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 media, van-der-Waals pressure, kinetic relations, Riemann solver, ghost fluid approach
@article{M2AN_2007__41_6_1089_0,
author = {Merkle, Christian and Rohde, Christian},
title = {The sharp-interface approach for fluids with phase change : {Riemann} problems and ghost fluid techniques},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1089--1123},
year = {2007},
publisher = {EDP Sciences},
volume = {41},
number = {6},
doi = {10.1051/m2an:2007048},
mrnumber = {2377108},
zbl = {1134.35074},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2007048/}
}
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: Modélisation mathématique et analyse numérique PY - 2007 SP - 1089 EP - 1123 VL - 41 IS - 6 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2007048/ DO - 10.1051/m2an:2007048 LA - en ID - M2AN_2007__41_6_1089_0 ER -
%0 Journal Article %A Merkle, Christian %A Rohde, Christian %T The sharp-interface approach for fluids with phase change : Riemann problems and ghost fluid techniques %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 1089-1123 %V 41 %N 6 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2007048/ %R 10.1051/m2an:2007048 %G en %F M2AN_2007__41_6_1089_0
Merkle, Christian; Rohde, Christian. The sharp-interface approach for fluids with phase change : Riemann problems and ghost fluid techniques. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 6, pp. 1089-1123. doi: 10.1051/m2an:2007048
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