  Modeling the dynamics of most astrophysical structures requires an adequate
description of the radiation-matter interaction. Several numerical
(magneto)hydrodynamics codes were upgraded with a radiation module to fulfill
this request. However, those among them that use either the flux-limited
diffusion (FLD) or the M1 radiation moment approaches are restricted to the
local thermodynamic equilibrium (LTE). This assumption may be not valid in some
astrophysical cases. We present an upgraded version of the LTE
radiation-hydrodynamics module implemented in the PLUTO code, originally
developed by Kolb et al. (2013), which we have extended to handle non-LTE
regimes. Starting from the general frequency-integrated comoving-frame
equations of radiation hydrodynamics (RHD), we have justified all the
assumptions made to obtain the non-LTE equations actually implemented in the
module, under the FLD approximation. An operator-split method is employed, with
two substeps: the hydrodynamic part is solved with an explicit method by the
solvers already available in PLUTO, the non-LTE radiation diffusion and energy
exchange part is solved with an implicit method. The module is implemented in
the PLUTO environment. It uses databases of radiative quantities that can be
provided independently by the user: the radiative power loss, the Planck and
Rosseland mean opacities. Our implementation has been validated through
different tests, in particular radiative shock tests. The agreement with the
semi-analytical solutions (when available) is good, with a maximum error of 7%.
Moreover, we have proved that non-LTE approach is of paramount importance to
properly model accretion shock structures. Our radiation FLD module represents
a step toward the general non-LTE RHD modeling. The module is available, under
request, for the community.
