Numerical models of viscous accretion flows near black holes

We report on a numerical study of viscous fluid accretion onto a black hole. The flow is axisymmetric and uses a pseudo-Newtonian potential to model relativistic effects near the event horizon. The numerical method is a variant of the ZEUS code. As a test of our numerical scheme, we are able to reproduce results from earlier, similar work by Igumenshchev and Abramowicz and Stone and coworkers. We consider models in which mass is injected onto the grid as well as models in which an initial equilibrium torus is accreted. In each model we measure three "eigenvalues" of the flow: the accretion rate of mass, angular momentum, and energy. We find that the eigenvalues are sensitive to r_in, the location of the inner radial boundary. Only when the flow is always supersonic on the inner boundary are the eigenvalues insensitive to small changes in r_in. We also report on the sensitivity of the results to other numerical parameters.