  We report on recent progress in the physical and numerical modeling of
compressible two-phase flows that involve phase transition between the liquid
and gaseous state of the fluid.
  The high-speed dynamics of cavitation bubbles is studied in well-resolved
simulations (DNS) with a sharp-interface numerical model on a micro scale. The
underlying assumption of the employed evaporation/condensation model is that
phase change occurs in thermal non-equilibrium and that the associated
timescale is larger than that of the wave dynamics. Results for the collapse of
a spherical vapor bubble close to a solid wall are discussed for three
different bubble-wall configurations. The major challenge for such numerical
investigations is to accurately reproduce the dynamics of the interface between
liquid and vapor during the entire collapse process, including the high-speed
dynamics of the late stages, where compressibility of both phases plays a
decisive role.
  Direct interface resolving simulations are intractable for real world
technical applications such as turbulent flows involving cavitation clouds with
millions of vapor bubbles and a wide range of time and length scales. For this
reason, we developed a coarse grained model for large-eddy simulation (LES) of
turbulent two-phase flows with cavitation. In LES, vapor bubbles constitute
sub-grid scales that have to be modeled accordingly. On the grid scale, we
solve the compressible Navier-Stokes equations for a homogeneous mixture of
liquid and vapor. For deriving an appropriate equation of state, we assume that
the characteristic time scale of phase change is much smaller than the
numerical time step and that phase change is isentropic and in mechanical
equilibrium at the saturation pressure. This macroscopic model is applied to
realistic technical problems and to more generic flows to study the mutual
interaction of turbulence and cavitation.
