  Context. It has been suggested that convection in Red Supergiant (RSG) stars
gives rise to large-scale granules causing observable surface inhomogeneities.
This convection is also extremely vigorous, and suspected to be one of the
causes of mass-loss in RSGs. It must thus be understood in details. Evidence
has been accumulated that there are asymmetries in the photospheres of RSGs,
but detailedstudies of granulation are still lacking. Interferometric
observations offer an exciting possibility to tackle this question, but they
are still often interpreted using smooth symmetrical limb-darkened intensity
distributions, or very simple spotted ad hoc models. Aims. We explore the
impact of the granulation on visibility curves and closure phases using the
radiative transfer code OPTIM3D. We simultaneously assess how 3D simulations of
convection in RSG with CO5BOLD can be tested against these observations.
Methods. We use 3D radiative-hydrodynamics (RHD) simulations of convection to
compute intensity maps at various wavelengths and time, from which we derive
interferometric visibility amplitudes and phases. We study their behaviour with
time, position angle, and wavelength, and compare them to observations of the
RSG alpha Ori Results. We provide average limb-darkening coefficients for RSGs.
We detail the prospects for the detection and characterization of granulation
(contrast, size) on RSGs. We demonstrate that our RHD simulations provide an
excellent fit to existing interferometric observation of alpha Ori, contrary to
limb darkened disks. This confirms the existence of large convective cells on
the surface of Betelgeuse.
