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

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

2004-06-03

arxiv.org/abs/astro-ph/0406073v2

Astrophys.J. 628 (2005) 353-367

Astronomy and Astrophysics

Astrophysics

15 pages, 11 figures. To appear in the ApJ. Substantially revised to include the energy equation and an application to fallbac

Scientific paper

10.1086/430511

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.

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