  We present the two-dimensional inflow-outflow solutions of radiation
hydrodynamic (RHD) equations of supercritical accretion flows. Compared with
prior studies, we include all components of the viscous stress tensor. We
assume steady state flow and use self-similar solutions in the radial direction
to solve the equations in $ r-\theta $ domain of the spherical coordinates. The
set of differential equations have been integrated from the rotation axis to
the equatorial plane. We find that the self-similarity assumption requires that
the radial profile of density is described by $ \rho(r) \propto r^{-0.5} $.
Correspondingly, the radial profile of the mass inflow rate decreases with
decreasing radii as $ \dot{M}_\mathrm{in} \propto r $. Inflow-outflow structure
has been found in our solution. In the region $ \theta > 65^{\circ} $ there
exist inflow while above that flow moves outward and outflow could launch. The
driving forces of the outflow are analyzed and found that the radiation force
is dominant and push the gas particles outwards with poloidal velocity $ \sim
0.25 c $. The properties of outflow are also studied. The results show that the
mass flux weighted angular momentum of the inflow is lower than that of
outflow, thus the angular momentum of the flow can be transported by the
outflow. We also analyze the convective stability of the supercritical disk and
find that in the absence of the magnetic field, the flow is convectively
unstable. Our analytical results are fully consistent with the previous
numerical simulations of the supercritical accretion flow.
