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THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC SIMULATIONS OF ACCRETION TO AN INCLINED ROTATOR: THE "CUBED SPHERE" METHOD Authors: Koldoba, A.V., Romanova, M.M., Ustyugova, G.V., Lovelace R.V.E. We
describe a three-dimensional, Godunov-type numerical magnetohydrodynamics
(MHD) method designed for studying disk accretion to a
rotating magnetized star in the general case where the
star's rotation axis, its magnetic moment, and the normal
to the disk all have different directions. The equations
of ideal MHD are written in a reference frame rotating
with the star, with the z-axis aligned with the
star's rotation axis. The numerical method uses a "cubed
sphere" coordinate system that has advantages of Cartesian
and spherical coordinate systems but does not have the
singular axis of the spherical system. The grid is formed
by a sequence of concentric spheres of radii Rj
~ qj,
with j = 1,
... ,
NR and q = constant > 1. The grid
on the surface of the sphere consists of six sectors, with
the grid on each sector topologically equivalent to the
equidistant grid on the face of a cube. The magnetic field
is written as a dipole component plus deviations, and
only the deviations are calculated. Simulation results are
discussed for the funnel flows to a star with dipole
moment m
at an angle
J
= 30° to the
star's rotation axis W,
which is aligned with the normal to the disk. Results are
given for different grids (NR × N2)
from 26 × 152 (coarsest) to 50 × 292
(finest). We observe that the qualitative features of the
accretion flows are very similar for the different grids,
but the coarser grid is affected by numerical viscosity.
We compare our three-dimensional results for J
= 0 with the
axisymmetric (two-dimensional), spherical coordinate system
simulations of funnel flows of Romanova et al. Two important
new three-dimensional features are found in these simulations:
(1) The funnel flow to the stellar surface is mainly in
two streams that approach the star from opposite directions.
(2) In the x-z cross section of the flow containing
mand W,
the funnel flow often takes the longer of the two possible
paths along magnetic field lines to the surface of the
star. A subsequent paper will give a detailed description
of the method and results on three-dimensional funnel flows
at different inclination angles J.
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