  At present, the giant impact (GI) is the most widely accepted model for the
origin of the Moon. Most of the numerical simulations of GI have been carried
out with the smoothed particle hydrodynamics (SPH) method. Recently, however,
it has been pointed out that standard formulation of SPH (SSPH) has
difficulties in the treatment of a contact discontinuity such as a core-mantle
boundary and a free surface such as a planetary surface. This difficulty comes
from the assumption of differentiability of density in SSPH. We have developed
an alternative formulation of SPH, density independent SPH (DISPH), which is
based on differentiability of pressure instead of density to solve the problem
of a contact discontinuity. In this paper, we report the results of the GI
simulations with DISPH and compare them with those obtained with SSPH. We found
that the disk properties, such as mass and angular momentum produced by DISPH
is different from that of SSPH. In general, the disks formed by DISPH are more
compact: while formation of a smaller mass moon for low-oblique impacts is
expected with DISPH, inhibition of ejection would promote formation of a larger
mass moon for high-oblique impacts. Since only the improvement of core-mantle
boundary significantly affects the properties of circumplanetary disks
generated by GI and DISPH has not been significantly improved from SSPH for a
free surface, we should be very careful when some conclusions are drawn from
the numerical simulations for GI. And it is necessary to develop the numerical
hydrodynamical scheme for GI that can properly treat the free surface as well
as the contact discontinuity.
