The Riemann problem for a two-phase mixture hyperbolic system with phase function and multi-component equation of state

In this paper a hyperbolic system of partial differential equations for two-phase mixture flows with \(N\) components is studied. It is derived from a more complicated model involving diffusion and exchange terms. Important features of the model are the assumption of isothermal flow, the use of a ph...

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Bibliographic Details
Published in:arXiv.org 2022-08
Main Authors: Hantke, Maren, Matern, Christoph, Warnecke, Gerald, Yaghi, Hazem
Format: Article
Language:English
Subjects:
Boundary value problems
Equations of state
Hyperbolic functions
Hyperbolic systems
Isothermal flow
Liquid phases
Mixtures
Partial differential equations
Two phase flow
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Summary:In this paper a hyperbolic system of partial differential equations for two-phase mixture flows with \(N\) components is studied. It is derived from a more complicated model involving diffusion and exchange terms. Important features of the model are the assumption of isothermal flow, the use of a phase field function to distinguish the phases and a mixture equation of state involving the phase field function as well as an affine relation between partial densities and partial pressures in the liquid phase. This complicates the analysis. A complete solution of the Riemann initial value problem is given. Some interesting examples are suggested as bench marks for numerical schemes.
ISSN:2331-8422