The numerical approximation of non-isothermal liquid-vapor flow within
the compressible regime is a difficult task because complex physical
effects at the phase interfaces can govern the global flow behavior.
We present a sharp interface approach which treats the interface
as a shock-wave like discontinuity. Any mixing of fluid phases is
avoided by using the flow solver in the bulk regions only, and a
ghost-fluid approach close to the interface. The coupling states
for the numerical solution in the bulk regions are determined by
the solution of local multi-phase Riemann problems across the interface.
The Riemann solution accounts for the relevant physics by enforcing
appropriate jump conditions at the phase boundary. A wide variety
of interface effects can be handled in a thermodynamically consistent
way. This includes surface tension or mass/energy transfer by phase
transition. Moreover, the local normal speed of the interface, which
is needed to calculate the time evolution of the interface, is given
by the Riemann solution. The interface tracking itself is based on
a level-set method. The focus in this paper is the description of
the multi-phase Riemann solver and its usage within the sharp interface
approach. One-dimensional problems are selected to validate the approach.
Finally, the three-dimensional simulation of a wobbling droplet and
a shock droplet interaction in two dimensions are shown. In both
problems phase transition and surface tension determine the global