  Red supergiants are massive evolved stars that contribute extensively to the
chemical enrichment of our Galaxy. It has been shown that convection in those
stars gives rise to large granules that cause surface inhomogeneities and shock
waves in the photosphere. The understanding of their dynamics is crucial to
unveil the unknown mass-loss mechanism, their chemical composition and stellar
parameters. We present a new generation of red supergiants simulations with a
more sophisticated opacity treatment done with 3D radiative- hydrodynamics
CO5BOLD. In the code, the coupled equations of compressible hydrodynamics and
non-local radiation transport are solved in the presence of a spherical
potential. The stellar core is replaced by a special spherical inner boundary
condition, where the gravitational potential is smoothed and the energy
production by fusion is mimicked by a simply producing heat corresponding to
the stellar luminosity. The post-processing radiative transfer code OPTIM3D is
used to extract spectroscopic and interferometric observables. We show that the
relaxation of the assumption of frequency-independent opacities shows a steeper
mean thermal gradient in the optical thin region that affect strongly the
atomic strengths and the spectral energy distribution. Moreover, the weaker
temperature fluctuations reduce the incertitude on the radius determination
with interferometry. We show that 1D models of red supergiants must include a
turbulent velocity calibrated on 3D simulations to obtain the effective surface
gravity that mimic the effect of turbulent pressure on the stellar atmosphere.
We provide an empirical calibration of the ad-hoc micro- and macroturbulence
parameters for 1D models using the 3D simulations: we find that there is not a
clear distinction between the different macroturbulent profiles needed in 1D
models to fit 3D synthetic lines.
