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In numerical models of thin astrophysical disks that use an Eulerian scheme,gas orbits supersonically through a fixed grid. As a result the time step issharply limited by the Courant condition. Also, because the mean flow speedwith respect to the grid varies with position, the truncation error variessystematically with position. For hydrodynamic (unmagnetized) disks analgorithm called FARGO has been developed that advects the gas along its meanorbit using a separate interpolation substep. This relaxes the constraintimposed by the Courant condition, which now depends only on the peculiarvelocity of the gas, and results in a truncation error that is more nearlyindependent of position. This paper describes a FARGO-like algorithm suitablefor evolving magnetized disks. Our method is second order accurate on a smoothflow and preserves the divergence-free constraint to machine precision. Themain restriction is that the magnetic field must be discretized on a staggeredmesh. We give a detailed description of an implementation of the code anddemonstrate that it produces the expected results on linear and nonlinearproblems. We also point out how the scheme might be generalized to make theintegration of other supersonic/super-fast flows more efficient. Although ourscheme reduces the variation of truncation error with position, it does noteliminate it. We show that the residual position dependence leads tocharacteristic radial variations in the density over long integrations.

Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows