  Millimeter-sized, spherical silicate grains abundant in chondritic
meteorites, which are called as chondrules, are considered to be a strong
evidence of the melting event of the dust particles in the protoplanetary disk.
One of the most plausible scenarios is that the chondrule precursor dust
particles are heated and melt in the high-velocity gas flow (shock-wave heating
model). We developed the non-linear, time-dependent, and three-dimensional
hydrodynamic simulation code for analyzing the dynamics of molten droplets
exposed to the gas flow. We confirmed that our simulation results showed a good
agreement in a linear regime with the linear solution analytically derived by
Sekiya et al. (2003). We found that the non-linear terms in the hydrodynamical
equations neglected by Sekiya et al. (2003) can cause the cavitation by
producing negative pressure in the droplets. We discussed that the
fragmentation through the cavitation is a new mechanism to determine the upper
limit of chondrule sizes. We also succeeded to reproduce the fragmentation of
droplets when the gas ram pressure is stronger than the effect of the surface
tension. Finally, we compared the deformation of droplets in the shock-wave
heating with the measured data of chondrules and suggested the importance of
other effects to deform droplets, for example, the rotation of droplets. We
believe that our new code is a very powerful tool to investigate the
hydrodynamics of molten droplets in the framework of the shock-wave heating
model and has many potentials to be applied to various problems.
