Studies of Thermally Unstable Accretion Disks around Black Holes with Adaptive Pseudo-Spectral Domain Decomposition Method I. Limit-Cycle Behavior in the Case of Moderate Viscosity

摘要

We present a numerical method for spatially 1.5-dimensional andtime-dependent studies of accretion disks around black holes, that isoriginated from a combination of the standard pseudo-spectral method and theadaptive domain decomposition method existing in the literature, but with anumber of improvements in both the numerical and physical senses. Inparticular, we introduce a new treatment for the connection at the interfacesof decomposed subdomains, construct an adaptive function for the mappingbetween the Chebyshev-Gauss-Lobatto collocation points and the physicalcollocation points in each subdomain, and modify the over-simplified1-dimensional basic equations of accretion flows to account for the effects ofviscous stresses in both the azimuthal and radial directions. Our method isverified by reproducing the best results obtained previously by Szuszkiewicz &Miller on the limit-cycle behavior of thermally unstable accretion disks withmoderate viscosity. A new finding is that, according to our computations, theBernoulli function of the matter in such disks is always and everywherenegative, so that outflows are unlikely to originate from these disks. We areencouraged to study the more difficult case of thermally unstable accretiondisks with strong viscosity, and wish to report our results in a subsequentpaper.