Riemann solvers for phase transition in a compressible sharp-interface method

•Formulation of exact and approximate Riemannn solvers with phase transition effects.•Modelling of the interfacial process based on non-equilibrium thermodynamics.•Results with a sharp-interface method were validated against molecular dynamics data.•Numerical method was applied to a 2D shock-droplet interaction. In this paper, we consider Riemann solvers with phase transition effects based on the Euler–Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition process via the theory of classical irreversible thermodynamics. Closure is obtained by appropriate Onsager coefficients for evaporation and condensation. We use the proposed Riemann solvers in a sharp-interface level-set ghost fluid method to couple the individual phases with each other. The proposed sharp-interface method is validated against molecular dynamics data of evaporating Lennard–Jones truncated and shifted fluid. We further study the effects of phase transition on a shock-drop interaction with the novel approximate Riemann solvers.