"fig:"){width="8.0cm"}

  Type of star    $\log{(p_{\rm scl})}$   $\log{(T_{\rm scl})}$   $\log{(\rho_{\rm scl})}$   $p_{\rm btm}$   $T_{\rm btm}$   $\rho_{\rm btm}$   $d/R$   $r_{\rm b}/d$          $F_{\rm btm}$
  -------------- ----------------------- ----------------------- -------------------------- --------------- --------------- ------------------ ------- --------------- ---------------------
  Intermediate            7.881                   4.872                    -5.116               737.152          6.226           118.276         0.1          6          $0.2\times 10^{-4}$
  Massive                 5.820                   5.022                    -7.602               927.728          5.095           226.088        0.379         1                        0.651

$p_{\rm btm}$, $T_{\rm btm}$, $\rho_{\rm btm}$ are scaled by $p_{\rm scl}$, $T_{\rm scl}$, $\rho_{\rm scl}$ respectively. The input flux $F_{\rm btm}=F_{\rm b}/(c_{\rm r}a_{\rm f})$ is scaled by $(p_{\rm scl}^{1.5}/d_{\rm scl}^{0.5})$, where $F_{\rm b}$ is the modified dimensionless input flux.

An initial stratified layer constructed by the above method is specified by the six parameters: $\rho_{\rm t}$, $p_{\rm t}$, $T_{\rm t}$, $a_{\rm f}$, $r_{\rm b}$ and $d$ (the subscript t denotes values at the top), and two distributions: $F_{\rm rad}$ and $\Delta\nabla$. Their values are chosen to make the initial state close to the reference model.

In the interior of the massive star, convection is not very efficient. The zone extends for about $3.41$ pressure scale heights (PSHs) ($0.25$ of the stellar radius $R$). The upper convective boundary is located in the deep interior. The typical value of $\Delta\nabla$ is on the order of $0.001$ in the convection zone, 