  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 bulk
behavior.
