Comparison of macro- and microscopic solutions of the Riemann problem II. Two-phase shock tube

•Comparison of CFD with molecular dynamics for a two-phase Riemann problem.•Molecular dynamics data show non-classical waves in the Riemann solution.•CFD solutions based on the HEM method do not agree with molecular dynamics.•A sharp interface method that utilizes an undercompressive shock wave compares well.•Heat transfer across the interface must be taken into account in CFD simulations. The Riemann problem is one of the basic building blocks for numerical methods in computational fluid mechanics. Nonetheless, there are still open questions and gaps in theory and modeling for situations with complex thermodynamic behavior. In this series, we compare numerical solutions of the macroscopic flow equations with molecular dynamics simulation data. To enable molecular dynamics for sufficiently large scales in time and space, we selected the truncated and shifted Lennard-Jones potential, for which also highly accurate equations of state are available. A comparison of a two-phase Riemann problem is shown, which involves a liquid and a vapor phase, with an undergoing phase transition. The loss of hyperbolicity allows for the occurrence of anomalous wave structures. We successfully compare the molecular dynamics data with two macroscopic numerical solutions obtained by either assuming local phase equilibrium or by imposing a kinetic relation and allowing for metastable states.