  It has been realized that the shock wave effects play an important role in
neutrino oscillations during the supernova explosion. In recent years, with the
development of simulations about supernova explosion, we have a better
understanding about the density profiles and the shock waves in supernovae than
before. It has been shown that the appearance of shock waves not only varies
with time, but is also affected by the mass of the supernova. When the mass of
the supernova happens to be in a certain range (e.g. it equals 10.8 times the
mass of the sun), there might be a reverse shock wave, another sudden change of
density except the forward shock wave, emerging in the supernova. In addition,
there are some other time-dependent changes of density profiles in different
supernova models. Because of these complex density profiles, the expression of
the crossing probability at the high resonance, $P_H$, which we used previously
would be no longer applicable. In order to get more accurate and reasonable
results, we use the data of density profiles in three different supernova
models obtained from simulations to study the variations of $P_s$ (the survival
probability of $\nu_e\rightarrow\nu_e$), as well as $P_c$ (the conversion
probability of $\nu_x\rightarrow\nu_e$). It is found that the mass of the
supernova does make a difference on the behavior of $P_s$, and affects $P_c$ at
the same time. With the results of $P_s$ and $P_c$, we can estimate the number
of $\nu_e$ remained after they go through the matter in the supernova.
