Studies of Thermally Unstable Accretion Disks around Black Holes with Adaptive Pseudospectral Domain Decomposition. I. Limit‐Cycle Behavior in the Case of Moderate Viscosity

Abstract

We present a numerical method for spatially 1.5-dimensional, time-dependent studies of accretion disks around black holes. The method originates from a combination of the standard pseudospectral and adaptive domain decomposition methods 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. A new finding is that, according to our computations, the Bernoulli function of the matter in such disks is always and everywhere negative, so that outflows are unlikely to originate from these disks. We are encouraged to study the more difficult case of thermally unstable accretion disks with strong viscosity in ongoing work.