  We present results of the first global magnetohydrodynamic (MHD) simulations
of accretion disks fed by Roche lobe overflow, including vertical
stratification, in order to investigate the roles of spiral shocks,
magnetorotational instability (MRI), and the accretion stream on disk structure
and evolution. Our models include a simple treatment of gas thermodynamics,
with orbital Mach numbers at the inner edge of the disk $M_{\rm in}$ of 5 and
10. We find mass accretion rates to vary considerably on all time scales, with
only the Mach 5 model reaching a clear quasi-stationary state. For Mach 10, the
model undergoes an outside-in magnetically-driven accretion event occurring on
a time scale of $\sim10$ orbital periods of the binary. Both models exhibit
spiral shocks inclined with respect to the binary plane, with their position
and inclination changing rapidly. However, the time-averaged location of these
shocks in the equatorial plane is well-fit by simple linear models. MRI
turbulence in the disk generates toroidal magnetic field patterns (butterfly
diagrams) that are in some cases irregular, perhaps due to interaction with
spiral structure. While many of our results are in good agreement with local
studies, we find some features (most notably those related to spiral shocks)
can only be captured in global models such as studied here. Thus, while global
studies remain computationally expensive -- even as idealized models -- they
are essential (along with more sophisticated treatment of radiation transport
and disk thermodynamics) for furthering our understanding of accretion in
binary systems.
