The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques
Abteilung für Angewandte Mathematik, lbert-Ludwigs-Universität Freiburg, Hermann-Herder Str. 10, 79104 Freiburg, Germany. email@example.com
2 Institut für Angewandte Mathematik und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
Revised: 20 April 2007
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.
Mathematics Subject Classification: 35M10 / 76T10
Key words: Dynamical phase transitions in compressible media / van-der-Waals pressure / kinetic relations / Riemann solver / ghost fluid approach.
© EDP Sciences, SMAI, 2007