Global weak solutions for a model of two-phase flow with a single interface

TL;DR

This paper establishes the existence of global weak solutions for a hyperbolic system modeling two-phase inviscid fluid flow with phase transitions and interfaces, using a specialized front tracking method.

Contribution

It provides explicit bounds on initial data for global weak entropic solutions and introduces a tailored front tracking scheme for this model.

Findings

Existence of global weak solutions under certain initial data bounds

Explicit bounds for initial data ensuring solution existence

Development of a specialized front tracking scheme for phase transition models

Abstract

We consider a simple nonlinear hyperbolic system modeling the flow of an inviscid fluid. The model includes as state variable the mass density fraction of the vapor in the fluid and then phase transitions can be taken into consideration; moreover, phase interfaces are contact discontinuities for the system. We focus on the special case of initial data consisting of two different phases separated by an interface. We find explicit bounds on the (possibly large) initial data in order that weak entropic solutions exist for all times. The proof exploits a carefully tailored version of the front tracking scheme.