Same as Fig. 3 for simulation runs with τ_810 nm = 1.22 × 10⁶. In this highly optical thick case, the results for gray RT + gray FLD are identical to the frequency-dependent RT + gray FLD. Here, the dotted lines represent the results for the frequency-dependent RT + gray FLD method in a low-resolution simulation if an upper limit of the optical depth per grid cell of τ_max ≤ 1 is used (see Sect. 3.2 for a description of this numerical trick).