Spectral Methods for Time-Dependent Studies of Accretion Flows. III. Three-Dimensional, Self-gravitating, Magnetohydrodynamic Disks
arXiv:astro-ph/0612742 · doi:10.1088/0004-637X/700/1/741
Abstract
Accretion disks are three-dimensional, turbulent, often self-gravitating, magnetohydrodynamic flows, which can be modeled in detail with numerical simulations. In this paper, we present a new algorithm that is based on a spectral decomposition method to simulate such flows. Because of the high order of the method, we can solve the induction equation in terms of the magnetic potential and, therefore, ensure trivially that the magnetic fields in the numerical solution are divergence free. The spectral method also suffers minimally from numerical dissipation and allows for an easy implementation of models for sub-grid physics. Both properties make our method ideal for studying MHD turbulent flows such as those found in accretion disks around compact objects. We verify our algorithm with a series of standard tests and use it to show the development of MHD turbulnce in a simulation of an accretion disk. Finally, we study the evolution and saturation of the power spectrum of MHD turbulence driven by the magnetorotational instability.
10 pages, 7 figures. Submitted to ApJ. High resolution plots and animations of the simulations are available at this http://www.physics.arizona.edu/~chan/research/astro-ph/0612742/index.html
References in corpus (25)
- Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks
- Athena: A New Code for Astrophysical MHD
- HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics
- FARGO: a fast eulerian transport algorithm for differentially rotating disks
- An Unsplit Godunov Method for Ideal MHD via Constrained Transport
- Three-dimensional MHD Simulations of Radiatively Inefficient Accretion Flows
- Global Magnetohydrodynamical Simulations of Accretion Tori
- MHD simulations of the magnetorotational instability in a shearing box with zero net flux. II. The effect of transport coefficients
- Impact of dimensionless numbers on the efficiency of MRI-induced turbulent transport
- The Effect of Resistivity on the Nonlinear Stage of the Magnetorotational Instability in Accretion Disks
- Magnetohydrodynamical Non-radiative Accretion Flows in Two-Dimensions
- Nonlinear Outcome of Gravitational Instability in Disks with Realistic Cooling
- Local Hydrodynamic Stability of Accretion Disks
- Global Three-Dimensional Simulations of Black Hole Accretion Disks: X-ray Flares in the Plunging Region
- Global MHD Simulations of Cylindrical Keplerian Disks
- Description of Pseudo-Newtonian Potential for the Relativistic Accretion Disk around Kerr Black Holes
- Global General Relativistic Magnetohydrodynamic Simulations of Accretion Tori
- 3D-MHD simulations of an accretion disk with star-disk boundary layer
- Vortices in Thin, Compressible, Unmagnetized Disks
- The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs
- Simulations of accretion flows crossing the last stable orbit
- A Local Model for Angular Momentum Transport in Accretion Disks Driven by the Magnetorotational Instability
- Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows
- Spectral Methods for Time-Dependent Studies of Accretion Flows. I. Two-dimensional, Viscous, Hydrodynamic Disks
- Spectral Methods for Time-Dependent Studies of Accretion Flows. II. Two-Dimensional Hydrodynamic Disks with Self-Gravity