  Despite all advances in multi-dimensional hydrodynamics, investigations of
stellar evolution and stellar pulsations still depend on one-dimensional
computations. The present work devises an alternative to the mixing length
theory or turbulence models usually adopted for the modelling of convective
transport in such studies. Assuming that the largest convective patterns
generate the majority of convective transport, the convective velocity field is
described using two parallel radial columns to represent up- and downstream
flows. Horizontal exchange in the form of fluid flow and radiation over their
connecting interface couples the two columns and allows a simple circulating
motion. The main parameters of this convective description have a
straightforward geometrical meaning, namely the diameter of the columns
(corresponding to the size of the convective cells) and the ratio of cross
section between up- and downdrafts. For this geometrical setup, the
time-dependent solution of the equations of radiation hydrodynamics is computed
from an implicit scheme which has the advantage of being not affected by the
Courant-Friedrichs-Lewy time step limit. In order to demonstrate the approach,
results for the example of convection zones in Cepheids are presented.
