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In this paper a hyperbolic system of partial differential equations fortwo-phase mixture flows with $N$ components is studied. It is derived from amore complicated model involving diffusion and exchange terms. Importantfeatures of the model are the assumption of isothermal flow, the use of a phasefield function to distinguish the phases and a mixture equation of stateinvolving the phase field function as well as an affine relation betweenpartial densities and partial pressures in the liquid phase. This complicatesthe analysis. A complete solution of the Riemann initial value problem isgiven. Some interesting examples are suggested as bench marks for numericalschemes.

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