A new two-columns description for convective transport in stars

Assuming that the largest convective patterns generate the majority of convective transport, we devise a numerical scheme simplifying the convective velocity field using two parallel radial columns to represent up- and downstream flows. Horizontal exchange is described by fluid flow and radiation over the interface between those two columns. The main parameters of this convective description have a straightforward geometrical meaning, namely the diameter of the columns (representing the size of the convective cells) and the ratio of cross section between up- and downdrafts. For this geometrical setup, the equations of radiation hydrodynamics are solved time-dependently using an implicit scheme which has the advantage of being devoid of any time step limits. In order to demonstrate our approach, we present comparisons with detailed 2D hydrodynamics computations for the example of convection zones in Cepheids.