  We constructed a multi-fluid two-dimensional hydrodynamic model with detailed
radiative transfer to depict the escape of particles. We found that the tidal
forces supply significant accelerations and result in anisotropic winds. An
important effect of the tidal forces is that it severely depresses the outflow
of particles near the polar regions. As a consequence, most particles escape
the surface of the planet from the regions of low-latitude. Comparing the tidal
and non-tidal locking cases, we found that their optical depths are very
different so that the flows also emerge with a different pattern. In the case
of the non-tidal locking, the radial velocities at the base of the wind are
higher than the meridional velocities. However, in the case of tidal locking,
the meridional velocities dominate the flow at the base of the wind, and they
can transfer effectively mass and energy from the day sides to the night sides.
Further, we also found that the differences of the winds show middle extent at
large radii. It expresses that the structure of the wind at the base can be
changed by the two-dimensional radiative transfer due to large optical depths,
but the extent is reduced with an increase in radius. Because the escape is
depressed in the polar regions, the mass loss rate predicted by the non-tidal
locking model, in the order of magnitude of $10^{10}$ g s$^{-1}$, is a factor
of 2 lower than that predicted by one-dimensional hydrodynamic model. The
results of tidal locking show that the mass loss rate is decreased a order of
magnitude, only 4.3$\times$ $10^{9}$ g s$^{-1}$, due to large optical depths on
the night side. We also found that the distributions of hydrogen atoms show
clear variations from the day side to night side, thus the origin of the excess
absorption in Ly $\alpha$ should be reexamined by using multi-dimensional
hydrodynamic models.
