  We investigate the hydrodynamics of the core helium flash near its peak. Past
research concerned with the dynamics of this event is inconclusive. However,
the most recent multidimensional hydrodynamic studies suggest a quiescent
behavior and seem to rule out an explosive scenario. Previous work indicated,
that depending on initial conditions, employed turbulence models, grid
resolution, and dimensionality of the simulation, the core helium flash leads
either to the disruption of a low-mass star or to a quiescent quasi-hydrostatic
evolution. We try to clarify this issue by simulating the evolution with
advanced numerical methods and detailed microphysics. Assuming spherical or
axial symmetry, we simulate the evolution of the helium core of a $1.25
M_{\odot}$ star with a metallicity Z=0.02 during the core helium flash at its
peak with a grid-based hydrodynamics code. We find that the core helium flash
neither rips the star apart, nor that it significantly alters its structure, as
convection plays a crucial role in keeping the star in hydrostatic equilibrium.
In addition, our simulations show the presence of overshooting, which implies
new predictions concerning mixing of chemical species in red giants.
