  We construct a numerical model of steady-state, general relativistic (GR)
super-Eddington accretion flows in an optically thick, advection-dominated
regime, motivated by tidal disruption events wherein super-Eddington accretion
assumes a pivotal role. Our model takes into account the loss of angular
momentum due to radiation and the scale-height derivative in the basic
equations of the GR slim disk. For comparison purposes, we also provide a new
analytical solution for a radiation-pressure-dominant GR slim disk, which
neglects the angular momentum loss due to radiation and the scale-height
derivative. We find that the radiation pressure enhances by incorporating the
scale height derivative into the basic equations. As a result, the surface
density near the disk's inner edge decreases, whereas the disk temperature and
scale height increase, brightening the disk spectrum in the soft X-ray
waveband. Notably, an extremely high mass accretion rate significantly enhances
the effect of the scale-height derivative, affecting the entire disk. In
contrast, the inclusion of the radiation-driven angular momentum loss only
slightly influences the disk surface density and temperature compared with the
case of the scale-height derivative inclusion. The X-ray luminosity increases
significantly due to scale height derivative for $\dot{M}/\dot{M}_{\rm Edd}
\gtrsim 2$. In addition, the increment is higher for the non-spinning black
hole than the spinning black hole case, resulting in a one-order of magnitude
difference for $\dot{M}/\dot{M}_{\rm Edd}\gtrsim100$. We conclude that
incorporating the scale-height derivative into a GR slim disk model is crucial
as it impacts the disk structure and its resultant spectrum, particularly on a
soft-X-ray waveband.
