  We present the first 3D hydrodynamics simulations of the excitation and
propagation of internal gravity waves (IGWs) in the radiative interiors of
low-mass stars on the red giant branch (RGB). We use the PPMstar explicit gas
dynamics code to simulate a portion of the convective envelope and all the
radiative zone down to the hydrogen-burning shell of a 1.2$M_{\odot}$ upper RGB
star. We perform simulations for different grid resolutions (768$^3$, 1536$^3$
and 2880$^3$), a range of driving luminosities, and two different
stratifications (corresponding to the bump luminosity and the tip of the RGB).
Our RGB tip simulations can be directly performed at the nominal luminosity,
circumventing the need for extrapolations to lower luminosities. A rich,
continuous spectrum of IGWs is observed, with a significant amount of total
power contained at high wavenumbers. By following the time evolution of a
passive dye in the stable layers, we find that IGW mixing in our simulations is
weaker than predicted by a simple analytical prescription based on shear mixing
and not efficient enough to explain the missing RGB extra mixing. However, we
may be underestimating the efficiency of IGW mixing given that our simulations
include a limited portion of the convective envelope. Quadrupling its radial
extent compared to our fiducial setup increases convective velocities by up to
a factor 2 and IGW velocities by up to a factor 4. We also report the formation
of a $\sim 0.2\,H_P$ penetration zone and evidence that IGWs are excited by
plumes that overshoot into the stable layers.
