On the Structure of Advective Accretion Disks At High Luminosity
  Global solutions of optically thick advective accretion disks around black holes are constructed. The solutions are obtained by solving numerically a set of ordinary differential equations corresponding to a steady axisymmetric geometrically thin disk. We pay special attention to consistently satisfy the regularity conditions at singular points of the equations. For this reason we analytically expand a solution at the singular point, and use coefficients of the expansion in our iterative numerical procedure. We obtain consistent transonic solutions in a wide range of values of the viscosity parameter alpha and mass acretion rate. We compare two different form of viscosity: one takes the shear stress to be proportional to the pressure, while the other uses the angular velocity gradient-dependent stress.   We find that there are two singular points in solutions corresponding to the pressure-proportional shear stress. The inner singular point locates close to the last stable orbit around black hole. This point changes its type from a saddle to node depending on values of alpha and accretion rate. The outer singular point locates at larger radius and is always of a saddle-type. We argue that, contrary to the previous investigations, a nodal-type inner singular point does not introduce multiple solutions. Only one integral curve, which corresponds to the unique global solution, passes simultaneously the inner and outer singular points independently of the type of inner singular point. Solutions with the angular velocity gradient-dependent shear stress have one singular point which is always of a saddle-type and corresponds to the unique global solution. The structure of accretion disks corresponding to both viscosities are similar. 
Ioulia V. Artemova, Gennadi S. Bisnovatyi-Kogan, Igor V. Igumenshchev,   Igor D. Novikov