  In this paper we present solutions to three short comings of Smoothed
Particles Hydrodynamics (SPH) encountered in previous work when applying it to
Giant Impacts. First we introduce a novel method to obtain accurate SPH
representations of a planet's equilibrium initial conditions based on equal
area tessellations of the sphere. This allows one to imprint an arbitrary
density and internal energy profile with very low noise which substantially
reduces computation because these models require no relaxation prior to use. As
a consequence one can significantly increase the resolution and more flexibly
change the initial bodies to explore larger parts of the impact parameter space
in simulations. The second issue addressed is the proper treatment of the
matter/vacuum boundary at a planet's surface with a modified SPH density
estimator that properly calculates the density stabilizing the models and
avoiding an artificially low density atmosphere prior to impact. Further we
present a novel SPH scheme that simultaneously conserves both energy and
entropy for an arbitrary equation of state. This prevents loss of entropy
during the simulation and further assures that the material does not evolve
into unphysical states. Application of these modifications to impact
simulations for different resolutions up to $6.4 \cdot 10^6$ particles show a
general agreement with prior result. However, we observe resolution dependent
differences in the evolution and composition of post collision ejecta. This
strongly suggests that the use of more sophisticated equations of state also
demands a large number of particles in such simulations.

Earth and Planetary Astrophysics;Computational Physics;Fluid Dynamics