Three Dimensional MHD Simulations of Accretion to an Inclined Rotator: The "Cubed Sphere" Method

摘要: We describe a three-dimensional, Godunov-type numerical magnetohydrodynamics (MHD) method designed for studying disk accretion to rotating magnetized star in the general case where star's rotation axis, its magnetic moment, and normal all have different directions. The uses "cubed sphere" coordinate system which has advantages of Cartesian spherical systems but does not singular axis ofthe system. grid is formed by sequence concentric spheres radii $R_j \propto q^j$ with $j=1..N_R$ $q={\rm const}>1$. on surface sphere consists six sectors each sector topologically equivalent equidistant face cube. Simulation results are discussed funnel flows (FF) dipole moment $\rvecmu$ at an angle $\Theta=30^\circ$ ${\bf \Omega}$ aligned disk. Two important new 3D features found these simulations: (1) flow stellar mainly two streams approach from opposite (2) In $x-z$ cross section containing \Omega}$, often takes longer possible paths along field lines star. A subsequent paper will give detailed description inclination angles $\Theta$.