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We present global solutions that describe advection-dominated accretion flowsaround black holes. The solutions are obtained by numerically solving a set ofcoupled ordinary differential equations corresponding to a steady axisymmetricheight-integrated flow. The solutions satisfy consistent boundary conditions atboth ends. We obtain well-behaved transonic solutions for a wide range ofvalues of the viscosity parameter $\alpha$, from 0.001 to 0.3. We do not findany need for shocks in our solutions, and disagree with previous claims thatviscous accretion flows with low values of $\alpha$ must have shocks. We see aqualitative difference between solutions with low values of the viscosityparameter, $\alpha\ \sles\ 0.01$, and those with large values, $\alpha\sgreat\0.01$. The solutions with low $\alpha$ have their sonic transitions occurringclose to the radius of the marginally bound orbit. These flows arecharacterized by regions of super-Keplerian rotation, and have pressure maximaoutside the sonic point. The solutions are similar in many respects to thehydrostatic thick tori developed previously as models of active galacticnuclei. In contrast, the solutions with large $\alpha$ have sonic transitionsfarther out, close to or beyond the marginally stable orbit, and have nosuper-Keplerian rotation or pressure maxima. We believe these flows will benearly quasi-spherical down to the sonic radius and will not have empty funnelsalong the rotation axis. The large $\alpha$ solutions are more likely to berepresentative of real systems.Comment: 22 pages of text, 9 figures. Paper submitted to the Astrophysical  Journa

Global Structure and Dynamics of Advection‐dominated Accretion Flows around Black Holes