In this thesis a fundamental physical process, radiative transfer, is modeled numerically. The implementation as a code module for the hydrodynamical simulation code Flash 4 is presented. The coupling to an efficient chemical network that explicitly tracks the three hydrogen species H, H_2, H+ and the two carbon species C+ and CO is described as well as the modeling of all relevant thermal stellar feedback mechanisms, i.e. photoelectric heating, pumping of molecular hydrogen by UV photons, photoionization and H_2 dissociation heating. These modeled processes coupled to the chemical network, make it possible to capture the non-equilibrium time-dependent thermal and chemical state of the present-day interstellar medium and dense molecular
clouds affected by radiative feedback of massive stars. All included radiative feedback processes are extensively tested. The results obtained with this code module are compared to ones calculated from dedicated photo-dissociation region (PDR) codes. Good agreement is found
in all modeled hydrogen species once the radiative transfer solution reaches equilibrium. In addition, it is shown that the implemented radiative feedback physics is insensitive to the spatial resolution of the simulation mesh and under which conditions a well-converged evolution in time can be obtained.
The last test cases explore the robustness of the developed numerical scheme in treating the combined ionizing and non-ionizing radiation.
In a follow-up study, different simplified numerical radiative transfer models are compared in the context of ionization front instabilities. The growth of unstable modes is found to be strongly dependent on the coupling of the thermal state to the ionization state. Depending on the implemented model, radically different conclusions can be drawn. For an equilibrium ionization model with a bimodal temperature structure for ionized and ambient gas, the
swept up surrounding shell is found to be unstable.
However, if the temperature of the ionized gas is calculated from the equilibrium ionization heating rate no instability is found. Finally, a damped ionization front instability is obtained from the newly implemented code module, which is unable to impact and perturb the shell sufficiently for it to break up
