Application of the Cubed-Sphere Grid to Tilted Black Hole Accretion Disks

Abstract

In recent work we presented the first results of global general relativistic magnetohydrodynamic (GRMHD) simulations of tilted (or misaligned) accretion disks around rotating black holes. The simulated tilted disks showed dramatic differences from comparable untilted disks, such as asymmetrical accretion onto the hole through opposing "plunging streams" and global precession of the disk powered by a torque provided by the black hole. However, those simulations used a traditional spherical-polar grid that was purposefully underresolved along the pole, which prevented us from assessing the behavior of any jets that may have been associated with the tilted disks. To address this shortcoming we have added a block-structured "cubed-sphere" grid option to the Cosmos++ GRMHD code, which will allow us to simultaneously resolve the disk and polar regions. Here we present our implementation of this grid and the results of a small suite of validation tests intended to demonstrate that the new grid performs as expected. The most important test in this work is a comparison of identical tilted disks, one evolved using our spherical-polar grid and the other with the cubed-sphere grid. We also demonstrate an interesting dependence of the early-time evolution of our disks on their orientation with respect to the grid alignment. This dependence arises from the differing treatment of current sheets within the disks, especially whether they are aligned with symmetry planes of the grid or not.

The Polish doughnuts revisited

“…Of course, a stationary torus may exist only within an equipotential surface located inside the Roche lobe, i.e., the critical self-crossing equipotential within the cusp (Abramowicz 1985). Figure 5 illustrates that the results of the analytic models are well matched with results of modern 3-D MHD numerical simulations (here taken from Fragile et al 2007Fragile et al , 2009. For the correct choice of parameters, the model can reproduce many of the relevant features of the numerical results, including the locations of the cusp and pressure maximum, as well as the vertical thickness of the disk.…”

“…Abramowicz et al 1988), and more recent, fully 3-D, non-stationary MHD simulations (e.g. Machida & Matsumoto 2008;Fragile et al 2009). It corresponds to a distribution that is slightly sub-Keplerian for large radii, and closer to the black hole it crosses the Keplerian distribution twice, at r center > r ms and at r cusp < r ms , forming a super-Keplerian part around r ms .…”

High-order central ENO finite-volume scheme for ideal MHD

“…In recent years, cubed-sphere grids have gained increasing popularity for simulating fluid flow in domains between concentric spheres, first in the area of climate and weather modelling [18,19,20,21,22,23,24], but more recently also in areas like astrophysics [25,26]. Very recently, Ivan et al [14,15] have proposed a second-order parallel solution-adaptive computational framework for solving hyperbolic conservation laws on 3D cubed-sphere grids and applied the formulation to the simulation of several magnetized and nonmagnetized space-physics problems.…”

An axis-free overset grid in spherical polar coordinates for simulating 3D self-gravitating flows

“…For flows possessing an approximate global spherical symmetry, the "cubed sphere" grid (Ronchi et al 1996) has been developed and is currently applied to several astrophysical problems (e.g. Koldoba et al 2002;Romanova et al 2003;Zink et al 2008;Fragile et al 2009). It is an overset grid consisting of six identical patches covering a solid angle of 4π steradians.…”