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 twophase 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 benchmarks for numerical schemes.

Automated summary

In this paper, a hyperbolic system of partial differential equations for two-phase mixture flows with N components is investigated. The system is derived from a more complex model that includes diffusion and exchange terms. Important features of the model include the assumption of isothermal flow, the use of a phase field function to differentiate phases, and a mixture equation of state involving the phase field function and an affine relation between partial densities and partial pressures in the liquid phase. Analysis is complicated due to these factors. A complete solution to the Riemann initial value problem is provided, and interesting examples are suggested as benchmarks for numerical schemes.