  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 numerical method uses
a "cubed sphere" coordinate system which has advantages of Cartesian and
spherical coordinate systems but does not have the singular axis ofthe
spherical system. The grid is formed by a sequence of concentric spheres of
radii $R_j \propto q^j$ with $j=1..N_R$ and $q={\rm const}>1$. 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.
Simulation results are discussed for the funnel flows (FF) to a star with
dipole moment $\rvecmu$ at an angle $\Theta=30^\circ$ to the star's rotation
axis ${\bf \Omega}$ which is aligned with the normal to the disk. Two important
new 3D features are found in these simulations: (1) The funnel flow to the
stellar surface is mainly in two streams which approach the star from opposite
directions. (2) In the $x-z$ cross section of the flow containing $\rvecmu$ and
${\bf \Omega}$, 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 3D funnel flows
at different inclination angles $\Theta$.
