  Radiative shocks (also called supercritical shocks) are high Mach number
shock waves that photoionize the medium ahead of the shock front and give rise
to a radiative precursor. They are generated in the laboratory using
high-energy or high-power lasers and are frequently present in a wide range of
astronomical objects. Their modelisation in one dimension has been the subject
of numerous studies, but generalization to three dimensions is not
straightforward. We calculate analyticaly the absorption of radiation in a grey
uniform cylinder and show how it decreases with chi R, the product of the
opacity chi and of the cylinder radius R. Simple formulas, whose validity range
increases when chi R diminishes, are derived for the radiation field on the
axis of symmetry. Numerical calculations in three dimensions of the radiative
energy density, flux and pressure created by a stationary shock wave show how
the radiation decreases whith R. Finally, the bidimensional structures of both
the precursor and the radiation field are calculated with time-dependent
radiation hydrodynamics numerical simulations and the influence of
two-dimensional effects on the electron density, the temperature, the shock
velocity and the shock geometry are exhibited. These simulations show how the
radiative precursor shortens, cools and slows down when R is decreased.
