  Vortices, turbulence, and unsteady non-laminar flows are likely both
prominent and dynamically important features of astrophysical disks. Such
strongly nonlinear phenomena are often difficult, however, to simulate
accurately, and are generally amenable to analytic treatment only in idealized
form. In this paper, we explore the evolution of compressible two-dimensional
flows using an implicit dual-time hydrodynamical scheme that strictly conserves
vorticity (if applied to simulate inviscid flows for which Kelvin's Circulation
Theorem is applicable). The algorithm is based on the work of Lerat, Falissard
& Side (2007), who proposed it in the context of terrestrial applications such
as the blade-vortex interactions generated by helicopter rotors. We present
several tests of Lerat et al.'s vorticity-preserving approach, which we have
implemented to second-order accuracy, providing side-by-side comparisons with
other algorithms that are frequently used in protostellar disk simulations. The
comparison codes include one based on explicit, second-order van-Leer
advection, one based on spectral methods, and another that implements a
higher-order Godunov solver. Our results suggest that Lerat et al's algorithm
will be useful for simulations of astrophysical environments in which vortices
play a dynamical role, and where strong shocks are not expected.
