  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 modelling 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.
