Context. Material accreted onto classical T Tauri stars is expected to form a hot quasi-periodic plasma structure that radiates in X-rays. Simulations of this phenomenon only partly match observations. They all rely on a static model for the chromosphere and on the assumption that radiation and matter are decoupled.Aims. We explore the effects of a shock-heated chromosphere and of the coupling between radiation and hydrodynamics on the structure and dynamics of the accretion flow.Methods. We simulated accretion columns that fall onto a stellar chromosphere using the 1D ALE code AstroLabE. This code solves the hydrodynamics equations along with the first two moment equations for radiation transfer, with the help of a dedicated opacity table for the coupling between matter and radiation. We derive the total electron and ion densities from collisional-radiative model.Results. The chromospheric acoustic heating affects the duration of the cycle and the structure of the heated slab. In addition, the coupling between radiation and hydrodynamics leads to a heating of the accretion flow and of the chromosphere: the whole column is pushed up by the inflating chromosphere over several times the steady chromosphere thickness. These last two conclusions are in agreement with the computed monochromatic intensity. Acoustic heating and radiation coupling affect the amplitude and temporal variations of the net X-ray luminosity, which varies between 30 and 94% of the incoming mechanical energy flux, depending on which model is considered.