The Riemann problem for non-ideal isentropic compressible two phase flows

•We study the Riemann problem for a non-conservative five-equations two-pressure (5E2P) model of compressible gas–liquid two-phase flows.•The mathematical model comprises 2-pressure of an isentropic equation of state for van der Waals gas and Tait׳s pure liquid.•The solution influenced by the van der Waals excluded volume is highlighted.

We consider the Riemann problem for a five-equation, two-pressure (5E2P) model of non-ideal isentropic compressible gas–liquid two-phase flows. This system is more complex due to the extended thermodynamics model for van der Waals gases, that is, typical real gases for gas phase and Tait׳s equation of state for liquid phase. The overall model is strictly hyperbolic and non-conservative form. We investigate the structure of Riemann problem and construct the solution for it. To construct solution of Riemann problem approximately assuming that all waves corresponding to the genuinely non-linear characteristic fields are rarefaction and then we discuss their properties. Lastly, we discuss numerical examples and study the solution influenced by the van der Waals excluded volume.