We present a new numerical scheme describing the convective velocity field using two parallel radial columns in order to represent up- and downstream flows. The two columns are coupled by horizontal exchange via fluid flow and radiation over their common interface. For this geometrical setup, the equations of radiation hydrodynamics are solved time dependently using an implicit scheme which has the advantage of allowing very large time steps. Finally we demonstrate our approach for the example of a Cepheids convection zone.