When we model black hole accretion sources such as active galactic nuclei and black hole X-ray binaries as advection-dominated accretion flows ( ADAFs ) , it is neccesary to use the global solution to the equations rather than the simpler self-similar solution , since the latter is inaccurate in the region near the black hole where most of the radiation is emitted .
However , technically , it is a difficult task to calculate the global solution because of the transonic nature of the flow , which makes it a two-point boundary value problem .
In this paper we propose a simplified approach for calculating the global ADAF solution .
We replace the radial momentum equation by a simple algebraic relation between the angular velocity of the gas and the Keplerian angular velocity , while keeping all other equations unchanged .
It is then easy to solve the differential energy equations to obtain an approximate global solution .
By adjusting the free parameters , we find that for almost any accretion rate and for \alpha = 0.1 - 0.3 we can get good simplified global solutions .
The predicted spectra from the approximate solutions are very close to the spectra obtained from the true global solutions .