  Aims. Our aim is to test how different binning strategies previously studied
in one-dimensional models perform in three-dimensional radiative hydrodynamic
simulations of stellar atmospheres. Methods. Realistic box-in-a-star
simulations of the near-surface convection and photosphere of three spectral
types (G2V, K0V, and M2V) were run with the MANCHA code with grey opacity.
After reaching the stationary state, one snapshot of each of the three stellar
simulations was used to compute the radiative energy exchange rate with grey
opacity, opacity binned in four $\tau$-bins, and opacity binned in 18 $\{ \tau,
\lambda \}$-bins. These rates were compared with the ones computed with opacity
distribution functions. Then, stellar simulations were run with grey, four-bin,
and 18-bin opacities to see the impact of the opacity setup on the mean
stratification of the temperature and its gradient after time evolution.
Results. The simulations of main sequence cool stars with the MANCHA code are
consistent with those in the literature. For the three stars, the radiative
energy exchange rates computed with 18 bins are remarkably close to the ones
computed with the opacity distribution functions. The rates computed with four
bins are similar to the rates computed with 18 bins, and present a significant
improvement with respect to the rates computed with the Rosseland opacity,
especially above the stellar surface. The Rosseland mean can reproduce the
proper rates in sub-surface layers, but produces large errors for the
atmospheric layers of the G2V and K0V stars. In the case of the M2V star, the
Rosseland mean fails even in sub-surface layers, owing to the importance of the
contribution from molecular lines in the opacity, underestimated by the
harmonic mean. Similar conclusions are reached studying the mean stratification
of the temperature and its gradient after time evolution.
