  Context. Theoretical predictions from models of red giant branch stars are a
valuable tool for various applications in astrophysics ranging from galactic
chemical evolution to studies of exoplanetary systems. Aims. We use the
radiative transfer code OPTIM3D and realistic 3D radiative-hydrodynamical (RHD)
surface convection simulations of red giants to explore the impact of
granulation on interferometric observables. Methods. We compute intensity maps
for the 3D simulation snapshots in two filters: in the optical at 5000 \pm 300
{\AA} and in the K band 2.14 $\pm$ 0.26 {\mu}m FLUOR filter, corresponding to
the wavelength-range of instruments mounted on the CHARA interferometer. From
the intensity maps, we construct images of the stellar disks, accounting for
center-to-limb variations. We then derive interferometric visibility amplitudes
and phases. We study their behavior with position angle and wavelength.
Results. We provide average limb-darkening coefficients for different
metallicities and wavelength-ranges. We detail the prospects for the detection
and characterization of granulation and center-to-limb variations of red giant
stars with today's interferometers. We find that the effect of
convective-related surface structures depends on metallicity and surface
gravity. We provided theoretical closure phases that should be incorporated
into the analysis of red giant planet companion closure phase signals. We
estimate 3D-1D corrections to stellar radii determination: 3D models are ~ 3.5%
smaller to ~ 1% larger in the optical with respect to 1D, and roughly 0.5 to
1.5% smaller in the infrared. Even if these corrections are small, they are
important to properly set the zero point of effective temperature scale derived
by interferometry and to strengthen the confidence of existing red giant
catalogues of calibrating stars for interferometry.
