On the effect of injection of gas in the numerical simulation of accretion flows

We investigate the effects of various ways of injection of gas at the outer boundary in the numerical simulations of non-viscous accretion flows.We study three models.In Model A,we inject material around the equatorial plane.In Models B and C,fullrange θ injection is used(we employ spherical coordinates).In all three models,the injected material has the same density distribution with polar angle θ.From the equatorial region to the polar regions,angular momentum of the injected material of Model B decreases faster than that in Model C.For all of the models,after a transient episode of infall at the beginning of the simulations,the gas piles up in the equatorial regions outside the black hole and forms a thick torus bounded by a centrifugal barrier.We find that the accretion rates of Models B and C are more than ten times higher than that in Model A.In Model A,there is weak accretion only in the torus and outflows are found on the surface of the torus.In Model B,we find strong inflows on the surface of its torus,and the accretion in the torus is weak.In Model C,strong inflows also occur on the surface of its torus,but the accretion regions are narrower and there are strong outflows in its torus.In all of our models,the time-averaged density,pressure and angular momentum in the equatorial region can be described by a radial power law,with P ∝r-3/2,P ∝r-2 and l∝r0.