Open AccessThe Riemann problem for a weakly hyperbolic two-phase flow model of a dispersed phase in a carrier fluid
Author(s) -
Maren Hantke,
Christoph Matern,
Vincent Ssemaganda,
Gerald Warnecke
Publication year - 2019
Publication title -
quarterly of applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.603
H-Index - 41
eISSN - 1552-4485
pISSN - 0033-569X
DOI - 10.1090/qam/1556
Subject(s) - riemann problem , partial differential equation , two phase flow , mathematics , riemann's differential equation , riemann hypothesis , hyperbolic partial differential equation , phase (matter) , conservation law , flow (mathematics) , compressibility , mathematical analysis , isothermal process , riemann solver , compressible flow , physics , mechanics , thermodynamics , geometry , riemann xi function , quantum mechanics , finite volume method
We consider Riemann problems for a two-phase isothermal flow model of a dispersed phase in a compressible carrier phase. It is a weakly hyperbolic system of conservative partial differential equations. This model is the conservation part of a more complete physical model involving phase transitions in case both phases are of the same material. The purpose of this paper is to better understand the mathematical properties of the simplified model. We investigate the characteristic structure of the Riemann problems and construct their exact solutions. Solutions may contain delta shocks or vaporless states. We give examples for initial data corresponding to a system of water bubbles dispersed in liquid water. The analysis is complicated considerably by the fact that a liquid such as water requires an affine equation of state.