Application of Adaptive Pseudospectral Domain Decomposition on Studies of Limit-cycle Behavior of Black Hole Accretion Disks

摘要

We present a numerical method for spatially 1.5dimensional, time dependent studies of accretion disks around black holes. The method originates from a combination of the standard pseudospectral and adaptive domain decomposition meth ods found in the literature, but with a number of improvements in both the numerical and physical senses. In particular, we introduce a new treatment for the connection at the interfaces of decomposed subdomains, construct an adaptive function for the mapping between the Chebyshev-Gauss-Lobatto collocation points and the physical collocation points in each subdomain, and modify the oversimplified one-dimensional basic equations of accretion flows to account for the effects of viscous stresses in both the azimuthal and radial directions. Our method is verified by reproducing the best results obtained previously by Szuszkiewicz & Miller on the limit-cycle behavior of thermally unstable accretion disks with moderate viscosity.