  This work presents a new method to compute time and wavelength dependent
center-to-limb brightness distributions for Classical Cepheids. Our model
atmospheres are based on second-order accurate 1-D hydrodynamic calculations,
performed in spherical geometry. The brightness intensity distributions, and
the resulting limb darkening, are computed through the dynamic atmospheres by
using a full set of atomic and molecular opacities. Our results confirm
important differences with respect to equivalent hydrostatic models. The amount
of limb darkening, and the shape of the limb profiles, show a strong dependence
on the pulsational phase of the Cepheid, which cannot be reproduced by static
models. Non-linear effects in our hydrodynamic equations add a new level of
complexity in the wavelength dependence of our limb profiles, which are
affected by the presence of shock-waves traveling through the atmosphere. These
effects, already detectable by present-day interferometers, should be taken
into consideration when deriving limb darkened diameters for nearby Cepheids
with the accuracy required to measure their radial pulsations.
