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

A sharp interface method for compressible liquid-vapor flow with phase transition and surface tension