  In cold Cepheids close to the red edge of the classical instability strip, a
strong coupling between the stellar pulsations and the surface convective
motions occurs. This coupling is by now poorly described by 1-D models of
convection, the so-called "time-dependent convection models" (TDC). The
intrinsic weakness of such models comes from the large number of unconstrained
free parameters entering in the description of turbulent convection. A way to
overcome these limits is to compute two-dimensional direct simulations (DNS),
in which all the nonlinearities are correctly solved. Two-dimensional DNS of
the convection-pulsation coupling are presented here. In an appropriate
parameter regime, convective motions can actually quench the radial pulsations
of the star, as suspected in Cepheids close to the red edge of the instability
strip. These nonlinear simulations can also be used to determine the limits and
the relevance of the TDC models.
