  To study the energy-dependent characteristics of thermodynamic and
hydrodynamic parameters, based on the framework of a multi-source thermal
model, we analyze the soft transverse momentum ($p_{T}$) spectra of the charged
particles ($\pi^{-}$, $\pi^{+}$, $K^{-}$, $K^{+}$, $\bar{p}$, and $p$) produced
in gold-gold (Au-Au) collisions at the center-of-mass energies
$\sqrt{s_{NN}}=7.7$, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV from the STAR
Collaboration and in lead-lead (Pb-Pb) collisions at $\sqrt{s_{NN}}=2.76$ and
5.02 TeV from the ALICE Collaboration. In the rest framework of emission
source, the probability density function obeyed by meson momenta satisfies the
Bose-Einstein distribution, and that obeyed by baryon momenta satisfies the
Fermi-Dirac distribution. To simulate the $p_{T}$ of the charged particles, the
kinetic freeze-out temperature $T$ and transverse expansion velocity
$\beta_{T}$ of emission source are introduced into the relativistic ideal gas
model. Our results, based on the Monte Carlo method for numerical calculation,
show a good agreement with the experimental data. The excitation functions of
thermodynamic parameter $T$ and hydrodynamic parameter $\beta_{T}$ are then
obtained from the analyses, which shows an increase tendency from 7.7 GeV to
5.02 TeV in collisions with different centralities.
