  Following the Boz$\dot{\textrm{e}}$k-Wyskiel parametrization tilted initial
condition, an alternative way to construct a longitudinal tilted fireball based
on the Glauber collision geometry is presented. This longitudinal tilted
initial condition combined with the Ideal-CLVisc (3 + 1)D hydrodynamic model, a
nonvanishing directed flow coefficient $v_{1}$ in a wide rapidity range is
observed. After comparing the model's results with experimentally observed data
of directed flow coefficient $v_{1}(\eta)$ from $\sqrt{s_{NN}}$ = 200 GeV Cu +
Cu, Au + Au collisions at RHIC energy to $\sqrt{s_{NN}}$ = 2.76 TeV and
$\sqrt{s_{NN}}$ = 5.02 TeV Pb + Pb collisions at the LHC energy. We find that
the directed flow measurements in heavy-ion collisions can set strong
constraints on the imbalance of forward and backward incoming nuclei and on the
magnitude asymmetry of pressure gradients along the $x$ direction.
