On a Model of Multiphase Flow

Abstract

We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity, and the mass density fraction of the vapor in the fluid. For a class of initial data having large total variation we prove the global existence of solutions to the Cauchy problem.

Front tracking for a model of immiscible gas flow with large data

“…Amadori and Corli [1] extend the p-system with an extra equation, λ t = 0, to model multiphase flow, and use front tracking to prove existence of a weak solution for large data. As for system (1.1), the pressure function in [1] is a function of both v and the new variable, λ, making the two systems similar.…”

“…As for system (1.1), the pressure function in [1] is a function of both v and the new variable, λ, making the two systems similar. However, since the adiabatic gas constant, γ, is equal to one in [1], vacuum can never occur for their system as it can for system (1.1).…”

“…As for system (1.1), the pressure function in [1] is a function of both v and the new variable, λ, making the two systems similar. However, since the adiabatic gas constant, γ, is equal to one in [1], vacuum can never occur for their system as it can for system (1.1). Furthermore, the wave curves in [1] are monotone in λ, resulting in a considerably simpler analysis of the wave interactions compared with the analysis necessary for the model considered here.…”

“…However, since the adiabatic gas constant, γ, is equal to one in [1], vacuum can never occur for their system as it can for system (1.1). Furthermore, the wave curves in [1] are monotone in λ, resulting in a considerably simpler analysis of the wave interactions compared with the analysis necessary for the model considered here. The system treated in [1] is a simplified version of the model discussed by Fan in [12].…”

“…Furthermore, the wave curves in [1] are monotone in λ, resulting in a considerably simpler analysis of the wave interactions compared with the analysis necessary for the model considered here. The system treated in [1] is a simplified version of the model discussed by Fan in [12]. Similar models, but with a rather different pressure law, are also considered in [11] and [19] applying completely different methods.…”