Sophisticated radiative transfer methods have been used for decadesto model one-dimensional static stellar atmospheres.They predict an outward decrease of the atmospheric temperature that is now observable with simple one-baseline interferometers viameasurements of limb darkening.However, the surface layers of many stars are affected by convectionwhich requires a treatment bytime-dependent multi-dimensional radiation hydrodynamics simulations.Solar granulation is directly observable with “ordinary” telescopes.The simulated granule pattern and evolution compares well with the observed ones.The upcoming radio interferometer ALMA could be used to probe the convectioninduced shock-pattern in the chromosphere that is predicted by simulationsand that is not easily observable otherwise.The typical granular scale on other near main-sequence stars is too smallto be accessible by interferometers.However, scaling argumentsand recent numerical simulationspredict very large structures on cool supergiantsand AGB stars.These stars were and are candidates for optical/near-infrared interferometry.The complexity of the predicted surface phenomenarequires good (or at least some) spatial resolution in conjunction withtemporal and frequency resolution.To fully exploit and interpret these data the simulations have to be improvedin terms of treatment of microphysics (especially opacities in the radiative transfer step)and spatial resolution.