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arXiv · 2208.10850

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

Maren Hantke·Christoph Matern·Gerald Warnecke·Hazem Yaghi
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Abstract

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.

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Maren Hantke, Christoph Matern, Gerald Warnecke, Hazem Yaghi. 2022-08-23. The Riemann problem for a two-phase mixture hyperbolic system with phase function and multi-component equation of state. https://arxiv.org/abs/2208.10850

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