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

TL;DR

This paper analyzes a hyperbolic PDE system modeling two-phase multi-component flows, deriving a complete solution to the Riemann problem and proposing benchmark examples for numerical validation.

Contribution

It introduces a novel hyperbolic system with phase field and multi-component equations, providing a complete Riemann problem solution for complex two-phase flow models.

Findings

Complete Riemann problem solution for the system

Benchmark examples for numerical schemes

Insights into phase field and multi-component interactions

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.