Exact Riemann solutions for the drift-flux model of gas–liquid two-phase flows with van der Waals gas

Abstract

We develop a van der Waals drift-flux model to describe gas–liquid two-phase flow and solve its Riemann problem analytically. Employing a unified parametric approach, we derive the exact expressions for all elementary waves and rigorously establish the existence and uniqueness of solutions. Additionally, we propose a simple criterion to determine whether shocks or rarefaction waves arise in the 1-family and 3-family. Finally, the theoretical analysis is confirmed by numerical simulation. This work presents a comprehensive analysis of the Riemann problem for the drift-flux model with non-ideal gas, providing an exact mathematical framework for studying the non-ideal two-phase flow dynamics.