while about $-0.06$ in the stable region below. The computed domain of our massive star model contains about $6.8$ PSHs ($d=0.379R$) total. It includes the whole convection zone and a lower stable layer. The upper boundary is a little higher than the actual top of the convection zone of the 1D reference model. The distance between the bottom of computed domain and the center of the star is $r_{\rm
b}=0.379R$. The initial distributions of the radiative flux $F_{\rm
rad}$ and superadiabatic gradient $\Delta\nabla$ for the various models are shown in Fig. \[init\] by dotted lines without amplification factors (e.g., $a_{\rm f}=1$). The other characteristics of the initial models are given in Table \[dpm\].

For the massive star, the values of $F_{\rm btm}$ and other quantities are computationally manageable and $a_{\rm f}$ can be chosen to be $1$. On the other hand, the parameters of the convection zone of the intermediate mass star have to be modified to make the calculations feasible. We use several values of $a_{\rm f}$ to check for the parametric behaviors of the modified models. The convection in the red giant extents to a height of about $14$ PSHs ($0.4R$). A direct simulation of such a deep 