Spectral Methods for Time-Dependent Studies of Accretion Flows. I. Two-dimensional, Viscous, Hydrodynamic Disks

Abstract

We present a numerical method for studying the normal modes of accretion flows around black holes. In this first paper, we focus on two-dimensional, viscous, hydrodynamic disks, for which the linear modes have been calculated analytically in previous investigations. We use pseudo-spectral methods and low storage Runge-Kutta methods to solve the continuity equation, the Navier-Stokes equation, and the energy equation. We devise a number of test problems to verify the implementation. These tests demonstrate the ability of spectral methods to handle accurately advection problems and to reproduce correctly the stability criteria for differentially rotating hydrodynamic flows. They also show that our implementation is able to handle sound wave correctly with non-reflective boundary conditions, to recover the standard solution for a viscous spreading ring, and produce correctly the Shakura-Sunyaev steady disk solution. Finally, we have applied our algorithm to the problem of a non-axisymmetric viscous spreading ring and verify that such configuration is unstable to non-antisymmetric perturbations.

15 pages, 11 figures. To appear in the ApJ. Substantially revised to include the energy equation and an application to fallback disks. High resolution plots and animations of the simulations are available at http://www.physics.arizona.edu/~chan/research/astro-ph/0406073/index.html

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Cited by in corpus (11)

• Introducing PHAEDRA: a new spectral code for simulations of relativistic magnetospheres
• On the time variability of geometrically-thin black hole accretion disks I : the search for modes in simulated disks
• MHD Simulations of Accretion onto Sgr A*: Quiescent Fluctuations, Outbursts, and Quasi-Periodicity
• Generalized pseudo-Newtonian potential for studying accretion disk dynamics in off-equatorial planes around rotating black holes: Description of a vector potential
• 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
• Newtonian analogue of corresponding spacetime dynamics of rotating black holes: Implication on black hole accretion
• Oscillations of the Inner Regions of Viscous Accretion Disks
• Two temperature viscous accretion flows around rotating black holes: Description of under-fed systems to ultra-luminous X-ray sources
• Spectral Methods for Time-Dependent Studies of Accretion Flows. II. Two-Dimensional Hydrodynamic Disks with Self-Gravity
• Spectral Methods for Time-Dependent Studies of Accretion Flows. III. Three-Dimensional, Self-gravitating, Magnetohydrodynamic Disks
• Spherical accretion in the Schwarzschild spacetime in the Newtonian analogous construct