In doing so, $P$, $T$ and the profile of $F_{\rm rad}/F_{\rm b}$ are similar to the reference stellar model and only the magnitude of $F_{\rm rad}$ is enhanced. In the interior of stars, for constant luminosity, $F_{\rm rad}$ is inversely proportional to the square of radius $r$. If the structures calculated in spherical coordinates are into the Cartesian frame, the systems will undergo large adjustments and will substantially deviate from the initial 1D stellar models. The radiation conductivity is multiplied by a factor $c_{\rm r}=(r_{\rm
b}+z)^2/r_{\rm b}^2$ to avoid such adjustment. Here $r_{\rm b}$ is the distance from the bottom of computed domain to the stellar center. Hence, for the calculations, we use an effective opacity $\kappa^\ast=\kappa/(c_{\rm r} a_{\rm f})$ instead of the real $\kappa$.

![Initial distributions of radiative flux and superadiabatic gradient for intermediate mass star (IMS) model (solid lines) and massive star (MS) model (dotted lines). The MS model is taken from 1D stellar model and the IMS model is constructed according to the 1D stellar model. Case I1, I2 and I3 listed in Table [\[runs\]]{} has the same initial $\Delta\nabla$ and different initial $F_{\rm rad}$. The solid line in upper panel is an example of initial distribution 