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The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques

Published online by Cambridge University Press:  15 December 2007

Christian Merkle  and
Christian Rohde
Christian Merkle
Affiliation:
Abteilung für Angewandte Mathematik, lbert-Ludwigs-Universität Freiburg, Hermann-Herder Str. 10, 79104 Freiburg, Germany. christian@mathematik.uni-freiburg.de
Christian Rohde
Affiliation:
Institut für Angewandte Mathematik und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
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Abstract


Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor fluid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost fluid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions sharply, i.e., without artificial smearing in the physically irrelevant elliptic region. Numerical experiments demonstrate the reliability of the method.

Keywords

Dynamical phase transitions in compressible mediavan-der-Waals pressurekinetic relationsRiemann solverghost fluid approach.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 6 , November 2007 , pp. 1089 - 1123
Copyright
© EDP Sciences, SMAI, 2007

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