  Hydrodynamical simulations of stellar interactions require stable models of
stars as initial conditions. Such initial models, however, are difficult to
construct for giant stars because of the wide range in spatial scales of the
hydrostatic equilibrium and in dynamical timescales between the core and the
envelope of the giant. They are needed for, e.g., modeling the common envelope
phase where a giant envelope encompasses both the giant core and a companion
star. Here, we present a new method of approximating and reconstructing giant
profiles from a stellar evolution code to produce stable models for
multi-dimensional hydrodynamical simulations. We determine typical stellar
stratification profiles with the 1D stellar evolution code MESA. After an
appropriate mapping, hydrodynamical simulations are conducted using the
moving-mesh code AREPO. The giant profiles are approximated by replacing the
core of the giant with a point mass and by constructing a suitable continuation
of the profile to the center. Different reconstruction methods are tested that
can specifically control the convective behaviour of the model. After mapping
to a grid, a relaxation procedure that includes damping of spurious velocities
yields stable models in three-dimensional hydrodynamical simulations. Initially
convectively stable configurations lead to stable hydrodynamical models while
for stratifications that are convectively unstable in the stellar evolution
code, simulations recover the convective behaviour of the initial model and
show large convective plumes with Mach numbers up to 0.8. Examples are shown
for a $2M_\odot$ red giant and a $0.67M_\odot$ asymptotic giant branch star. A
detailed analysis shows that the improved method reliably provides stable
models of giant envelopes that can be used as initial conditions for subsequent
hydrodynamical simulations of stellar interactions involving giant stars.
