A hyperbolic two-phase flow model involving five partial differential equations is constructed for liquid–gas interface modelling. The model is able to deal with interfaces of simple contact where normal velocity and pressure are continuous as well as transition fronts where heat and mass transfer occur, involving pressure and velocity jumps. These fronts correspond to extra waves in the system. The model involves two temperatures and entropies but a single pressure and a single velocity. The closure is achieved by two equations of state that reproduce the phase diagram when equilibrium is reached. Relaxation toward equilibrium is achieved by temperature and chemical potential relaxation terms whose kinetics is considered infinitely fast at specific locations only, typically at evaporation fronts. Thus, metastable states are involved for locations far from these fronts. Computational results are compared to the experimental ones. Computed and measured front speeds are of the same order of magnitude and the same tendency of increasing front speed with initial temperature is reported. Moreover, the limit case of evaporation fronts propagating in highly metastable liquids with the Chapman–Jouguet speed is recovered as an expansion wave of the present model in the limit of stiff thermal and chemical relaxation.

A new model for interface problems with capillary effects in compressible fluids is presented together with a specific numerical method to treat capillary flows and pressure waves propagation. This new multiphase model is in agreement with physical principles of conservation and respects the second law of thermodynamics. A new numerical method is also proposed where the global system of equations is split into several submodels. Each submodel is hyperbolic or weakly hyperbolic and can be solved with an adequate numerical method. This method is tested and validated thanks to comparisons with analytical solutions (Laplace law) and with experimental results on droplet breakup induced by a shock wave.

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