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.