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

Christian Merkle; Christian Rohde

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 6, page 1089-1123
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Merkle, Christian, and Rohde, Christian. "The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques." ESAIM: Mathematical Modelling and Numerical Analysis 41.6 (2007): 1089-1123. <http://eudml.org/doc/250027>.

@article{Merkle2007,
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. },
author = {Merkle, Christian, Rohde, Christian},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Dynamical phase transitions in compressible media; van-der-Waals pressure; kinetic relations; Riemann solver; ghost fluid approach.; dynamical phase transitions in compressible media; van-der-Waals pressure; ghost fluid approach},
language = {eng},
month = {12},
number = {6},
pages = {1089-1123},
publisher = {EDP Sciences},
title = {The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques},
url = {http://eudml.org/doc/250027},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Merkle, Christian
AU - Rohde, Christian
TI - The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/12//
PB - EDP Sciences
VL - 41
IS - 6
SP - 1089
EP - 1123
AB - 
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.
LA - eng
KW - Dynamical phase transitions in compressible media; van-der-Waals pressure; kinetic relations; Riemann solver; ghost fluid approach.; dynamical phase transitions in compressible media; van-der-Waals pressure; ghost fluid approach
UR - http://eudml.org/doc/250027
ER -

References

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