DFG grant Wa 633/17 within the DFGCNRS research group FOR 563/1 and by the DFG grant DR 401/4-1. The authors thank the DFG for this funding
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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