Magnetorotational turbulence provides a viable mechanism for angular momentum transport in accretion disks .
We present global , three dimensional ( 3D ) , magnetohydrodynamic accretion disk simulations that investigate the dependence of the turbulent stresses on resolution .
Convergence in the time-and-volume-averaged stress-to-gas-pressure ratio , \overline { \langle \alpha _ { P } \rangle } , at a value of \sim 0.04 , is found for a model with radial , vertical , and azimuthal resolution of 12-51 , 27 , and 12.5 cells per scale-height ( the simulation mesh is such that cells per scale-height varies in the radial direction ) .
The gas pressure dependence of the quasi-steady state stress level is also examined using models with different scaleheight-to-radius aspect ratio ( H / R ) , revealing a weak dependence of \overline { \langle \alpha _ { P } \rangle } on pressure .

A control volume analysis is performed on the main body of the disk ( |z| < 2 H ) to examine the production and removal of magnetic energy .
Maxwell stresses in combination with the mean disk rotation are mainly responsible for magnetic energy production , whereas turbulent dissipation ( facilitated by numerical resistivity ) predominantly removes magnetic energy from the disk .
Re-casting the magnetic energy equation in terms of the power injected by Maxwell stresses on the boundaries of , and by Lorentz forces within , the control volume highlights the importance of the boundary conditions ( of the control volume ) .
The different convergence properties of shearing-box and global accretion disk simulations can be readily understood on the basis of choice of boundary conditions and the magnetic field configuration .
Periodic boundary conditions restrict the establishment of large-scale gradients in the magnetic field , limiting the power that can be delivered to the disk by Lorentz forces and by stresses at the surfaces .
The factor of three lower resolution required for convergence in \langle \alpha _ { P } \rangle for our global disk models compared to stratified shearing-boxes is explained by this finding .