Evaluating the Magnetorotational Instability's Dependence on Numerical
  Algorithms and Resolution
  We have studied saturated, MRI-driven turbulence using three-dimensional,
isothermal simulations with resolutions that extend from 64 to 192 zones in
each direction. The simulations were performed with several higher order
Godunov algorithms. A variety of reconstruction strategies as well as a variety
of Riemann solvers are tried. We show that the details of the isothermal
MRI-driven turbulence depend principally on the Riemann solver and secondarily
on the reconstruction strategy. Furthermore, we find that the effective
viscosity parameter parameter tends to show progressively smaller decrements
with increasing resolution when the best reconstruction strategy (WENO) and the
best Riemann solver (linearized)are used. We attribute this result to the more
sophisticated dissipation mechanisms that are used in higher-order Godunov
schemes. Spectral analysis and transfer functions have been used to quantify
the dissipative processes in these higher-order Godunov schemes.
